Investigation of light-harvesting dynamics of photosynthetic pigment-protein complexes using

Investigation of light-harvesting dynamics of photosyntheticpigment-protein complexes using ultrafast spectroscopy

by

Scott McClure

A thesis submitted in conformity with the requirementsfor the degree of Master of ScienceGraduate Department of Chemistry

University of Toronto

c© Copyright 2013 by Scott McClure

Abstract

Investigation of light-harvesting dynamics of photosynthetic pigment-protein complexes using ultrafast

spectroscopy

Scott McClure

Master of Science

Graduate Department of Chemistry

University of Toronto

2013

We investigate the ultrafast electronic excitation dynamics of phycobiliproteins from cryptophyte

algae using two-dimensional electronic spectroscopy and frequency-resolved transient absorption spec-

troscopy. We detail the development of a transient absorption spectrometer that utilizes balanced and

fast detection methods to reduce noise and maintain high temporal and spectral resolution. We observe

coherent oscillations and attribute them to vibrational coherences using the wave packet formalism.

Analysis of the dynamic Stokes shift and motion of the wave packet on the potential-energy surface

indicate the coherences are predominantly situated in the excited electronic state of the protein. These

measurements imply that the ultrafast energy transfer within phycobiliproteins is coupled to the vibra-

tional motion of its constituent chromophores. We demonstrate the capability and necessity of multiple

ultrafast spectroscopic techniques for determining the origin of coherent motion in photosynthetic light-

harvesting complexes.

ii

Acknowledgements

This is my attempt to express my gratefulness to all the people who have been instrumental to my

success over the last two years:

To Greg, your passion for science is steadfast and you emanate genuine enthusiasm about all of your

students projects. After meeting with you to discuss a problem I had encountered in my research, I was

always motivated to return to the lab or once again search my data for the solution with renewed vigour.

These qualities, along with your impressive scientific knowledge, made you an excellent supervisor for

me. I appreciate your support and encouragement throughout these two years.

To Kelly, your smile and jovial spirit are perennial. You were the first face I encountered when joining

the group and I will not forget your welcoming personality. Your assistance with all of the administrative

tasks that I was too inept to learn has been a constant source of comfort. I enjoyed chatting with you

and thank you for always lending a sympathetic ear.

To Yasser, your demeanour is friendly and your consideration for others is sincere. I thank you for

aiding me in the chemistry lab of which I had little familiarity. I was always delighted to meet you in

the hallways to discuss our current research and other casual topics. You are an excellent teacher and

it is through your presentations that I developed a thorough understanding of quantum dots and solar

cells.

To Yaser, I was always thrilled to see you in group meetings as your depth of knowledge of physical

chemistry — but more importantly your ability to explain those concepts in simple terms — was greatly

beneficial for me. I am especially grateful for your explanation of the concept of the wave packet, which

became the foundation of my research.

To Aggie, your quest to understand complex quantum-mechanical concepts from the foundation of

first-principles was indeed laudable. As a fellow student of physics, I appreciated your perspective as

we mutually traversed the unfamiliar realm of chemistry. I found our conversations illuminating and I

appreciated all of your efforts to keep the social aspect of our group vibrant as well.

To Yoichi, you are one of the friendliest people I have ever met. Your smile was enduring and

your disposition was always positive (even after biking to school through a Canadian snow storm!).

Your ability to quickly comprehend new experimental techniques in the lab was a constant source of

amazement. I relished the time we spent outside of the lab setting as well, discussing informal topics

over a drink.

To Ryan, your scientific curiosity for the world is inspiring. Your work ethic and perseverance

through academic problems (and Lab-238 problems) are virtues to be admired. I thoroughly enjoyed

our conversations about science, politics (you are a U.S. citizen — American is ambiguous), and the

ones that probably belong in an episode of Seinfeld. I thank you for showing unwavering patience when

answering my questions.

To Tia, I thank you for being my office mate and companion as we ventured through the Masters

graduate program in chemistry. Concurrently, we took required classes, learned about ultrafast spec-

troscopy, and taught undergraduate students. I vividly remember my first day at U of T and how you

kindly took me on a tour of the campus. The quantity of people that you know at this school will never

cease to amaze me.

To Elsa, I remember meeting with you during your tour of the group and hoping that you would

decide to join us. Through discussing the topics of 2D spectroscopy with you, I actually learned a lot

more myself. Your perseverance through the frustrations of actually performing ultrafast spectroscopy

iii

(sometimes in an aqueous environment!) is admirable. It was also a delight to spend time with you and

Benoit outside of the academic setting (the Sortilege was excellent, the Tom Selleck was not).

To Aurelia, your vast theoretical background always kept me questioning my experimental results for

the better. Thank you for all of your brilliant questions and comments that have required me to think

deeply about my results. You have wonderful hospitality and you are an excellent cook as well!

To Yin, your work ethic is beyond extraordinary. It was nice to always have a familiar face around

the office even late at night and on weekends. I have lost count of all of the times I have come to ask you

a question about the experimental setup. You were very helpful to me and I owe much of my knowledge

of the inner workings of the lab equipment to you.

To Evgeny, your calm persona is a testament to your inner wisdom. You quietly and efficiently go

about your work and achieve great success. Indeed your considerable experimental results speak louder

than any words of any voice. As I try to recount the number of your custom-made optical parts that

I have copied, I am amazed at the breadth of your experimental ingenuity. I truly appreciate how you

would always make time for me and my questions.

To Jessica, I find it remarkable how you have managed to balance being a mom as well as a research

scientist. All of the time in my days was occupied by the latter role and thus I do not know how you

managed to do both. But you did and it speaks to your strong character. I vividly recall the day I

needed help with the spectral interferometry code in Lab 43. Rather than simply answering my one

question, you spent more than an hour thoroughly describing every single step of the algorithm. You

always had a calm demeanour and a gentle smile and I thank you for your kindness.

To Cathal, it was with great joy to spend time with you in the academic context (especially thanks

for all of the Matlab help) and in the social context conversing over a drink. I greatly admire your ability

to intelligently discuss seemingly any topic with grace and clarity. Your shirts were a source of constant

entertainment. As I have told you many times, the first time I met you and saw the Yoda/Oscar-the-

Grouch hybrid shirt, I immediately assumed you were a great guy. Your friendship over these two years

has undoubtedly proven this assumption true.

To Megan, you have helped me the most outside of the academic setting which, as I have tried to

convey, was just as important in defining the success of my Masters. Persistently and yet gently you

have succeeded in persuading me to try things that I was too timid to attempt before meeting you. For

example, it was because of you that I faced the fearful rollercoasters at Wonderland for the first time in

my life. You have always been kind to me and your cheerful spirit is delightful. Whenever I heard your

voice down the hallways or in the main office, I was immediately filled with elation. I was so happy to

be present to see you achieve your PhD.

To Tihana, I could not have performed my research without you and the dutifully prepared protein

samples. I am indebted to you for your constant assistance and kindness. Your depth of wisdom and

understanding is astounding. I knew that if I went to you with any problem, it was guaranteed that you

knew the answer. I greatly enjoyed our conversations in the office (especially discussing our favourite

tennis player) and our occasional walks home from campus were always a treat.

To Chanelle, your cheeriness is infectious as is your laughter. No matter how stressed out I became

at times during my research, your simple presence was enough to melt away all tensions. Our escapades

involving liquid nitrogen were fun; although sometimes we initially lacked the confidence, in the end

we always accomplished a task and with the utmost of enjoyment. You have a unique way of instantly

welcoming others with your radiant smile, and I was captivated the first time we met. I greatly admire

iv

your life choices as well and you are a constant source of motivation for me.

To Dan, we are at such ease together that it seems like our friendship could simply not have begun

a mere two years ago. You are one of the most thoughtful and considerate people I have ever met. Your

boundless generosity and welcoming character are considerable, as are your computational skills. It was

a sheer delight to take a coffee with you or converse over a drink. Our conversations on science, politics

and superheroes were always enlightening and entertaining. I thank you most sincerely for being an

awesome friend these last two years.

To Rayomond and Zaheen, I am happy to have been your first protege, just like Aristotle was to

Plato. You taught me the lighter side of academia and were a constant source of entertainment. You

two are exemplary proof that style can exist in science. Beneath your charm and wit, it is clear that you

possess a thorough knowledge of science and a wisdom of life. You helped me understand the principles

of physical chemistry and guided me through the graduate program at U of T. I absolutely relished our

conversations over a drink or a meal at Mothers.

To Paul, it is with great pleasure that I came to know you and work with you in the lab. Since our

first collaboration involving the CCD, I have come to rely on your skills indefinitely. You are an excellent

teacher with a seemingly limitless knowledge of optics and physical principles. You are always available

with a pen and paper to answer my questions with a brilliant schematic. Your calm composure in the

lab was especially helpful to me when problems with the experiment would otherwise cause me much

stress. Away from the lab, I looked forward to our coffees in the morning and I always enjoyed spending

time with you and Carolynn as we discussed the Seahawks and I narrated my moves in Monopoly Deal.

Most importantly, I am honoured to have you as a great friend.

To Duffy, quite simply put I owe you gratitude beyond measure. This thesis was accomplished

through two years of direct collaboration with you. When I joined the group, I recognized your talent

immediately and I realized that if I was to have success I needed to follow you around. I did just that,

and I thank you for being so generous with your time and knowledge. Your resolve for perfection in

experiments is extraordinary. Apart from providing training on the methods of ultrafast spectroscopy,

you conveyed to me the proper methods of a scientist. There is a procedure for everything is a doctrine

suitable not only for experimental implementation but also for life in general. You see the beauty of

true science and you have inspired me to keep it at the forefront of my inquiry of the world. I learned

an unfathomable amount of wisdom from you in the lab, in the office, and even at a conference in

Switzerland. You are a great friend who has continuously supported me throughout my Masters (even

though I prefer Star Wars over that other one).

With gratitude to you all, Scott.

v

Contents

1 Introduction 1

1.1 Motivation for research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline of research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Photosynthesis and cryptophytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Energy transfer within photosynthetic complexes . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Excitons in photosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 Steady-state spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.7 Low-temperature measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Two-dimensional electronic spectroscopy of PE545 18

2.1 Populations and coherences in 2DES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 NOPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Pulse compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.5 2DES experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 Spectral interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 2DES results on rhodamine 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.8 2DES results on PE545 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Development of a transient-absorption spectrometer 52

3.1 Noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 Optical apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 Balanced and fast detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3.1 Summary of settings for electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4 Transient absorption spectroscopy of PC577 67

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2 Testing the spectrometer with cresyl violet perchlorate . . . . . . . . . . . . . . . . . . . . 70

4.3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.4 Transient absorption results of PC577 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.5 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5.1 Population dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5.2 Coherent dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.5.3 Minimum of potential-energy surface . . . . . . . . . . . . . . . . . . . . . . . . . . 83

vi

4.5.4 Dynamic Stokes shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.5.5 A higher-lying state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5 Transient absorption of phycoerythrobilin-containing complexes 89

5.1 Results on PE545 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2 Comparison to 2DES results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 Results on PEB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6 Conclusion 98

Bibliography 99

vii

List of Tables

3.1 Noise suppresion through averaging. The standard deviation from the mean of the ex-

traction points in 3.4a is inversely related to the number of KCPs (averages), as well as

the intensity of light on a particular pixel of the CCD. . . . . . . . . . . . . . . . . . . . . 56

4.1 The coefficients of the biexponential fit to the population decay, extracted at 577 nm and

620 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.2 The eight oscillatory modes with decay constants extracted from the emission wavelength

of 616 nm using the fitting procedure described in the text. . . . . . . . . . . . . . . . . . 78

viii

List of Figures

1.1 The evolution of cryptophytes. Over 1.6 billion years ago a cyanobacterium was engulfed

by a eukaryotic cell and became a symbiotic component. This photosynthetic lineage

evolved into three different clades. Within the red-algae clade, an ancestral cell was

engulfed by a protozoan, with the engulfed cell becoming employed as photosynthetic

machinery within the protozoan. The cryptophytes are derived from this lineage and,

over hundreds of millions of years, they have diversifed into hundreds of species that

occupy a variety of different ecological niches. . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Light absorption in cryptophytes. Light of blue wavelengths and red wavelengths is mostly

absorbed by chlorophyll pigments within the photosystem complexes contained in the

membrane of the thylakoid separating the outer stroma from the inner lumen. Light

of green wavelengths is absorbed by phycobiliproteins found freely floating inside the

thyakoid lumen. The energy is subsequently transferred between chromophores within

one phycobiliprotein, then transferred to other phycobiliproteins, and finally transferred

to a photosystem on an overall timescale of tens of picoseconds. [Image not to scale] . . . 6

1.3 Steady-state spectra of single-bilin phycobiliproteins. (a) The linear absorption spectrum

and fluorescence spectrum of a phycobiliprotein mutated to only express the chromophore

phycoerythrobilin. (b) The linear absorption spectrum and fluorescence spectrum of a

phycobiliprotein mutated to only express the chromophore phycoviolobilin. . . . . . . . . 7

1.4 The absorption of excitons in the pigment-protein aggregate, PC645 [22] (Left) The inter-

action between the constituent chromophores of PC645 can be represented in matrix form;

the diagonal elements represent the site energies (in cm−1) of each chromophore, while the

off-diagonal elements represent the coupling values (in cm−1) between the chromophores.

The absorption spectrum of the hypothetical isolated chromophores would show peaks

corresponding to the individual resonances of each chromophore. (Right) Diagonalization

of the matrix produces the eigenenergies (excitons) of the system. The exciton absorbance

peaks form the basis of the aggregate absorption spectrum. . . . . . . . . . . . . . . . . . 10

1.5 Schematic of the excitation of a molecule into its excited state by resonant electromagnetic

radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.6 The linear absorption spectrum of the phycobiliprotein, PC577. This pigment-protein

aggregate is composed of eight chromophores that absorb light at about 577 nm and

612 nm. Due to both homogeneous and inhomogeneous effects within the complex, the

spectrum exhibits broad features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

ix

1.7 Temperature-dependence of linear absorption spectra of PE545. (a) The linear absorption

spectrum of PE545 (CCMP 705) at room temperature. (b) The linear absorption spectrum

of PE545 (CCMP 705) at 77 K. The spectra have been normalized relative to each other. 16

1.8 Temperature-dependence of steady-state fluorescence spectra of PC645. The spectrum

at 77 K (shaded area) shows much more discrete structure than the room-temperature

spectra (black line). The two spectra are normalized relative to each other. . . . . . . . . 17

2.1 A schematic of a representative spectrum of two-dimensional electronic spectroscopy. We

show the spectrum for a hypothetical pair of two-level systems with strongly coupled tran-

sitions. The diagonal features are similar to the observed features in a linear absorption

spectrum, with each peak representing the electronic transition to one of the two excited

states. The off-diagonal cross peaks show a correlation between the two transitions since

excitation at the energy of one transition then leads to emission at the energy of the

second transition. The peaks in many spectra are congested due to broadening in the

sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Schematic of the noncollinear optical parametric amplifier (NOPA). The 800-nm output

beam of the regenerative amplifier is divided into two beams with an energy ratio of 95:5

by a beam splitter (BS1). About 15% of the high-energy beam is frequency-doubled by a

barium borate (BBO1) crystal. The energy of this beam is controlled by a half-waveplate

(λ/21) and polarizer (P1) pair; the residual 800-nm component is reflected by the polarizer

into a beam block (B1). The 400-nm light pumps a second BBO crystal (BBO2) before

striking a beam block (B2). A delay stage (DS) varies the pathlength of the pump beam.

The low-energy component of the original 800-nm beam is focused with a lens (L) into a

sapphire crystal (Sp), generating a white-light continuum. The energy of the white light

is controlled by a second half-waveplate (λ/22) and polarizer (P2) pair. The white-light

beam is re-collimated by an off-axis parabolic mirror (PM) before traversing a fused-

silica window (W). The white-light beam is then focused into the second BBO using a

zero-degree spherical mirror (CM1). The pump beam amplifies a spectral region of the

white-light beam within the second BBO. The amplified light is re-collimated by a second

zero-degree spherical mirror (CM2) before leaving the NOPA. For clarity, some turning

mirrors and irises are not shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Schematic of a single-prism prism compressor. The beam passes through the single prism

(P) a total of four times. The first pass refracts the pulses into their constituent spectral

components. A retroreflector (R) sends the refracted beam back throught the prism with

the dispersed colours spatially opposite relative to the tip of the prism. A roof mirror

(RM) sends the collimated beam through the prism a third time, where the colours are

refracted in the opposite direction as before and they begin to overlap once again. The

retroreflector sends the beam back through the prism where the beam is again collimated

and the spectral components are now temporally overlapped. . . . . . . . . . . . . . . . . 27

x

2.4 Schematic of the four-wave mixing setup. The beam is diffracted into four coherent

copies by focusing onto a two-dimensional phase mask (PM). A spherical mirror (CM1)

recollimates the four beams. The three beams that excite the sample travel through

independent fused-silica wedge pairs (WP). The wedge pairs are mounted on translation

stages which control the wedge placement in the beam path; thus the beams can be

delayed relative to each other. A second spherical mirror (CM2) focusses the beams onto

the sample (S). The three excitation beams strike a beam block (B) whereas the fourth

beam and the spatially overlapped emitted signal are aligned into the detector. . . . . . . 28

2.5 Raw data of the laser dye rhodamine 101 after the first (automated) stage of spectral

interferometry. (a) The data after subtracting 12 of the homodyne and heterodyne terms

of the total signal at the detector via the spectral interferometry algorithm. This spectrum

is obtained by splicing together the interferograms while varying the relative temporal

delay (coherence time) of the first two excitation fields (b) The interferogram at τ1 = 0.

The spectral fringes are due to the interference of the signal field and the LO field at the

detector. The fringe spacing is proportional to the inverse of the temporal separation of

the two fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6 The Fourier-transform part of spectral interferometry. (a) The inverse Fourier transform

of the data shown in Fig. 2.5a along the emission-wavelength axis. The data contain

the contributions of 13 homodyne and heterodyne terms from the signal field, LO field,

and scattered excitation-beam fields. (b) A trace of Fig. 2.6b along τ1 = 0. The highest-

amplitude features correspond to terms involving Es and ELO. (c) The data after applying

a Heaviside filter to isolate only the EsE∗LO heterodyne term. (d) The trace of the filtered

data along τ1 = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.7 The final steps of spectral interferometry. (a) The filtered data of Fig. 2.6c after Fourier-

transforming back to the wavelength domain. (b) A slice of the filtered data along τ1

= 0. (c) The data after removing the amplitude and phase of the LO field leaving only

the characteristic parameters of the signal field. (d) A slice along τ1 = 0 showing the

amplitude As(λ) of the emitted signal field. (e) The Fourier transform of the data after

spectral interferometry along the coherence-time axis produces a 2DES spectrum. Shown

is the magnitude of the complex data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.8 Autocorrelation of the pulse used in the two-dimensional electronic spectroscopy measure-

ments of PE545. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.9 Representative two-dimensional electronic spectra of the laser dye rhodamine 101, showing

the magnitude of the total signal for population (τ2) times of 100 fs and 120 fs. The crosses

indicate the diagonal time-trace extraction, [absorption, emission] = [537 ± 1 THz, 537

± 1 THz] and cross peak time-trace extraction points, [absorption, emission] = [575 ± 1

THz, 541 ± 1 THz]. The black line indicates the diagonal of the spectrum (absorption

frequency = emission frequency). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.10 Time-trace extractions from the magnitude of the nonrephasing, rephasing and total parts

of the signal of rhodamine 101. The extractions are at the coordinates indicated by the

crosses in Fig. 2.9. (a) The diagonal extraction [absorption, emission] = [537 ± 1 THz,

537 ± 1 THz]. (b) The cross-peak extraction [absorption, emission] = [575 ± 1 THz, 541

± 1 THz]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

xi

2.11 The power spectra of the magnitude of the total time traces of rhodamine 101 shown in

Fig. 2.10, for (a) the diagonal extraction and (b) the cross-peak extraction. . . . . . . . . 40

2.12 The amino-acid composition of the PE545 apoproteins from two different cryptophyte

species. The letters correspond to the particular amino acid; a green colour indicates the

amino acid at that particular site of the transcript is found in the apoprotein of both

species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.13 Two-dimensional electronic spectra of the phycobiliprotein PE545 from species 705. The

real component of the complex data are shown for two different population (τ2) times.

The spectra for PE545 from species 344 appear similar. . . . . . . . . . . . . . . . . . . . 42

2.14 Two-dimensional electronic spectra of the phycobiliprotein PE545 (CCMP705). The mag-

nitude of the complex data is shown for four different population (τ2) times. The spectra

for PE545 (CCMP344) appear similar. The two crosses for τ2 = 132 fs spectrum signify

the spectral location where we extract the time traces. . . . . . . . . . . . . . . . . . . . . 43

2.15 Population dynamics in PE545. Population time traces were extracted at the two spectral

locations marked by the crosses in Fig. 2.14, corresponding to a diagonal peak (blue trace)

and the observed cross peak (green trace). Species 344 is shown in (a) and species 705 is

shown in (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.16 The oscillatory modes in PE545 from species 344. The power spectra were obtained by

Fourier transforming the time-trace extractions of the 2DES magnitude measurements.

The left column shows the modes from the diagonal-peak extraction and the right column

shows the modes from the cross-peak extraction. The data are displayed in their total

form as well as deconvoluted into the inherent rephasing and non-rephasing components. . 46

2.17 The oscillatory modes in PE545 from species 705. The power spectra were obtained by

Fourier transforming the time-trace extractions of the 2DES magnitude measurements.

The left column shows the modes from the diagonal-peak extraction and the right column

shows the modes from the cross-peak extraction. The data are displayed in their total

form as well as deconvoluted into the inherent rephasing and non-rephasing components. . 47

2.18 Transient-absorption dynamics of PE545 from species 344. (a) A representative frequency-

resolved transient-absorption spectrum. The dynamics occur across the spectral viewing

window of the pulse and as a function of population time (τ2). (b) Power spectrum

showing the oscillatory modes at the emission frequency of 544 THz, obtained by Fourier

transforming a time-trace extraction at this frequency. (c) Power spectrum showing the

oscillatory modes at the emission frequency of 519 THz, obtained by Fourier transforming

a time-trace extraction at this frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.19 Transient-absorption dynamics of PE545 from species 705. (a) A representative frequency-

resolved transient-absorption spectrum. The dynamics occur across the spectral viewing

window of the pulse and as a function of population time (τ2). (b) Power spectrum

showing the oscillatory modes at the emission frequency of 544 THz, obtained by Fourier

transforming a time-trace extraction at this frequency. (c) Power spectrum showing the

oscillatory modes at the emission frequency of 519 THz, obtained by Fourier transforming

a time-trace extraction at this frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

xii

3.1 Analysis of noise in the laser. (a) Histograms showing the deviation of the pulse energy

from the mean, over 500 000 pulses. The left panel corresponds to the output of the

regenerative amplifer. The right panel corresponds to the amplified output from the

NOPA. Superimposed on both distributions is a Gaussian fit. (b) A Fourier transform

of the laser intensity over time, representing noise under typical operating conditions. In

addition to white noise, several discrete modes are noticeable over two orders of magnitude.

(c) The correlation between four consecutive laser pulses. Uncorrelated data would be

circular in the x-y plane whereas these data roughly follow the diagonal — indicating high

correlation and the potential to filter low-frequency noise. . . . . . . . . . . . . . . . . . . 54

3.2 The concept of balanced detection. The intensity fluctuations inherent to the laser cause

artificial variations in the detected signal from the sample. Balanced detection uses a copy

of the laser beam as a reference to these fluctuations. Our setup measures the intensity of

the reference beam with a photodiode and then correlates the intensity with the strength

of the signal measured by the camera. The data can then be corrected for the laser

fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3 The effect of fast detection methods. We increased the repetition rate of the chopper and

upgraded the camera to a model with faster acquisition rates. By these methods, we are

integrating over the energy fluctuations of fewer laser pulses and thus filtering out the

intensity drift in the laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.4 Noise suppression results. (a) The laser spectrum used for analyzing noise. The color

gradient indicates the percent deviation of each detected wavelength from the mean over

12,000 measurements. The three points indicate single-wavelength extractions. (b) We

plot the normalized intensity of the CCD signal, integrated over wavelength (red trace) and

the normalized intensity of the photodiode (black trace). The integrated CCD intensity,

balanced to the photodiode intensity, is shown in the blue trace. The traces have been

offset for clarity. The traces are a function of kinetic cycles, meaning there are four

measurements of the photodiode voltage for every single measurement of the spectrum on

the CCD. (c) The two red lines correspond to the integrated noise intensity of all pixels of

the CCD. The two blue lines correspond to the noise at the single pixel of the CCD where

the intensity is at a maximum. The lighter traces of each pair are unbalanced and the

darker traces are balanced to the noise present in the photodiode. Each trace is a function

of the number of kinetic cycle pairs. We label 350 kinetic cycle pairs because the data

were typically measured at this value. The noise of the integrated spectrum decreases as

the square root of the number of averages. Shown are the data of one measurement under

typical operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

xiii

3.5 Schematic of the experimental apparatus for measuring transient absorption spectra. For

clarity, irises used to isolate beams and some turning mirrors are not shown. A beamsplit-

ter (BS) generates three beams from the incident beam. The two reflected portions are

used as the probe and diagnostic beams while the transmitted portion is used as the pump

beam. The diagnostic beam, which is reflected off the beamsplitter at a slightly different

angle than the probe beam, is directed into a photodiode (PD) by a pick-off mirror (M1).

The probe beam propagates through a UV-fused-silica window (W) to compensate for

extra glass in the pump arm. Both the probe and the pump propagate through sepa-

rate half-waveplate (λ/2) and polarizer (P) pairs for independent power adjustment. A

chopper (C) blocks the pulses at a rate of 625 Hz. The path length of the pump beam is

adjusted using a retroreflector (R) mounted on a delay stage (D). A zero-degree spherical

mirror (CM1) with focal length 250 mm focuses the pump beam onto the sample while

a separate mirror (CM2) with focal length of 100 mm focuses the probe beam onto the

sample. The angle of incidence of the pump beam onto the sample is 4◦ from normal and

the beam is blocked after traversing the sample with a beam block (B). The probe beam

is re-collimated by an achromatic lens (L1) placed after the sample. A second achro-

matic lens (L2) focuses the collimated beam into the spectrometer (G) which images the

wavelength-dependent signal onto a CCD detector. . . . . . . . . . . . . . . . . . . . . . . 59

3.6 An overview of the electronics used for fast and balanced detection. The setup is designed

to record transient absorption spectra and balance the laser intensity every eight laser

shots. The output of the laser is set at 5 kHz, and the electronics downcount the pulse

train to sets of eight pulses. A data acquisition (DAQ) card serves as the central hub

for controlling and monitoring the measurements. A photodiode reads the intensity of

each laser pulse and relays the measurement to the DAQ card after being enhanced by a

preamplifier. Two TTL (Ch. 7 and Ch. 8) signals coming from the timing delay generator

(TDG) of the laser are used to control the synchronization and delay of the electronics.

Ch. 8 is used to clock the timing of the DAQ card relative to the analog signals being

received from the photodiode. Ch. 7 drives the chopper that periodically blocks the pump

pulses of the laser. A copy of Ch. 7 is selectively controlled by a delay generator before

triggering the camera to measure spectra. Labview software acts as the user interface. . . 60

3.7 Possible magnitude of the photodiode signal before (a) and after (b) optimizing the timing

of the CH8 TTL to have the DAQ card read the peak of the voltage generated by the

laser pulse incident on the photodiode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.8 CCD camera exposure/fire signal as well as the TTL signal from CH7 of the timing delay

generator (relayed through the chopper box and delay generator) corresponding to the

timing of pulses (blocked and unblocked) incident on the camera. ∆t, the time between

the first exposure of the camera and the first pulse of the first quintet, is maximized via

the digital delay generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

xiv

3.9 Representative spectra obtained with the CCD camera. In kinetic scan mode, a single

camera exposure integrates four pulse events (either blocked or unblocked) into one spec-

trum, cleans the chip and repeats several hundred times. When the timings are correct,

the spectra should be integrations of either four blocked pulses or four unblocked pulses.

Obtaining a spectrum with an amplitude between fully on and fully off indicates the

exposure is integrating both on and off pulse events and the delay via the digital delay

generator should be adjusted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.10 Representative Labview display of the photodiode voltage generated from each laser pulse.

(a) Possible photodiode voltage data before calibration (b) Display with ∆V maximized

through CH8 TTL timing (c) Display with chopper blade phase adjusted to either com-

pletely block or completely unblock all of the pulses (d) Correct display showing complete

pulse-quartets after adjusting the timing of the camera trigger via the digital delay generator. 65

4.1 Transient absorption spectroscopy of a wave packet. The pump pulse excites a a coher-

ent superposition of states from the minimum of the ground electronic potential-energy

surface. The potential surfaces are shown as the energy-dependence of different nuclear

configurations in the vibrational phase space (here we show only one vibrational coordi-

nate, in reality there are many for complex molecules). The initial nuclear configuration

in the excited state is not in equilibrium with the minimum of the potential. Analagous

to a classical spring perturbed from its equilibrium, the wave packet will oscillate about

the minimum of the excited-state surface. We can stimulate emission back down to the

ground state with the probe pulse. The energetic spacing between the ground- and excited

electronic state is not constant relative to nuclear configuration and thus — depending

on when we stimulate emission — the energy (and corresponding wavelength) of the in-

teracting light will be different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2 Visualization of the x-ray crystal structure of PC577. The complex is composed of eight

bilin chromophores (two dihydrobiliverdins (purple) and six phycocyanobiliverdins (blue))

covalently bound to a protein scaffold (green). The protein of PC577 has an open structure

that separates the chromophores near the center. . . . . . . . . . . . . . . . . . . . . . . . 70

4.3 Estimating the pulse duration. (a) The solvent response to the overlap of the pump

and probe pulses showing the intensity of the constituent spectral components. (b) The

integrated magnitude of the spectrum in part (a). . . . . . . . . . . . . . . . . . . . . . . . 71

4.4 The linear absorption spectrum and fluorescence spectrum of the laser dye cresyl violet

perchlorate, plotted along with the spectrum of the laser pulse used for the transient

absorption measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5 A representative transient absorption spectrum of cresyl violet perchlorate. The amplitude

of the data corresponds to the wavelength-normalized, intensity differential of the probe

light after interacting with the pumped sample and the unpumped sample (∆I/I). Positive

features represent enhanced signal emission when pumping, while blue features represent

enhanced sample absorption when pumping. Negative times signify the interaction of

the sample with the probe pulse before the pump pulse. Coherent oscillations are visible

above the background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

xv

4.6 A representative line-out from a transient absorption measurement of cresyl violet at 607

nm, showing the coherent oscillations over 7 ps, on a background decay due to population

relaxation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 The emitted signal of cresyl violet perchlorate as a function of the pump delay time,

showing the underlying coherent oscillations as a function of frequency. The background

decay features were independently removed at each emission wavelength. . . . . . . . . . . 73

4.8 The power spectrum of cresyl violet perchlorate taken by Fourier-transforming the time

domain of the emission signal at 607 nm. The five strongest peaks are fit to Lorentzian

functions (red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.9 Steady-state and dynamic spectroscopy of PC577. (a) The linear absorption spectrum

of PC577 (blue) and the laser pulse spectrum (orange) used for the transient absorption

measurements. The dashed line highlights the peak of the linear absorption spectrum (b)

A representative transient absorption spectrum of PC577 measured from 0 to 4 ps in 4-fs

steps (we show the first 2 ps after excitation). The amplitude of the data corresponds to

the change in the intensity of the probe light after interacting with the pumped sample.

Positive features represent increased signal emission when pumping, while blue features

represent enhanced sample absorption when pumping. Positive times signify that the

pump pulse arrived before the probe pulse. (c) The emission signal of PC577 showing the

underlying coherent oscillations for the first picosecond after excitation. The background

decay features were independently removed at each emission wavelength. A sharp node is

seen around 638 nm. The oscillations on either side of this node are nearly out-of-phase

relative to each other. The dashed line indicates a biexponential fit to the node in the

oscillations (d) The steady-state fluorescence spectrum of PC577 after excitation at 550

nm. The dashed line highlights the peak of the fluorescence spectrum. . . . . . . . . . . . 76

4.10 Coherent oscillations at 616 nm. We display the mean (black line) and standard deviation

(blue shaded area) of line-outs from five independent measurements. . . . . . . . . . . . . 77

4.11 Analysis of oscillatory modes. (a) The power spectrum of PC577 from the background-

subtracted transient-absorption data. Bright features correspond to high-amplitude os-

cillations at that particular emission wavelength. Shown is one of five measurements. (b)

A representative power spectrum for the oscillations at the emission wavelength of 616

nm. (c) The amplitude and phase of the 8.0 THz oscillation present in the PC577 data

are plotted as a function of the signal emission wavelength. They are plotted on the same

graph with corresponding axes for visual comparison. Both the amplitude and phase ex-

hibit a sharp change around 638 nm. These features are signatures of excited-state wave

packets because 638 nm corresponds to the fluorescence maximum. . . . . . . . . . . . . . 79

xvi

4.12 The motion of a wave packet on the excited-state potential-energy surface. Excitation

occurs from a stationary equilibrium population in the minimum of the ground-state

potential. Coherent broadband excitation will excite a superposition of states (a wave

packet). This wave packet will oscillate between the energetic turning-points on the

excited-state potential with a period, T, as well as broaden due to anharmoncity of the

surface. Steady-state fluorescence occurs from the minimum of the excited-state potential,

although we can stimulate emission at any point. This schematic illustrates the wave

packet as a superposition of harmonics of one vibrational degree of freedom. In a real

sample, the wave packet is probably a superposition of different vibrational degrees of

freedom as well. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1 A representative transient absorption spectrum of PE545 (species 705). (a) The full

transient absorption spectrum, measured from 0 to 4 ps in 4-fs steps. The amplitude of

the data corresponds to the change in the intensity of the probe light after interacting with

the pumped sample. Positive features represent increased signal emission when pumping.

(b) A time trace (blue dots) extracted at the emission wavelength of 563 nm (dashed line

in part (a)) with a corresponding biexponential fit function (red line). . . . . . . . . . . . 90

5.2 The residuals of the transient absorption data of PE545 (species 705) shown in Fig. 5.1a

after removing the background population decay. The plot displays the first picosecond

after excitation when oscillatory dynamics are evident. . . . . . . . . . . . . . . . . . . . . 91

5.3 Coherent oscillations at the emission wavelength of 558 nm. We display the mean (black

line) and standard deviation (blue shaded area) of line-outs from five independent mea-

surements of PE545 (species 705). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.4 The power spectrum of the Fourier transform of the transient absorption data of PE545

(species 705) extracted at 558 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.5 The amplitude (red) and phase (blue) of the 15-THz mode of the phycobiliprotein PE545

(species 705) extracted from the signal emission wavelength of 558 nm. . . . . . . . . . . . 92

5.6 A representative transient-absorption spectrum of PEB — measured from 0 to 4 ps in

4-fs steps — showing coherent dynamics and population dynamics on the short timescale.

The amplitude of the data corresponds to the change in the intensity of the probe light

after interacting with the pumped sample. Positive features represent increased signal

emission when pumping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.7 A representative transient-absorption spectrum of PEB — measured from 0 to 4 ns in

25-ps steps — showing population dynamics on the long timescale. The amplitude of the

data corresponds to the change in the intensity of the probe light after interacting with

the pumped sample. Positive features represent increased signal emission when pumping. 95

5.8 Representative transient absorption data of PEB after removing the background decay

features independently at each emission wavelength. Oscillatory dynamics are centered

at the emission wavelength of 561 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.9 Coherent oscillations at the emission wavelength of 561 nm. We display the mean (black

line) and standard deviation (blue shaded area) of line-outs from seven independent mea-

surements of PEB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.10 The power spectrum of the Fourier transform of the transient absorption data of PEB

taken from the average time trace extracted at 561 nm from seven measurements. . . . . . 97

xvii

Chapter 1

Introduction

1.1 Motivation for research

The power of the sun is unparalleled. The overwhelming majority of life on earth, beginning with the

photosynthetic organisms that form the basis of nearly all ecosystems, is powered by sunlight. Indeed

the power available from the sun is so abundant that the annual energy consumption by all of mankind

is only 0.02% of the total solar energy at the Earth’s surface [52]. Despite this colossal opportunity,

electricity derived from sunlight is only about 0.02% of total global electricity production [18]. Fossil

fuels, which are indirect byproducts of photosynthesis hundreds of millions of years ago, form up to

90% of our current energy consumption and yet the amount of energy available from all current and

foreseeable future sources of oil is matched by solar irradiance in a single day [18].

The cost of harvesting sunlight is a key factor preventing its wide-scale adoption as a source of power.

The problem is that we are essentially comparing the cost per time of energy resources; the price of fossil

fuels, divided over the hundreds of millions of years necessary to produce them, will always seem more

economically feasible than the price of solar harvesting within the span of a few decades. Where sunlight

has a distinct advantage, however, is through its abundance, versatility, lack of geopolitical involvement,

and sheer continuity. We simply need to engineer cost-effective technologies to harvest this sunlight.

There are many approaches to solving this problem; here we investigate light harvesting in the biological

context. It is by studying the architecture of light-harvesting machinery within photosynthetic organisms

that we may uncover the secrets to efficient and cheap solar collection that billions of years of evolution

have optimized.

Photosynthesis is on average about 11% efficient at converting solar energy into chemical energy

[52]. It may at first seem strange that after billions of years of evolution the efficiency is not closer

to perfect. However, since photosynthetic organisms are living entities, their photosynthetic machinery

must conform to the overall architecture of their cells. The objective of any organism — including

photosynthetic organisms — is to pass on its genetic material, rather than obtain energy as perfectly as

possible. A cell is an incredibly complex machine that must respond to a myriad of conditions in order to

survive and reproduce. Photosynthesis is a complicated process that involves bringing molecular building

blocks together with enzymes to form the chemical storage units of cellular energy (glucose), all within the

crowded and multipurpose cellular environment. If an organism has maximized its ability to reproduce

given the current environmental and competitive factors, it has achieved its fitness. Thus, given the

1

Chapter 1. Introduction 2

evolutionary history of a particular photosynthetic organism, the efficiency of harvesting sunlight has

indeed been optimized.

As an entire process, photosynthesis may not be efficient, however intermediate steps are nearly

perfect. The initial stage of photosynthesis, light harvesting, involves transferring excitation energy and

has a quantum efficiency of nearly 100% (the probability that an absorbed photon will be transferred

to a reaction center and generate a separation of charge) [86]. The quantum efficiency is a metric that

describes the efficiency of the light-harvesting complexes within photosynthetic organisms — specifically

the ability of the constituent chromophores to transfer excitation energy to the reaction center. Some

researchers who are interested in designing more efficient solar cells, study photosynthetic organisms

because of their high energy-transfer capability. Unlike photosynthetic organisms, mankind is able to

use the separated charges (generated by sunlight) as a source of electricity and therefore does not have

to rely on transforming the energy into some sort of chemical storage unit (although energy storage is

also an important topic of research).

Solar cells manufactured from the element silicon are actually quite efficient. On the basis of efficiency

only, all solar-cell designs would incorporate bulk silicon as the main material. However, manufacturing

high-quality silicon is currently very expensive and thus scientists have been searching for alternative

materials. Current research investigates the capabilities of solar cells made from dye-sensitized inorganic

materials [69, 71], organic materials [34], quantum dots [43], pervoskites [49, 53], and hybrids of multiple

of these materials [37, 46]. The design of solar cells composed from these materials should certainly

be influenced by the architecture of light-harvesting structures in photosynthetic organisms. Since pho-

tosynthetic organisms can transfer excitation energy nearly perfectly using organic molecules, it seems

reasonable to try to imitate their methods.

Photosynthetic organisms have developed sophisticated light-harvesting machinery to achieve their

near-perfect efficiency within the confines of a biological setting and the limitations of chemical physics.

The energy from an interacting photon is held in the excited state of a light-absorbing molecule for

only nanoseconds before the molecule fluoresces, thus the excitation energy must be transferred quickly.

This time constraint puts a size limitation on the chromophore arrays attached to the reactive site the

films in organic solar cells — the exciton diffusion length. It also means that the chromophores must be

physically close together and yet avoid becoming too close whereby the excitation energy is diminished

by a mechanism known as concentration quenching [57]. The experimental limit where concentration

quenching occurs is surpassed by a factor of 5 in plants perhaps by arranging the chromophores in

precise orientations [86]. Thus in plants concentration quenching is prevented while still allowing a high

concentration of chromophores for optimization of energy transfer.

The chromophores themselves are even special in photosynthetic organisms. Photosynthetic chro-

mophores have very high molar extinction coefficients (a metric of the amount of light absorbed for a

given thickness of material); a single layer of the major light-harvesting complex in plants can absorb

20% of the incident light around 675 nm [87]. Photosynthetic organisms assemble many (often several

hundred) of these molecules into a given volume rather than fill the space with a single giant molecule.

This sort of design is thought to reduce electron screening effects on the absorption transition within

a single molecule; in contrast, a single semiconductor nanocrystal with the same volume as the major

light-harvesting complex in plants has only about 10% of its absorbance strength [86]. These ideas lead

to the more general speculation that the protein scaffolding influences the light absorption and energy

transfer properties by shifting the resonances and modifying the couplings between chromophores. Per-


haps in the design of solar cells, when the physical properties of the chromophores become limiting,

similar scaffolding can be used as a separate optimizing parameter.

Finally, several studies of photosynthetic organisms have suggested that they use the effects of quan-

tum mechanics to their advantage for light harvesting [92, 15, 27, 17, 95, 70]. Excitonic states (su-

perpositions of states of individual chromophores) are incorporated into photosynthetic light harvesting

and allow for the creation of new absorption bands rather than using different types of constituent

chromophores. These properties are certainly important when considering the practicality of solar-cell

designs on the industrial scale. As well, the initial part of light harvesting may be aided by employing a

quantum-coherent superposition of these excitonic states. Perhaps the very idea that biological systems

may use the quantum mechanical principles of superposition and interference of states is motivation that

these effects can be used in engineered solar cells.

In summary, the quantum efficiency of silicon solar cells and photosynthetic light-harvesting com-

plexes is close to 100%. If a photon is absorbed, it will most likely generate charges. The complicated

environment of engineered organic solar cells is more similar to photosynthetic antennae. The quantum

efficiency of these devices can also be close to 100% but is limited by short distances between the site of

photon absorption and the site of charge generation. Silicon solar cells are quite expensive so a possible

solution is to engineer organic solar cells with a high quantum efficiency over large distances (and larger

overall efficiency). The photosynthetic light-harvesting complex remains as the ultimate design that

achieves large exciton diffusion distances within the complicated environment of the cell.

1.2 Outline of research

In the research that follows, the main goal of the investigations is to obtain quantifiable information about

the quantum-coherent mechanisms within the process of light harvesting in a photosynthetic organism.

The inquiry is energy transfer in the light-harvesting process and the investigative tool is spectroscopy.

We begin with a broad introduction to the foundational concepts in photosynthesis, energy transfer

among molecules and spectroscopy in general.

It is important to note that the order of spectroscopic measurements should fit into a natural or-

dering system. A sample should be investigated first by linear, steady-state spectroscopy such as linear

absorption and fluorescence. These spectroscopies are not only critical for determining the adjustable pa-

rameters for the ultrafast techniques but just as importantly they reveal an abundance of physical, quan-

titative information about the sample. After steady-state measurements, ultrafast measurements can be

performed but always quantitative measurements such as transient absorption before two-dimensional

electronic spectroscopy. In the research that follows, we performed and we discuss two-dimensional

spectroscopic measurements before transient absorption measurements. This ordering is because the

transient absorption spectrometer was constructed afterwards to significantly enhance the information

attainable from the original transient absorption spectrometer.

1.3 Photosynthesis and cryptophytes

Photosynthesis is the overall process by which organisms create chemical energy (sugar) from solar en-

ergy. Due to the importance of photosynthesis for their survival, organisms have developed sophisticated

light-absorbing chromophores and protein complexes that solely function to capture sunlight. The pig-


ment chlorophyll is the main chromophore composing the photosynthetic reaction centers where the

energy of sunlight is used to drive the separation of charge carriers. This charge-separated state is the

first step to generating mobile charge carriers for the numerous electrochemical reactions of photosyn-

thesis. The funneling of energy to the reaction center is aided by auxiliary pigment-protein complexes

called antennae. Antennae increase the spectral and spatial absorbance cross-section for photosynthetic

organisms. The collection of solar energy and transfer of the energy to a reaction center is known as

light harvesting. [86].

Here we investigate the light-harvesting machinery of the single-celled algae cryptophytes. A brief

history of the evolution of cryptophytes is as follows (Fig. 1.1). Around 3 billion years ago cyanobacteria

first evolved and used light as their energy source. Approximately 1.5 billion years after, an ancenstral

cyanobacterium was engulfed by a heterotrophic eukaryotic cell that obtains its energy from consuming

other cells. In this case, however, the cyanobacterium was not ingested but instead it was subsequently

incorporated as a symbiotic component of the eukaryotic cell [11]. This event is known as primary

endosymbiosis. This mutually beneficial relationship gave protection to the cyanobacterium and allowed

the eukaryote obtain a continuous supply of chemical energy from the light-harvesting machinery inside.

Over the next 500 million years, these photosynthetic eukaryotic cells diversified into three main lineages

that are today classified as green algae, red algae and glaucophytes [28].

Within the red-algae clade, a secondary endosymbiosis event happened approximately 1 billion years

ago, whereby an ancestral red-algae cell was itself engulfed by a phagocytic protozoan. Similar to

primary endosymbiosis, the red-algae cell became a symbiotic component of the protozoan and eventually

evolved into a fully functional photosynthetic organelle inside the protozoan called a plastid. This highly

successful lineage of photosynthetic organisms subsequently diverged into many different clades including

the cryptophyceae, or cryptophytes [28]. Over hundreds of millions of years, cryptophytes have diversified

into about two hundred known species that are ubiquitous throughout the world in both freshwater and

marine habitats. Cryptophytes are typically tens of microns in diameter and they live at the bottom of

shallow waters, surviving under low-light conditions [25].

Similar to higher-order plants, cryptophytes contain chloroplasts and inside the chloroplasts are stacks

of membrane called thylakoids. These thylakoids contain the chlorophyll molecules which absorb the

blue and red spectral regions of visible light. Cryptophytes differ from higher-order plants in that they

contain additional light-harvesting pigment-protein complexes called phycobiliproteins (the aforemen-

tioned auxiliary antennae, as shown in Fig. 1.2). Each particular cryptophyte species contains only one

type of phycobiliprotein. These phycobiliproteins absorb visible light within the green spectral region

and thus capture light that would not be absorbed by the chlorophyll complexes alone.

The light-harvesting apparatus is constructed with proteins derived from the genetic material from

the engulfed red-algae nucleus that normally would encode the phycobilisome antenna complex[25]. Over

time, the red algae phycobilisome on the outer stromal side of the thylakoid disassembled and the in-

dividual phycobiliproteins transferred into the inner lumenal side of the thylakoid. This event made

cryptophytes unique in the biological context since their phycobiliproteins now freely diffuse throughout

the lumen of the thylakoid whereas all other known organisms use membrane-bound light-harvesting an-

tennae. It also makes cryptophytes interesting to study because the architecture of their light-harvesting

machinery is significantly different from other photosynthetic organisms and yet they achieve the same

nearly perfect quantum efficiency. In particular, the energy absorbed by the phycobiliproteins must

transfer in the excited state across (perhaps multiple) phycobiliproteins to the reaction center in the


Figure 1.1: The evolution of cryptophytes. Over 1.6 billion years ago a cyanobacterium was engulfedby a eukaryotic cell and became a symbiotic component. This photosynthetic lineage evolved into threedifferent clades. Within the red-algae clade, an ancestral cell was engulfed by a protozoan, with theengulfed cell becoming employed as photosynthetic machinery within the protozoan. The cryptophytesare derived from this lineage and, over hundreds of millions of years, they have diversifed into hundredsof species that occupy a variety of different ecological niches.


Figure 1.2: Light absorption in cryptophytes. Light of blue wavelengths and red wavelengths is mostlyabsorbed by chlorophyll pigments within the photosystem complexes contained in the membrane of thethylakoid separating the outer stroma from the inner lumen. Light of green wavelengths is absorbed byphycobiliproteins found freely floating inside the thyakoid lumen. The energy is subsequently transferredbetween chromophores within one phycobiliprotein, then transferred to other phycobiliproteins, andfinally transferred to a photosystem on an overall timescale of tens of picoseconds. [Image not to scale]

lumen membrane to be converted into a charge-separated state. Furthermore, the chromophores within

cryptophyte phycobiliproteins are arranged with separations of on average 20 A (double the distance of

chlorophyll molecules in the main light-harvesting complexes of plants) and thus in total the excitation

energy is being transferred (an exciton diffusion length) over distances of up to 100 nm [85].

The phycobiliproteins in cryptophytes are mainly differentiated by their constitutent bilins (the

type of chromophoric molecule) as the individual apoproteins (the protein scaffolding without the chro-

mophores) are remarkably similar between the complexes of different species. The bilins are composed

of four pyrrole rings that would normally form an overall cyclical structure. Constrained in the phyco-

biliprotein, however, the bilin is held in a linear conformation. The conjugation within the bilins and

bonding of the bilins to the apoprotein determines their resonances, similar to how changing the dimen-

sions of a quantum particle in a box alters the energy levels. The electronic interactions between the

different bilins is also important. These effects imply that we cannot simply measure the spectroscopic

characteristics of the isolated bilins but instead a physiologically relevent measurement must involve

the apoprotein as well. The congested spectra of phycobiliproteins are a linear superposition of eight

constituent bilins and thus it is often difficult to separate the contributions from each bilin. However, we

can measure a phycobiliprotein that has been mutated to express only one particular bilin. In Fig. 1.3,

we show the linear absorption spectrum and steady-state fluorescence spectrum of two phycobiliproteins

that respectively express only the bilin phycoviolobilin (PVB) and the bilin phycoerythrobilin (PEB).

The phycobiliprotein PE545 contains the PEB bilin as well as the bilin dihydrobiliverdin (DBV).

The peak of the linear absorption spectrum of PE545 is at 545 nm which we see from Fig. 1.3 is due

to the contituent PEB bilins. Interestingly, the peak of the steady-state fluorescence of PE545 is at 586

nm while that of PEB is at about 570 nm. Thus the energy absorbed by PE545 is transferred from the

PEB chromophores and to the DBV chromophores where the DBVs subsequently fluoresce.


Figure 1.3: Steady-state spectra of single-bilin phycobiliproteins. (a) The linear absorption spectrum andfluorescence spectrum of a phycobiliprotein mutated to only express the chromophore phycoerythrobilin.(b) The linear absorption spectrum and fluorescence spectrum of a phycobiliprotein mutated to onlyexpress the chromophore phycoviolobilin.

1.4 Energy transfer within photosynthetic complexes

In this section we describe in detail the process of energy transfer across photosynthetic pigment-protein

complexes. The fundamental reason for studying photosynthetic light-harvesting molecules is to gain an

understanding of how energy transfer can be so efficient within a biological context. Electronic energy

transfer is the process whereby the energy of the excited state of one molecule (the donor) is transferred

to another molecule (the acceptor). The process does not emit a photon (as in the process of fluorescence)

but instead the donor molecule de-excites to the ground state as the acceptor molecule is excited. The

electronic interactions between the donor and acceptor molecules mediates this exchange. Electronic

energy transfer occurs in a wide range of multi-chromophoric aggregates (for example, phycobiliproteins)

and can be roughly classified into three regimes based upon the underlying mechanism of the exchange.

The strength of the interactions between an excited donor chromophore with the surrounding acceptor

chromophores and with the bath environment determines which regime is applicable for a given molecule.

Within photosynthetic light-harvesting complexes, it seems that light harvesting occurs primarily in the

intermediate regime but may also rely on contributions from the other two limiting regimes.

The three regimes are classified according to the strength of the coupling between the donor chro-

mophore and the acceptor (either a single chromophore or the bath continuum) and requires a different

theoretical approach to be interpreted. The distance-dependent electronic interactions of the donor and

acceptor determine the magnitude of the coupling. We can treat chromophores as groups of electric

charges oscillating as a function of space and time [96]. These charges are often modelled by an overall

electric dipole of a given molecule. The emitted electric field generated by these charges has different

properties depending on the proximity to the charge; thus acceptor chromophores experience different

physical properties depending on how close they situated in space relative to the donor chromophore.

When the interchromophoric coupling value is much smaller than the system-bath coupling value

(the strength of interaction between the donor and the surrounding molecular environment), the domain

of Forster resonance energy transfer (FRET) describes the energy transfer process [16]. FRET is an

inductive mechanism whereby the interchromophoric coupling acts as a small perturbation to promote

energy transfer between chromophores amidst the overall equilibrium of the bath [86]. In FRET, the

electronic energy transfer occurs stepwise incoherently from one chromophore to another down the

energy gradient of the system. It is important to note that energy transfer via the FRET mechanism


is radiationless; there is not any emission or reabsorption of a photon. The process initiates when an

external electromagnetic field starts the oscillation of the electric charges of the donor molecule at their

resonant frequency. As the charges within the donor are coupled, other oscillations with frequencies

not resonant with the external field can also be excited. These frequencies then electrodynamically

activate modes inherent to the acceptor molecule and, analogous to a vibrating spring setting another

spring in motion by transferring its energy, the charges of the acceptor begin oscillating at their resonant

frequencies. In this way, a chromophore (the acceptor) can be excited indirectly by an external field

that is not resonant or correctly oriented relative to the electric dipole of the acceptor.

The rate of energy transfer between a donor and acceptor molecule via the Forster mechanism de-

pends on the magnitude of the interchromophoric coupling (within the perturbative limit that governs

the theory) and the spectral overlap of the donor emission spectrum and acceptor absorbance spectrum.

The magnitude of the coupling in Forster theory is often modelled using the dipole-dipole approxima-

tion which is dependent on the distance separating two molecules and the relative orientation of their

transition dipole moments. The dipole-dipole approximation is only valid with distances separating the

chromophores much larger than the chromophore size. For photosynthetic pigment-protein complexes,

this approximation implies Forster theory is only applicable for donor-acceptor spatial separations on

the order of a few nanometers, which is not typically true. For small separation distances on the order

of angstroms, the dipole-dipole approximation breaks down — thus Forster theory is invalid. At such

separation distances, the shape of the interacting molecules (and therefore the shape of the molecular

orbitals) is important for determining the true coupling value.

A better model for a system with small chromophore separation distances is the transition density

cube method which, instead of assigning the molecule one transition dipole, explicitly calculates the

Coulombic interactions of the true orbital shapes of the donor excited state and acceptor ground state

[84, 51]. At the opposite limit, when the separation distance becomes on the order of hundreds of

nanometers and greater, the interactions between the oscillating charges must now be considered as

electromagnetic radiation (photons are emitted by the donor and the absorbed by the acceptor) [96].

In the limit that the interchromophoric coupling is much greater than the system-bath coupling, we

cannot treat the entities that interact with light as single chromophores but instead we must consider

superpositions of the chromophores — termed excitons. The excitation energy is delocalized over multiple

chromophores and can be transferred to other superpositions of chromophores within the complex by a

quantum mechanical process. This coherent excitation of multiple chromophores continues indefinitely

in a lossless (non-interacting) environment until spontaneous de-excitation to the common ground state

via fluorescence. However in a realistic environment, interactions with the bath — via the system-bath

coupling — dampen the coherence and forces energy transfer to the lowest-energy exciton. The damping

is due to interactions with the phonon modes (often modelled as an Avogadro number of oscillators) of the

bath environment. Redfield theory (modified Redfield theory) is used to describe these situations when

the coupling between chromophores (groups of chromophores) becomes stronger than the system-bath

coupling [76].

These low-coupling and high-coupling models are generally not applicable to photosynthetic light-

harvesting complexes where the interchormophoric coupling strength is often comparable to the system-

bath coupling. This intermediate regime is much more difficult to characterize. Photosynthetic organisms

harvest light and transfer energy efficiently in this regime and thus researchers are extensively studying

the underlying processes. It is clear that the Fø”rster model does not adequately describe the dynamics


as there are notable theoretical results that predict a vanishing energy transfer rate within a photosyn-

thetic complex and yet experimental results show the opposite [86]. Furthermore, conventional Fø”rster

theory depends on the strong electronic transition of both donor and acceptor molecules and, in some

antenna complexes, forbidden transitions are necessary for energy transfer to occur [96]. One of the

techniques used to tackle the intermediate regime is generalized Fø”rster theory [68] which involves

amalgamating many of the chromophores into a group and then modelling the overall group interactions

[98]. Through this method, energy transfer occurs between the distinct groups that have weak cou-

pling to each other and arbitrarily strong intragroup coupling. This mechanism seems more suitable for

light-harvesting antenna complexes with relatively small distances of separation and interactions among

multiple chromophores at once.

To be robust, energy transfer during the process of light harvesting must be funneled downwards in

energy from the auxilliary antennae to the reaction center where mobile charge carriers are generated.

This downhill progression can be achieved by constructing the light-harvesting machinery with different

chromophores that progressively absorb at lower and lower energies, or using the same chromophore

throughout the funnel and selectively tuning the resonance of each one [86]. Both methods are prevalent

across the domain of photosynthetic organisms and many organisms use a combination of the processes.

It seems that biological antenna complexes use different mechanisms of energy transfer at different stages

of the overall light-harvesting process to funnel energy. Many photosynthetic antenna complexes consist

of both groups of chromophores characterized by small energy gaps and large excitonic couplings, as well

as groups of chromophores that have large energy gaps and small excitonic couplings [98]. Thus these

different groupings are categorized into the different aforementioned regimes.

Despite the distinct differences between the mechanisms and theories that describe photosynthetic

energy transfer within the varying regimes of coupling, we can identify common themes for light harvest-

ing. Notably, energy transfer of the light-harvesting process takes place over hundreds of chromophores

to eventually arrive at the specialized photosynthetic reaction center, and the rate of energy transfer

must be ultrafast so that the cumulative transfer time is less than the fluorescence lifetime (typically

nanoseconds). Combining these two characteristics implies that we are investigating energy-transfer

events on the scale of hundreds of femtoseconds to picoseconds. In order to understand the mechanisms

of energy transfer in photosynthetic organisms where the processes are convoluted within the inter-

mediate regime, it is necessary to study them extensively with multiple spectroscopic techniques. By

quantitative analysis of their interactions with light, often carefully controlled and manipulated through

coherent pulsed lasers, we can begin to understand the relevant processes in organisms that give them

success in harvesting light. This intrinsic timescale is why we need ultrafast spectroscopy to study

photosynthetic dynamics and this research is devoted to such measurements.

1.5 Excitons in photosynthesis

In this section we describe the important concept of the exciton with the context of biology. Excitons

are fundamentally a quantum-mechanical phenomenon and occur without the presence of any sort of

coherent light source. In solid-state physics, an exciton is a bound pairing of an electron and hole

[86]. In biology, an exciton refers to an excitation in a multi-chromophoric aggregate that is delocalized

over multiple of the constituent chromophores. An exciton occurs when the chromophores within an

aggregate are strongly coupled to each other, which is indicative of the electronic interaction between


Figure 1.4: The absorption of excitons in the pigment-protein aggregate, PC645 [22] (Left) The inter-action between the constituent chromophores of PC645 can be represented in matrix form; the diagonalelements represent the site energies (in cm−1) of each chromophore, while the off-diagonal elementsrepresent the coupling values (in cm−1) between the chromophores. The absorption spectrum of thehypothetical isolated chromophores would show peaks corresponding to the individual resonances ofeach chromophore. (Right) Diagonalization of the matrix produces the eigenenergies (excitons) of thesystem. The exciton absorbance peaks form the basis of the aggregate absorption spectrum.

the two transition dipole moments. As we have seen, strong coupling occurs when the chromophores are

physically near each other, oriented correctly and have spectral overlap.

Excitons influence how the aggregate interacts with light, and thus the spectroscopic properties of

the sample. Excitons absorb light. Thus with molecular aggregates, we cannot consider exciting one

particular chromophore but rather we excite the excitons, composing various contributions from all the

chromophores. Indeed the individual chromophores of the complex are not eigenstates of the system

because of the interchromophoric excitonic coupling.

Excitons can be calculated with a knowledge of the Hamiltonian of the system (Fig. 1.4). The

Hamiltonian of a multi-chromophoric aggregate is a mathematical representation of constructing the

aggregate from isolated chromophores. In isolation, each chromophore has an energetic transition to its

first-excited state depending on the resonance of its molecular geometry. When the chromophores are

brought together and held in place by a scaffold (such as the bilins held by the protein in a phycobilipro-

tein), they are no longer isolated and each resonance is tweaked by the electronic interactions with the

others. In the Hamiltonian matrix, the nth diagonal element represents the site energy of the nth con-

stituent chromophore (the resonance energy to the first excited state of the chromophore in isolation),

and the nmth off-diagonal element corresponds to the coupling value between the nth chromophore and

mth chromophore. Diagonalizing this matrix gives the spectroscopic properties of the aggregate, where

the diagonal elements (the eigenvalues) are now the resonance energies of the excitons (eigenstates). The

corresponding nth eigenvector represents the contribution of each constituent chromophore to the nth

exciton. The strength of each transition is given by the excitonic transition dipole moments.

A great example of how some organisms use excitonic effects to aid in their light harvesting is seen in


photosynthetic purple bacteria [91]. Similar to cryptophytes, these bacteria use auxiliary light-harvesting

pigment-protein complexes to increase the quantity and spectral content of the flow of excitation energy

to a photosynthetic reaction center. The excitation energy is funnelled down a red-shifting energy

gradient beginning at the site of photon absorption. At stages within this gradient, the resonance of

the chromophores peaks at 800 nm, 850 nm and 875 nm. Interestingly, the pigment-protein complexes

involved in this energy funnel are all composed of the same chromophore — bacteriochlorophyll — and

yet the resonances are spectrally different. The cause of this change is due to excitonic effects within

these complexes. The chromophores are positioned and separated to varying degrees for the purpose of

generating different coupling values (off-diagonal elements of the Hamiltonian). These distinct coupling

values then lead to different realizations of the exciton energies after diagonalization of the Hamiltonian.

In this way, the purple bacterium can use the same chromophore (biologically more efficient) and yet

create a downhill gradient for excitation-energy flow.

1.6 Steady-state spectroscopy

Much of this research uses the concepts of steady-state spectroscopy to interpret the dynamics in ul-

trafast spectroscopy. Indeed, the correct procedure is to first measure steady-state spectroscopy of a

sample before measuring the various ultrafast spectroscopies. In the following, we briefly describe the

details of steady-state spectroscopy in order to develop a solid foundation in the applicable spectroscopic

signatures before moving on to ultrafast spectroscopy. Many of the physical principles that are most

easily understood in the steady-state domain are directly relevant to understanding the characteristics

in ultrafast spectroscopic measurements.

When a molecule is resonant with incident electromagnetic radiation, the molecule will be excited

from its equilibrium ground state. A molecule in an excited state can decay back down to the ground

state by either transferring its excitation energy to another molecule, by energy dissipation into the

environment (bath) or by emitting a photon via fluorescence [63] (Fig. 1.5. The probability of each

process is dependent on the magnitude of electric interactions between the excited molecule and the

others in its immediate surroundings. In isolated phycobiliproteins (not in vivo), the quantum efficiency

of fluorescence is greater than 95%. This value is not dependent on the particular wavelength of the

absorbed light. Thus the excitation energy is transferred efficiently from the high-energy chromophores

to the low-energy chromophores before fluorescence occurs in the phycobiliproteins. Otherwise, the

complexes would exhibit a fluorescence spectrum with a peak that spectrally shifts with the wavelength

of absorbed light. In vivo, most of the absorbed light in a phycobiliprotein is transferred from the low-

energy bilin chromophore to another pigment-protein complex which, in part, explains the overall high

efficiency of the light-harvesting process in cryptophytes.

Many of the underlying concepts of any spectroscopic measurement are exemplified by the standard

linear absorption spectrum of a sample. The absorption spectrum for photosynthetic samples occurs

in the visible-light portion of the electromagnetic spectrum (450 nm – 750 nm) since this is where the

solar spectrum peaks (photosynthetic organisms evolved to harvest the most abundant wavelengths of

radiation). A linear absorption spectrum will show peaks only where the incident light acts as a driving

force on the system. Importantly, the energy of photons in the visible-light spectral region corresponds to

the resonance of the electrons in a sample — a photon of this energy will propel an electron to an excited

state of its molecule. Thus, the study of light-matter interactions within photosynthetic molecules is


Figure 1.5: Schematic of the excitation of a molecule into its excited state by resonant electromagneticradiation.

chiefly concerned with electronic transitions (although, as we will see, vibrational transitions can also

be coupled to an electronic transition).

Linear absorption spectroscopy measures the strength of electronic transitions. The strength of a

particular transition is described by the product of the electric dipole moment of a sample and the

strength of the electric field. Both of these values are wavelength-dependent. With linear absorption

spectroscopy, we can measure the dipole strength as we vary the photon energy (wavelength) and thus

obtain the spectrum of where the molecule most strongly absorbs light. In a linear absorption experiment,

either the amplitude of the electric field is constant as a function of wavelength or the instrument

is calibrated to the intensity variation with wavelength. Therefore a linear absorption measurement

quantifies the strength of the electric dipole of the sample alone, and is not dependent on the source of

the electric field (incident light).

Linear spectroscopy (and all of spectroscopy) can be modelled using both a classical electric-field

picture as well as a quantum-mechanical photon picture. Indeed, light-matter interactions — like all of

the processes in the universe — simply transpire and the procedure of science is to develop a model that

accurately reproduces the causes and effects of the interactions. Both the classical and quantum models

have unique intuitive descriptions for various parts of spectroscopy and here we switch between the two

models for ease of understanding.

Only where the driving frequency of the incident light is equal to the resonance frequency of the

system will there be a displacement of the electric charge. The first light-matter interaction creates a

coherent superposition between the ground electronic state and the first excited electronic state of the

sample

Ψ(t) = a1φ1eiE1t

h + a2φ2eiE2t

h , (1.1)

where a represents the amplitude of the electronic wavefunction φ with energy E, h is Planck’s constant

divided by 2π, and the subscripts 1 and 2 respectively refer to the ground state and the excited state.

This superposition is intrinsically non-stationary under the Hamiltonian of the system and therefore the

spatial probability of the electron shows time dependence, as given by

|Ψ(t)|2 = |a1φ1eiE1t

h + a2φ2eiE2t

h |2

= a21φ

21 + a2

2φ22 + φ1φ

∗2e

i(E1−E2)t

h + φ∗1φ2ei(E2−E1)t

h ,(1.2)


where we have taken the modulus squared of the wavefunction superposition to find the probability.

The oscillation frequency is proportional to the energy difference between the ground and excited state

involved in the electronic transition.

In a typical condensed-phase measurement, an Avogadro number of molecules are excited by the

incident light. All of the excited molecules in the sample act as microscopic antennae with electron

density moving in time; macroscopically, the incident light has induced a polarization in the sample.

Accelerating charges generate electromagnetic radiation and the molecules in the sample emit light at the

frequency of their oscillation. This light is emitted in all directions by the randomly oriented molecules

but destructively interferes with itself except in the direction corresponding to the incident light (the

phase-matching direction) [9]. In this direction, the emitted light is overlapped with the incident light

but shifted by π radians (via Maxwell’s equations). Thus a given frequency of emitted light destructively

interferes with the corresponding frequency in the incident light. Linear absorption spectroscopy will

necessarily measure a decrease in intensity at this particular frequency (the sample has absorbed this

frequency). The magnitude of the decrease depends on the strength of the resonance and thus linear

absorption spectroscopy measures the strength of the dipole at each wavelength (or frequency) of light.

Linear absorption spectra do not simply exhibit the electronic resonances of the sample; if this sce-

nario was true, we would observe delta-function absorption linewidths at the wavelengths corresponding

to the resonances. Instead, the spectra typically show broad spectral features that are centered at the

resonances but encompass many wavelengths. These features are due to two underlying physical effects

that are somewhat connected: the dephasing of the polarization in the sample and the inhomogeneity

of the sample.

We first discuss the dephasing of the polarization. The polarization represents a spatial oscillation of

the electron density in time and can dephase by population relaxation and pure dephasing. Because the

polarization has a finite temporal duration, the corresponding frequency bandwidth has a finite spread

(time and frequency are Fourier conjugates). A coherence between two states necessarily means there is

a small population on both states; a coherent superposition of two states must have a nonzero amplitude

for each state. The population on the excited state can relax to the ground state or be coupled to the

continuum states and transfer the excitation energy. This loss of population in the excited state leads

to a decrease in the amplitude of the superposition of the two states and therefore dephasing of the

coherence. The dephasing of the coherences exhibits a Lorentzian lineshape in the linear absorption

spectrum if the relaxation is exponential. The population dephasing is governed by the particular

physical properties of the sample. The other source of population dephasing, pure dephasing, occurs

when the different oscillating dipoles from each molecule in the sample lose a phase relationship with

the others, resulting in a decoherence of the macroscopic polarization. Pure dephasing is due to the

interactions of the molecules in the sample and is dependent on the particular sample. Pure dephasing

is not relevant for linear absorption spectra since the sample is excited with incoherent light and thus

the interacting molecules are not coherent to begin with. For femtosecond spectroscopy, however, pure

dephasing is an important contribution to the spectra.

The second contribution to the broadening of the linear absorption lineshape is the inhomogeneity of

the sample. This effect occurs when the individual molecules within a sample experience slightly different

environments and the subsequent interactions tweak the resonances of each molecule differently. Thus,

the linear-absorption spectrum will exhibit a distribution of resonances and the net effect will be a

broadened lineshape. This effect is important for the chromophores in the phycobiliprotein samples, as


Figure 1.6: The linear absorption spectrum of the phycobiliprotein, PC577. This pigment-protein ag-gregate is composed of eight chromophores that absorb light at about 577 nm and 612 nm. Due to bothhomogeneous and inhomogeneous effects within the complex, the spectrum exhibits broad features.

the protein scaffold influences the resonances of identical chromophores to different frequencies. Thus

the overall lineshape in a linear-absorption spectrum is broadened by multiple physical effects with

weighted contributions dependent on the particular sample. We show the linear absorption spectra of a

phycobiliprotein, PC577, in Fig. 1.6.

The experimental setup of linear absorption spectroscopy usually consists of an incoherent white-light

source (meaning light with all wavelengths of colour) and a photodetector. The light source need not

be coherent because we are not concerned with time-resolving the electric dipole moment, but rather

the overall strength of the resonances. Thus we do not need femtosecond pulses since we only need the

values of the steady state.

Up to this point, we have only considered electronic resonances of a sample with an incident electric

field. This consideration has necessarily invoked only the visible light portion of electromagnetic radiation

since the frequencies of visible light resonate with electronic transitions. In general, however, light-matter

interactions in molecules (including photosynthetic molecules) occur in the ultraviolet and infrared ranges

of the electromagnetic spectrum as well. These interactions also affect the dipole moment and thus the

charge distribution in the molecules. The most important of these contributions for our purposes is the

effect of nuclear vibrations.

When multiple atoms are covalently bound to form a molecule, vibrations of the molecule can occur.

The number of different molecular degrees of freedom (stretching, twisting, rotating) increases linearly

with the number of atoms in the molecule. The phycobiliproteins are composed of bilin chromophores in

a protein scaffold and thus there are many vibrational degrees of freedom (a single bilin chromophore is

composed of around 100 atoms and has about 300 vibrational degrees of freedom). Vibrational motion

is a result of the dipole moment of the sample being dependent on the displacement of the constituent

atoms of the molecule along the vibrational degrees of freedom. These vibrational modes are typically

resonant with infrared frequencies of light and, analogous to how linear absorption spectroscopy measures


electronic resonances, infrared spectroscopy measures vibrational resonances.

However, there is an additional mechanism whereby vibrational modes can be driven when exciting

the electronic transitions of a sample. Vibrational modes can be coupled to an electronic transition

and therefore a resonance with an electronic transition can lead to the excitation of a vibrational mode.

The coupling mechanism is commonly modelled as two displaced harmonic potentials. Each potential

corresponds to an electronic state, and the levels of each potential correspond to vibrational states. The

potentials are displaced along a nuclear degree of freedom, representing a certain vibrational mode. This

picture is strictly one-dimensional and the energy landscape of a molecule is multidimensional along the

many degrees of vibrational freedom.

This vibrational-coupling mechanism has important consequences for linear absorption spectroscopy

and indeed all spectroscopic measurements that probe the electronic properties of molecules. Linear

absorption measurements will exhibit peaks corresponding to vibrational modes coupled to the electronic

resonances. As there are multiple, independent vibrational coordinates, there may be several peaks. The

strength of the modes (their amplitude in the spectrum) is dependent on the overlap of the vibrational

states on the ground electronic state and the excited electronic state (the coupling strength between the

electronic and vibrational modes). In addition, the vibrational modes can be due to the surrounding

bath environment (such as the protein scaffold surrounding the bilin chromophores in phycobiliproteins)

and thus provide a dephasing pathway for the coherence of the ground and excited electronic state. This

vibronic character further broadens the linear absorption spectrum.

Overall, the features in a spectroscopic measurement are a representation in the frequency domain

of the underlying molecular dynamics. A typical spectrum encodes the time-dependent changes of the

molecular dipole moment for the system. As we have seen, the positions and momenta of the electrons and

nuclei within a molecule and the interactions with the other molecules and the surrounding environment

determines the sample characteristics that we measure with spectroscopy.

1.7 Low-temperature measurements

As we have seen, there are multiple contributions to the characteristic broadening of the features in

spectroscopic measurements. Homogeneous broadening can be reduced by lowering the temperature

at which the measurements are acquired. This effect is especially helpful for measuring the congested

spectra of molecule aggregates — such as phycobiliproteins — where the electronic S0-to-S1 (ground

singlet state to first-excited singlet state transition) peaks can be indistinguishable from each other.

As well, we can better resolve the fine-structure such as vibronic transitions that would normally be

hidden beneath the homogeneous congestion. Low-temperature measurements can also resolve the true

excitonic features of strongly interacting chromophores in a sample.

We performed steady-state spectroscopic measurements at 77 K. For these measurements we used a

cold-finger cryostat linked to a reservoir of liquid nitrogen. The cold-finger cryostat removes heat from

the sample via conduction so we do not need an evacuated, closed loop for the liquid nitrogen. However,

the air in the sample chamber is removed with a vacuum pump to speed the cooling process, to prevent

heat exchange via conduction from the walls of the cryostat, and to prevent condensation of humidity

on the sample cell as the temperature drops below the dew point.

We use glycerol as a cryoprotectant to help prevent crystallization of the sample. We added glycerol

to the aqueous solution of the phycobiliproteins in a ratio of 1:1. There is a tradeoff between preventing


Figure 1.7: Temperature-dependence of linear absorption spectra of PE545. (a) The linear absorptionspectrum of PE545 (CCMP 705) at room temperature. (b) The linear absorption spectrum of PE545(CCMP 705) at 77 K. The spectra have been normalized relative to each other.

crystallization of the sample and obtaining enough of an absorption cross-section relative to the scatter.

Indeed, the optical density of the sample is a limiting factor for low-temperature measurements. Both

the small path length of the sample cell (usually 0.5 mm to enable a tight seal within the evacuated

chamber) and the glycerol dilution necessarily require the starting optical density of the sample to be

at least 0.4 for a sample cell with a 1-mm path length.

In Fig. 1.7 we show the linear absorption spectra of the phycobiliprotein, PE545 (CCMP 705) both at

room temperature and at 77 K. The spectra show that reducing the homogeneous broadening reveals the

underlying resonant features of the constituent bilin molecules (phycoerythrobilin and dihydrobiliverdin

in PE545). This information is important for determining the excitonic energies of the complex. Because

the starting optical density of species 344 was significantly lower than that of species 705, we were not

able to observe clear spectra above the scatter in the measurements.

In Fig. 1.8, we show the effect of temperature on the steady-state fluorescence spectrum of the

phycobiliprotein PC645. Low-temperature fluorescence spectra are easier to measure experimentally as

lower optical densities of the sample (relative to the linear absorption measurements) are sufficient to

generate enough signal for fluorescence measurements. Once again, lowering the temperature to 77 K

reduces the homogenous broadening and gives more precise spectral locations of both the main electronic

transition and the vibronic shoulder in the spectrum.


Figure 1.8: Temperature-dependence of steady-state fluorescence spectra of PC645. The spectrum at 77K (shaded area) shows much more discrete structure than the room-temperature spectra (black line).The two spectra are normalized relative to each other.

Chapter 2

Two-dimensional electronic

spectroscopy of PE545

In this chapter we detail the ultrafast measurements of the phycobiliprotein PE545 using two-dimensional

electronic spectroscopy (2DES). In contrast to linear, steady-state spectroscopies, 2DES is a third-order

spectroscopy. 2DES is complementary to other steady-state and third-order techniques such as linear

absorption and transient absorption, respectively, and indeed should be measured only after performing

the other measurements first. However 2DES is unique among other spectroscopy measurements because

it is able to correlate the emission of light with the absorption of light by examining the light-matter

interactions in two spectral dimensions. In this chapter, we first describe the important concepts behind

the interpretation of 2D spectra, before detailing its experimental realization and finishing with its

application to studying the phycobiliprotein PE545. A critical step in the methods of two-dimensional

spectroscopy (and any ultrafast spectroscopy) is the generation of laser pulses with a temporal duration

on the femtosecond scale, and we describe these techniques as well.

2.1 Populations and coherences in 2DES

Conventional 2DES uses three femtosecond laser pulses to generate a third-order response in the sam-

ple. The third-order response is generated from an Avogardro number of molecular dipoles acting as

nanoscopic antennae emitting electromagnetic radiation. The electric dipoles emit radiation in all direc-

tions. However, the three input beams are incident on the sample with different pointing vectors that

impose conditions of destructive interference on the emitted radiation in all but one direction. This

restriction is essentially the conservation of the momenta of the incident photons and is deemed the

phase-matching direction [9]. The resultant directionality of the emitted signal benefits the measure-

ment procedure because these low-intensity third-order signals will be isolated from the high-intensity

background excitation pulses.

At the fundamental level, spectroscopy measurements involve both the generation of coherences and

populations in samples as well as the measurement of the electronic properties due to these effects.

Contrary to many introductions to the topic of spectroscopy, a coherence between states requires one

light-matter interaction and the population of a state requires two light-matter interactions. 2DES

specificially controls when and how these light-matter interactions occur and records information in

18

Chapter 2. Two-dimensional electronic spectroscopy of PE545 19

the intermediate steps. With this specific information, we can generate a two-dimensional spectrum of

a given sample. We manipulate these parameters experimentally by controlling the relative temporal

arrival of the three excitation pulses.

The first femtosecond excitation pulse creates a coherent superposition between the ground electronic

state and an excited electronic state. For our measurements of phycobiliproteins, we generate a coher-

ent superposition between the highest occupied molecular orbital (HOMO) and the lowest unoccupied

molecular orbital (LUMO), although this is not a requirement in general. Vibrational modes coupled

to the electronic transition can also be involved (as long as there is sufficient spectral bandwidth in the

excitation pulse) such that the resultant superposition could be between the ground state and a partic-

ular vibrational mode of the first excited state. The superposition of two states is no longer stationary

in time under the Hamitonian of the system and oscillates in time and space. This oscillation of electric

charge is analagous to the electrons in an attenna moving back and forth. The oscillatory behaviour of

the charge necessarily means that they are accelerating and, according to electrodynamics, accelerating

charges emit electromagnetic radiation.

For a coherent superposition of states, the frequency of the radiation is given by the energy spacing

between the two constituent states. The energy between the ground state and first excited electronic

state of photosynthetic samples is within the spectral region of visible-light frequencies (the samples

absorb visible light!) and thus the first excitation pulse creates a coherence that oscillates at optical

frequencies (around 400 THz to 700 THz). This coherence oscillates during a time period referred to as

the coherence time (τ1) and is defined as the duration between the times that the first pulse and the

second pulse interact with the sample. These optical frequencies will indeed be emitted and detected in

2DES measurements but they are much higher than the frequencies related to most sample dynamics

and thus they will generally not interfere with the relevant sample information.

The second excitation pulse will generate a second coherence between two of the electronic levels

of the sample (potentially including vibrational levels as well). There are many possible combinations

of the first coherence and this second coherence if the sample is a molecular aggregate consisting of

multiple electronic states: a population can be created on the ground electronic state; a population

can be created on the first excited electronic state; the two coherences could be generated on different

electronic states of the aggregate; a coherence can be created in a higher-lying electronic state. The

first two possibilities produce populations and do not contribute to any coherences in the emitted signal

of the sample because populations are eigenstates of the system Hamiltonian and do not oscillate (the

populations do decay though, and thus contribute to the population dynamics in the sample). The third

possibility implies that there are two concurrent coherences each oscillating at optical frequencies. These

optical frequencies will be slightly different if the two constituent excited states are slightly different in

energy relative to the ground state. These two frequencies then beat relative to each other and we

observe this wave interference at much lower frequencies (as given by their frequency difference, perhaps

50 THz and lower) than the intrinsic optical frequencies. These frequencies beat during the time between

the interaction of the second pulse with the sample and the arrival of the third pulse, and is referred to

as the population time (τ2). It is these lower frequencies that 2DES measurements investigate.

The third femtosecond excitation pulse induces a coherence between two electronic levels, again with

the coherent oscillations given by optical frequencies. This third excitation completes the generation

of the third-order response in the sample. The signal of this response is emitted by the sample either

immediately after the third pulse interacts with the sample or after a certain temporal delay known as


the echo time (τ3). This characteristic is analagous to nuclear magnetic resonance (NMR) spectroscopy

where the signals are strongly detected when all of the sample (magnetic) dipoles align in phase space.

As mentioned before, this signal is emitted in a precise phase-matching direction that is experimentally

configured to be non-collinear with the excitation pulses. The time between when the final excitation

pulse arrives at the sample and when the signal is emitted depends on the ordering of the excitation

pulses. 2DES measurements alter the temporal order of the first and second excitation pulses to generate

two different signals: the rephasing and nonrephasing signals. Samples emit rephasing signals when all

of the electric dipoles (which intrinsically have slightly different energies and thus different oscillation

periods in phase space) align. This temporal period corresponds to the echo time. In contrast, non-

rephasing signals emit light immediately after the third excitation pulse, in which case the dipoles are

not aligned (this characteristic makes nonrephasing signals weaker than rephasing signals). 2DES mea-

surements have the advantage of being able to separate the rephasing and non-rephasing components,

as well as observing their combined contribution in one spectrum. Some measurements and theoretical

results compare the rephasing and nonrephasing parts of the sample emission to gain insight into the

sample dynamics [94].

The signals emitted in third-order spectroscopic measurements are indeed composed of many different

physical processes. All of these processes happen concurrently (within the time average of detection) and

produce similar spectroscopic features. Furthermore, many of the processes likely involve vibrational

modes as well. For example, it is possible for the two excitation pulses to each generate a coherence

between the ground state and a different vibrational mode in the same excited state. This process will

create beating between the two vibrational modes (a vibrational coherence) which will look very similar

to the beating between the two pure electronic modes (an electronic coherence). Deconvoluting the

contributions of every process to two-dimensional electronic spectra is a challenging task.

2DES reveals much of the same information as other steady-state and ultrafast spectroscopic tech-

niques but it is the one technique that also directly reveals if two transitions are correlated. The

fundamental spectroscopic signatures of a light-matter interaction is the energy of the light that is ab-

sorbed by a sample and the energy of the light that is emitted. Many spectroscopic techniques provide

information on only one of these processes (for example, linear absorption measurements show only

absorption of light, and fluorescence measurements show only emission of light). However, since 2DES

resolves the light-matter interactions into two dimensions, we can observe both the absorption processes

and the emission processes at once.

We show a schematic of a representative two-dimensional electronic spectrum in Fig. 2.1. This

spectrum typifies the features of a model system composed of a pair of two-level systems with strongly

coupled transitions. The diagonal features in a two-dimensional electronic spectrum are roughly equiva-

lent to the linear absorption spectrum of the sample (the diagonal features are actually convolved with

the pulse spectrum). The main advantage of 2DES is the potential for cross peaks within the spectrum.

Cross peaks are the signature of a non-linear process in the sample whereby the energy of the absorbed

light was necessarily different than the energy of the emitted light. This signature gives us information

about the correlation of transitions within a sample. The correlation, in turn, provides insight into the

coupling of states in the sample, energy transfer between states, or both. At short times after pumping

the sample, the presence of cross peaks indicate strong coupling between two states; at longer times after

pumping, the presence of cross peaks can indicate energy transfer between states [55].


Figure 2.1: A schematic of a representative spectrum of two-dimensional electronic spectroscopy. Weshow the spectrum for a hypothetical pair of two-level systems with strongly coupled transitions. Thediagonal features are similar to the observed features in a linear absorption spectrum, with each peakrepresenting the electronic transition to one of the two excited states. The off-diagonal cross peaks showa correlation between the two transitions since excitation at the energy of one transition then leadsto emission at the energy of the second transition. The peaks in many spectra are congested due tobroadening in the sample.


2.2 NOPA

We now describe the optical components that we use to obtain laser pulses with a femtosecond-scale

duration and a broad spectral bandwidth. We spend much of the total experimental time optimizing

these components. The first step to producing tunable femtosecond pulses involves generating a pulsed

laser output with high power. This output beam is centered at a set wavelength and bandwidth, so it

must be tuned to a desired spectral region and bandwidth. The presence of a large bandwidth of spectral

components is necessary for producing short pulses. A detailed explanation follows.

A Ti:Sapphire oscillator first seeds a regenerative amplifier. The amplifier outputs pulses with 0.6

mJ of energy, 150 fs in duration and centered at 800 nm with a bandwidth of about 10 nm and at

a repetition rate of 5 kHz. We tune the spectrum of these pulses so that we can investigate different

samples with different characteristic absorption spectra. To accomplish this task, we input the amplifer

pulses into a homebuilt non-collinear optical parametric amplifier (NOPA) [107, 4, 95], as shown in Fig.

2.2. The NOPA functions by a nonlinear process whereby a white-light continuum is amplified by a

high-amplitude pump beam in the presence of a specialized optical crystal. Interestingly, the broadband

pulses that we use to investigate third-order effects in our samples are generated from two second-order

polarizability effects in the NOPA, as we explain below.

We first attenuate the pulses input to the NOPA to about 0.3 mJ of energy using a beam splitter.

We want the output pulses of the regenerative amplifier to have a high energy to aid in the stability

of the amplification process but for the NOPA we do not require such high powers (too much energy

could even damage the sensitive NOPA crystals). A second beam splitter divides the original beam

into two separate beams with an energy ratio of 95:5. The high-energy beam is used as the pump

source, and the low-energy beam is used as the white-light continuum source. The high-energy beam

passes through a barium borate (BBO) crystal and, through the process of second-harmonic generation,

the input beam is frequency-doubled. We use a BBO crystal because it is a material with a nonzero

second-order susceptibility. Second-harmonic generation occurs when two photons of the incident field

annihilate in the BBO to form one photon with double the frequency (double the energy) through energy

conservation. In the time-dependent electric-field picture, this process takes the form of

P (2)(t) = χ(2)E(t)2

= χ(2)(Ae−iωt +A∗e+iωt)2

= χ(2)(A2e−i2ωt + 2AA∗ +A∗2e+i2ωt),

(2.1)

where P (2) is the second-order induced polarization in the BBO crystal, χ(2) is the second-order suscep-

tibility of BBO, and A and ω respectively represent the amplitude and angular frequency of the incident

electric field (with ∗ indicating the complex conjugate). The second-order polarizability of BBO leads

to a polarization inside the crystal that oscillates at twice the frequency of the incident light. This

polarization consists of electrons of the BBO oscillating at 2ω and therefore emitting electromagnetic

radiation at this doubled frequency. In our setup, typically about 10 µJ of the incident beam is converted

to the 400-nm output beam. The residual 800-nm component is removed by passing the beam through

a polarizer aligned to the polarization of the 400-component; the 800-nm reflects off of the surface of the

polarizer and into a beam block.

The high-energy pump beam then traverses a waveplate-polarizer pair placed in tilt mounts so that we

can adjust the output power and spectral quality of the beam. A typical power entering the amplifying


Figure 2.2: Schematic of the noncollinear optical parametric amplifier (NOPA). The 800-nm outputbeam of the regenerative amplifier is divided into two beams with an energy ratio of 95:5 by a beamsplitter (BS1). About 15% of the high-energy beam is frequency-doubled by a barium borate (BBO1)crystal. The energy of this beam is controlled by a half-waveplate (λ/21) and polarizer (P1) pair; theresidual 800-nm component is reflected by the polarizer into a beam block (B1). The 400-nm lightpumps a second BBO crystal (BBO2) before striking a beam block (B2). A delay stage (DS) varies thepathlength of the pump beam. The low-energy component of the original 800-nm beam is focused witha lens (L) into a sapphire crystal (Sp), generating a white-light continuum. The energy of the whitelight is controlled by a second half-waveplate (λ/22) and polarizer (P2) pair. The white-light beam isre-collimated by an off-axis parabolic mirror (PM) before traversing a fused-silica window (W). Thewhite-light beam is then focused into the second BBO using a zero-degree spherical mirror (CM1). Thepump beam amplifies a spectral region of the white-light beam within the second BBO. The amplifiedlight is re-collimated by a second zero-degree spherical mirror (CM2) before leaving the NOPA. Forclarity, some turning mirrors and irises are not shown.


crystal is about 50 mW. One must be careful as higher powers can damage the amplifying crystal. The

400-nm light reflects off of a zero-degree mirror mounted on a translation stage. A spherical mirror

focuses the beam onto a second BBO crystal which is used to amplify a white-light continuum beam.

Using a translation stage, we adjust the relative path length of the pump-beam and thus the path-length

difference relative to the white-light continuum beam. We can then choose the spectral region of the

white-light continuum to amplify by delaying the pump pulse a specific amount so that it overlaps the

dispersed white light at a particular range of wavelengths.

The low-energy beam is focussed into a sapphire crystal which generates the white-light continuum

with the colours dispersed in time. The quality of the white light depends on the compression and spatial

quality of the input 800-nm pulses and focussing parameters into the sapphire. Ensuring the 800-nm

beam is exactly perpendicular to the lens is the single-most important parameter for high-quality white-

light generation. In practice, all these parameters must be carefully adjusted to obtain quality white

light. The white light is collimated and the spatial mode improved using an off-axis parabolic mirror

before being focussed into the amplifying BBO crystal. Fused-silica windows of varying thicknesses

(typically 0.25 mm to 2 mm) can be placed in the white-light continuum beam to disperse the colours

even more and therefore reduce the spectral bandwidth of the resultant amplified beam to a desired

level. Importantly, the window also delays the white-light spectral components relative to the residual

800-nm photons (which still form the majority of the beam intensity) and thus we do not amplify the

800-nm component with the pump.

We use the second BBO crystal to amplify a certain spectral region of the white-light continuum

beam using the 400-nm pump beam. Inside the crystal, the spectral components of the white-light

beam are amplified by difference-frequency generation, a second-order effect dependent on the second-

order susceptibility of the BBO. We focus the pump beam and white-light continuum near the back of

the BBO to minimize dispersion to the amplified light as it traverses the crystal. Difference-frequency

generation occurs when a photon of the pump is annihilated in the presence of a photon of the white-

light continuum, producing a photon at the frequency of the white-light continuum and a photon at the

difference of the two frequencies

ωi = ωp − ωs, (2.2)

where ωp is the frequency of a pump photon, ωs is the frequency of a white-light continuum photon, and

ωi is a photon generated at the difference frequency (termed the idler). By conservation of energy, every

photon generated at ωi requires a photon at ωp to be annihilated and an additional photon at ωs to

be generated as well [9]; thus the white-light field is amplified at the particular frequency, ωs. A single

difference-frequency generation event involves one photon of the pump beam combining with one photon

of the white light continuum (its wavelength could be anywhere from 500 - 800 nm). Since the spectral

components of the white-light continuum are dispersed in time, we can adjust the temporal overlap of

the pump and white-light beams to preferentially amplify a certain spectral region. The power of the

amplified light is typically about 15% of the incident pump-beam power.

We can describe the process of mixing two electric fields with different frequencies in a χ(2)-sample

using the time-dependent electric-field picture


P (2)(t) = χ(2)E(t)2

= χ(2)(A1e−iω1t +A∗

1e+iω1t +A2e

−iω2t +A∗2e

+iω2t)2

= χ(2)[A21e

−i2ω1t + 2A1A2e−i(ω1+ω2)t+ 2A1A

∗1 + 2A1A

∗2e

−i(ω1−ω2)t +A22e

−i2ω2t

+2A2A∗1e

−i(ω2−ω1)t + 2A2A∗2 + E2∗

1 e+i2ω1t + 2A∗1A

∗2e

+i(ω1+ω2) +A2∗2 e

+2iω2t],

(2.3)

where A1 and A2, and ω1 and ω2 respectively represent the amplitudes and angular frequencies of the

two interacting electric fields. We see that in theory, with two fields with different frequencies, there

can be contributions to the second-order polarization from multiple second-order effects: components

that describe second-harmonic generation (such as A21e

−i2ω1t); components that describe sum-frequency

generation (such as 2A1A2e−i(ω1+ω2)t); and components that describe difference-frequency generation

(such as 2A1A∗2e

−i(ω1−ω2)t). In reality, the relative strength of each contribution is determined by its

phase-matching conditions [9].

We maximize the component of difference-frequency generation by adjusting the phase-matching

angle of the BBO crystal. Exact phase-matching is difficult with non-linear mixing processes such as the

second-order effects in the BBO. Perfect phase-matching conditions depend on the refractive index of

the material and the frequencies of the electric fields. For difference-frequency generation with collinear

beams, phase-matching is fulfilled when [9]

nω3 = nω1 − nω2, (2.4)

where n represents the diffractive index of the material (BBO). For materials like BBO, the diffractive

index increases as a function of ω which makes broadband phase-matching difficult. To better satisfy this

condition simultaneously for a large spectral bandwidth, we mix the fields in a non-collinear geometry

to take advantage of the birefringence of BBO [107]. The property of birefringence implies that two

incident electric fields with orthogonal polarizations will experience different indices of refraction in the

material. By adjusting the angle of incidence of one of the incident fields, the projection of that field

onto a particular index of refraction is changed. Our NOPA uses the Type-I polarization configuration

for phase-matching [107].

In practice, we vary the angle of incidence of the pump beam relative to the plane of the BBO

to maximize the phase-matching conditions for difference-frequency generation at the desired spectral

region. The white-light continuum passes through the BBO nearly normal to the plane of the crystal,

while the pump beam passes through and overlaps the white-light continuum at approximately 6◦ from

normal. Because the refractive index begins to change almost exponentially for wavelengths lower than

about 550 nm, it becomes increasingly difficult to satisfy the phase-matching conditions over a range

of different spectral components in the white-light continuum. Thus, the spectral bandwidth of the

amplified light decreases drastically for pulses centered at wavelengths lower than 550 nm. Our NOPA

operates best at central wavelengths of about 600 nm, where the refraction index is nearly constant for

all wavelengths.

The generation of high-quality amplified light requires a thorough iterative procedure that involves

observing the diffraction rings of the magnified amplified beam. We monitor both the spectrum and the

spatial chirp (the physical spead of spectral components over the beam spot) of the amplified beam by

translating a fibre-optic cable attached to a spectrometer (Ocean Optics 2000+). When magnified, high-


quality amplified light has well-resolved Airy discs (the beam mode is mostly TEM00) due to diffraction

from the BBO when amplified and has minimal spatial chirp. Generally, we tweak the angle of incidence

of the pump beam in one direction, we tweak the angle of the BBO crystal to improve the diffraction

pattern, and then we adjust the delay of the pump beam to the desired colour of amplification. The

goal is to maximize the phase-matching conditions for difference-frequency generation while minimizing

distortions to the beam quality. This procedure takes time but it is critical (and much easier) to ensure

a high-quality output beam at this step of the ultrafast-spectroscopy procedure. After obtaining high-

quality amplified light, the beam is collimated with a zero-degree mirror and sent into the compression

setup. A polarizer set at the polarization of the amplified light removes most of the randomly polarized

residual light white, reducing the beam power from about 3.5 mW to 3 mW. The amplified beam typically

has an energy of approximately 1 µJ. The beam is vertically polarized relative to the table.

2.3 Pulse compression

The amplified pulses from the NOPA are about 100 fs in duration and typically have a frequency

bandwidth of about 70 THz. Since the pulses have a large bandwidth in the frequency domain, the

corresponding temporal duration (frequency and time are Fourier conjugates) can be very short through

destructive interference of the various spectral components. However, this transform-limit is only as-

certained when all of the constituent spectral components of the pulse are ovelapped temporally. In

contrast, if the spectral components are dispersed in time, their relative phases will prevent destructive

interference and the resultant pulse train will approach the characteristics of a white-light incoherent

beam.

When light travels through a material, its speed, vm, is reduced from the universal constant of the

speed of light in vacuum (c) due to the index of refraction (n) of the material

vm(λ) =c

n(λ). (2.5)

Since the index of refraction depends on the wavelength, different colours of light will traverse a given

material at different speeds. When a broadband pulse traverses any amount of dispersive material (such

as the waveplate and polarizer pairs), the different colours experience different indices of refraction and

thus travel at different speeds. The variation in speed then translates to a temporal separation of the

colours of the pulse — the pulse disperses in time.

We compensate for the material-induced dispersion through the methods of pulse compression. The

basic principle behind pulse compression is forcing different colours in the pulse to travel different path

lengths; in essence we are intentionally temporally dispersing the colours of the pulse in the opposite

direction as the material-induced dispersion. The pulses are typically compressed using a combination of

a grating and prism compressor. The grating and the prism compressors are separate optical setups that

use a grating and a prism to respectively diffract and refract the pulse. The setups then provide different

path lengths for the dispersed colours before recombining them back into a pulse. In practice the pulses

can be compressed to about 10 fs using our setup, a value that is suitable for investigating ultrafast

excitation dynamics in samples. The efficiency of each compressor (the amount of output power relative

to the power of the input beam) depends on the beam polarization. Both the grating and prism act

as polarizers themselves; the grating preferentially diffracts light polarized perpendicular to the grating


Figure 2.3: Schematic of a single-prism prism compressor. The beam passes through the single prism(P) a total of four times. The first pass refracts the pulses into their constituent spectral components. Aretroreflector (R) sends the refracted beam back throught the prism with the dispersed colours spatiallyopposite relative to the tip of the prism. A roof mirror (RM) sends the collimated beam through theprism a third time, where the colours are refracted in the opposite direction as before and they begin tooverlap once again. The retroreflector sends the beam back through the prism where the beam is againcollimated and the spectral components are now temporally overlapped.

lines and the (Brewster-cut) prism transmits nearly 100% of p-polarized light but reflects about 8%

of s-polarized light at each surface of each pass (the refraction itself is polarization-independent). To

maximize the conversion efficiency, we use a half-waveplate to rotate the beam polarization 90◦ relative

to the output of the NOPA before entering the compressors.

We use the grating compressor in a 4-f configuration with a grating blazed for 600-nm light and with

500 lines/mm. We use a spherical mirror to minimize the angular dispersion induced by the compressor.

We minimize the astigmatism caused by using the spherical mirror (or indeed any curved optic) with

the retroreflector by looking at the beam spot in the far field and adjusting the retroreflector distance

until the spot has a round beam mode. The prism compressor can be configured to use either a single

Brewster-cut fused-silica prism and a retroreflector, or two matched prisms. We typically compress the

pulses with the former configuration, shown in Fig. 2.3. We rotate the prism to the angle of minimum

deviation to maximize power throughput.

We can correct both second-order and third-order dispersion present in the pulses using a combination

of the grating and prism compressors. In practice, we adjust the path length of the beam within

each compressor apparatus in an iterative manner to minimize both orders of dispersion: increasing

(decreasing) the path length in the grating compressor by moving the grating adds negative (positive)

second-order and positive (negative) third-order dispersion; increasing (descreasing) the path length in

the prism compressor by moving the retroreflector adds negative (positive) second-order and negative

(positive) third-order dispersion. Since these parameters are coupled, it is usually a lengthy, iterative

procedure to produce nearly featureless pulses approaching the transform-limit. We must minimize


Figure 2.4: Schematic of the four-wave mixing setup. The beam is diffracted into four coherent copiesby focusing onto a two-dimensional phase mask (PM). A spherical mirror (CM1) recollimates the fourbeams. The three beams that excite the sample travel through independent fused-silica wedge pairs(WP). The wedge pairs are mounted on translation stages which control the wedge placement in thebeam path; thus the beams can be delayed relative to each other. A second spherical mirror (CM2)focusses the beams onto the sample (S). The three excitation beams strike a beam block (B) whereasthe fourth beam and the spatially overlapped emitted signal are aligned into the detector.

the dispersion without clipping the spectral components of the pulses. The autocorrelation of the

non-resonant response from a test sample (usually water or methanol) serves as the metric for pulse

compression. We use protected-silver mirrors to direct the beams through the entire ultrafast setup as

dielectric mirrors reflect the spectral components of the pulses at different intrinsic surfaces and thus

chirp the pulses.

2.4 Experimental setup

After we compress the pulses using the grating and prism compressors, we direct the beam into the

four-wave mixing setup for two-dimensional electronic spectroscopy measurements (Fig. 2.4). We use

this setup to generate four coherent copies of the incident beam and then focus them together at the

sample to generate a third-order signal. A two-dimensional phase mask diffracts the incident beam into

four beams. The phase mask is essentially a two-dimensional diffraction grating; our phase mask has

been etched onto a 2-mm-thick fused-silica substrate with an etching depth optimized for first-order

diffraction of 500-nm light. We collimate these four beams with a spherical mirror into the BOXCARS

geometry (the beams are arranged on the corners of a square). Each beam is about 12% of the incident

input power.

We use three beams to generate the third-order signal in the sample. Each of these three beams

traverses an independent fused-silica wedge pair (uncoated and with a 1◦ slope). One wedge of each pair


is mounted on an automated translation stage so that the delay of the beams relative to each other can

be adjusted. For example, as we move the wedges further into the beam, the amount of glass that the

beam encounters increases and thus the beam is delayed relative to the others that travelled through

less glass. The other wedge of each pair is stationary and mounted in the opposite orientation to correct

for the refraction that the beam experiences upon traversing the sloped edge of the wedge.

The relative delay of the beams is determined by the amount of wedge glass inserted. As we translate

the wedge further into the beam, the amount of glass increases. Since we require femtosecond resolution,

we must accurately determine the correlation between the distance of translation and the induced beam

delay — analagous to an ”inverse velocity”, in units of fs/mm. We calibrate the three wedge pairs

independently; the 1◦ angle of the wedges is machined with high precision but the overall thickness of

each wedge pair relative to the other pairs is less precise. We determine a first-order inverse velocity

using a continuous wave (CW) laser with an emission wavelength near the peak of the pulse spectrum.

We configure the CW beam and a wedge pair as an interferometer and count the number of fringes as we

move the translations stage a set distance. We obtain a wedge inverse velocity with a standard deviation

of ±0.1 fs/mm. We improve the calibration with a heterodyne-detected, frequency-resolved transient

grating measurement of a model sample (such as a laser dye) that absorbs at the peak of the pulse

spectrum. We iteratively tweak the wedge inverse velocities until the transient grating spectrum shows

a flat phase profile across the spectral range. Since the index of refraction of the wedge is wavelength-

dependent, it is difficult to make the phase profile perfectly constant, but it is possible to obtain wedge

inverse velocities with a standard deviation of ±0.0001 fs/mm and with a phase-profile slope on the

order of tenths of fs/mm.

We pass the fourth beam — which serves as the local oscillator (LO) — through a neutral density

filter. The filter both delays the LO beam, and lowers the intensity of the beam by a factor of 104. These

effects respectively make the delay of the LO similar to the other three beams and make its intensity is

comparable to the strength of the emitted signal field. The LO interacts with the sample about 250 fs

(∆t) before the third excitation beam which gives a frequency fringe spacing (∆f) in the interference

pattern between the LO and signal field of about 4 THz via,

∆f =1

∆t. (2.6)

We have the LO pulse arrive at the sample first so that we de not have pump-probe–like contributions

to the signal (which would occur, for example, if the LO came after the excitation pulses and acted like

a probe pulse).

We place a pinhole (diameter of 25 µm) at the focal plane of the four beams. As we translate the

pinhole parallel to the table, the light traversing the pinhole will exhibit spatial chirp (changes from red

to blue, and vice versa) if the pulses have a large bandwidth. This property is characteristic of using the

grating compressor where we face a tradeoff between temporal compression and deviation from a nice

spatial mode. Vertical translation of the pinhole should not exhibit any spatial chirp though.

We flow the sample with a peristaltic pump from the flow cell to an ice bath in a continuous loop.

This flowing minimizes photobleaching of the sample at the focus of the laser and also cools the sample to

prevent denaturation. There is an optimal flow rate; higher flow rates decrease damage to the sample but

also induce discrete signal intensity fluctuations as the peristaltic pump rollers push the sample through

the tubing. In practice we usually flow the sample at about 1 mL/minute. Finally, we focus the different

spectral components of the signal onto the same focal plane (the grating in the CCD spectrometer) by


adjusting the focal point of an achromatic lens.

2.5 2DES experimental procedure

2DES measurements are very comprehensive and require multiple steps to collect supplementary infor-

mation to be used in the procedure of the analysis of the measured signals. Below we describe the steps

and measurements performed before the actual 2DES measurements.

Step A: We compress the pulses. The pulses are compressed by measuring the autocorrelation

nonlinear response of the sample solvent (usually methanol or water) in the same cuvette that will be

used to hold the sample will be and measuring the autocorrelation. The important point is to keep the

amount of glass that the laser pulses traverse in the sample measurement the same as that used in the

autocorrelation measurement. After compressing the pulses to the required duration and minimizing the

dispersion, the autocorrelation spectra are recorded for later reference.

Step B: We record the spectrum of the local oscillator through a non-resonant sample (transparent to

the laser pulses); usually water or methanol. The spectrum of the local oscillator shows the bandwidth

of the excitation pulses and thus indicates the electronic and vibronic transitions that are resonant with

the pulses.

Step C: We calculate the temporal duration separating the local oscillator and the signal emission.

This procedure involves setting the population time at zero by moving the fused-silica wedges until the

first and second excitation pulses arrive at the sample concurrently. The emitted signal and the local

oscillator are both incident on the CCD. The two fields interfere and the CCD images the interference

as a spatial interference pattern with fringes of maxima and minima on the CCD chip. As the spatial

dimension of the chip is calibrated to the frequency domain, the frequency step between successive

maxima can be obtained . The temporal separation of the two fields is calculated from the fringe

spacing. Thus the time between the local oscillator and the signal field can be obtained by taking the

inverse of the constant spacing (in frequency units) between successive peaks of the spatial pattern.

Step D: The inversevelocity of the fused-silica wedges used to delay the beams must be known with

high accuracy since errors in the delay of the wedges will affect the 2DES measurements. We calibrate

the wedge velocities to high accuracy by measuring the frequency-resolved transient grating of a model

system (usually a laser dye that absorbs in the spectral region of the excitation pulses).

Step E: We perform a pump-probe measurement of the sample using the same optical setup that

we used for 2DES. We measure the same temporal range and time step that will be used in the 2DES

measurements. The pump-probe measurements are used for calibrating the phase of the 2DES measure-

ments.

2.6 Spectral interferometry

When describing electric fields it is often helpful to use the Euler relation relating an oscillation in real

space to a sum of exponentials in the complex plane

cos(x) =e−ix + e+ix

2. (2.7)


We can then represent the electric field emitted by the sample in complex notation as a function of time

as

Es(t) = As(t)[e−i(ωst+φs) + e+i(ωst+φs)], (2.8)

where As(t) represents the time-varying amplitude of the field, ωs represents the angular frequency, and

φs represents the phase. These complex quantities are beneficial for some electric-field calculations, but

it must always be remembered that we measure only the real part of the field,

<(Es(t)) = <(As(t)[e−i(ωst+φs) + e+i(ωst+φs)]) ∝ As(t)cos(ωst+ φs). (2.9)

In the following, we switch between notations at stages for mathematical convenience.

The amplitude and phase fully characterize the signal field. However, we measure the field with

a detector that abides by square-law detection [54], and thus we actually measure the intensity of a

homodyned signal (only one field)

Is(t) = |As(t)[e−i(ωst+φs) + e+i(ωst+φs)]|2

= As(t)2[e−i(ωst+φs) + e+i(ωst+φs)][e+i(ωst+φs) + e−i(ωst+φs)]

= As(t)2[2 + e−2i(ωst+φs) + e+2i(ωst+φs)]

= As(t)2[2 + 2cos(2(ωst+ φs))]

= As(t)2cos2(ωst+ φs).

(2.10)

In principle, the detected intensity contains the complete amplitude and phase information that fully

characterizes the field. However, in our experiments the emitted signals oscillate at optical frequencies

(ωs ≈ 1015 Hz) and thus the detector (the CCD) would need attosecond resolution to resolve the phase

information. In reality, the response function of the detector in the experiments time-averages the

intensity,

〈Is(t)〉 =⟨As(t)

2cos2(ωst+ φs)⟩

=As2, (2.11)

where 〈〉 denotes averaging over time. Thus we lose the phase information of the emitted signal field.

To retain phase information of the signal, we overlap the emitted field with another electric field;

this procedure is called heterodyne detection. In practice, we align the fourth beam in the four-wave

mixing setup to the phase-matching direction — the direction of the emitted signal. This fourth beam

— termed the local oscillator (LO) — is about a factor of 104 lower in energy. The phase-matching

direction has the advantage of being isolated from the three excitation pulses that would overwhelm the

weaker local oscillator and signal fields.

In our experimental setup, we spectrally resolve the constituent wavelengths of the emitted field by

sending the signal onto a diffraction grating before imaging onto the CCD. The CCD detector then

measures the intensity of the sum of the signal field and LO field in the wavelength domain,

Idet(λ) = |Es(λ) + ELO(λ)|2

= |As(λ)[e−iφ(λ) + e+iφ(λ)] +ALO(λ)[e−iφ(λ) + e+iφ(λ)]|2

= As(λ)2cos2(φs(λ)) +ALO(λ)2cos2(φLO(λ)) + 2AsALOcos(φs(λ))cos(φLO(λ)),

(2.12)


where we have described the fields in the detected wavelength domain with As(λ) and ALO(λ) the

amplitudes, and φs(λ) and φLO(λ) the spectral phases of the signal and LO fields, respectively. The

spectral phase in the wavelength domain is given by

φ(λ) = 2πc

λtLO, (2.13)

where c is the speed of light and tLO is the temporal separation of the signal and LO fields, ts − tLO.

As before, the detector will time-average the homodyne terms. The heterodyned cross-terms, however,

are proportional to the difference of the spectral phases of the two fields (or, equivalently in the time

domain, the relative temporal delay between the two fields) and the detector will resolve a fringe pattern

superimposed on the time-integrated background terms

Idet(λ) ∝ cos(φs(λ))cos(φLO(λ)) ∝ cos(φs(λ)− φLO(λ)). (2.14)

Using this fringe pattern, we can extract the phase information from the emitted signal field using a

procedure termed spectral interferometry [36]. Spectral interferometry requires the LO to be a coherent

copy of the electric fields used to generate the signal field [54]; this requirement is why we use the fourth

copy of the incident beam in the four-wave mixing setup. The procedure isolates the heterodyned signal

field from the LO and any other residual electric fields that the detector measures. In practice, the

detector does not measure solely the emitted field and LO field but also scattered light from the three

excitation beams. Scattering occurs when the excitation beams traverse an imperfection in the sample

cuvette or deflect off of a contaminant in the sample. The beams scatter in all directions and some

photons of the excitation beams invariably travel in the phase-matching direction along with the signal

and LO fields. The scattered fields at the detector are usually weak relative to the LO but they are

certainly non-negligible for proper phase extraction of the signal field. Thus, in the presence of scatter,

the detector actually measures,

Idet(λ) = |Es(λ) + ELO(λ) + E1(λ) + E2(λ) + E3(λ)|2

,(2.15)

where E1, E2, and E3 are the fields of the scattered light from the first, second, and third excitation

beams, respectively. In the real domain, this expression is equivalent to,

Idet = |Ascos(φs(λ)) +ALOcos(φLO(λ)) +A1cos(φ1(λ)) +A2cos(φ2(λ)) +A3cos(φ3(λ))|2

(2.16)

This expression leads to 25 terms; once again 5 are homodyne terms that time-integrate to a constant

but the remaining 20 heterodyned cross terms all produce interference patterns on the detector. The

spectral interferometry procedure extracts the phase information for the signal field by isolating the

heterodyned terms that contain the signal field and are therefore strongest in amplitude — namely the

terms corresponding to AsALOcos(ωst+ φs)cos(ωLOt) and its complex conjugate.

We can remove many of the undesired heterodyned terms by selectively blocking the excitation beams,

measuring the spectra at the detector at each step, and then taking the difference of the measurements

with and without the excitation beams blocks. In the first step, we block the third excitation beam, E3.

The detector measures,


Idet,−E1(λ) = |ELO(λ) + E2(λ) + E3(λ)|2. (2.17)

There is no signal field, Es, because Es is a third-order signal that is only generated when all three

excitation beams are present at the sample. In the second step, we block the other two excitation

beams, E2 and E3. The detector measures,

Idet,−E2,−E3(λ) = |ELO(λ) + E1(λ)|2. (2.18)

Subtracting these two measurements from the original,

Idetsub(λ) = Idet(λ)− Idet,−E1(λ)− Idet,−E2,−E3(λ)

= |Es(λ) + ELO(λ) + E1(λ) + E2(λ) + E3(λ)|2 − |ELO(λ) + E2(λ) + E3(λ)|2 − |ELO(λ) + E1(λ)|2(2.19)

removes 12 of the terms. This part of the spectral interferometry procedure is performed automatically

during the experiment. The data for a interferogram for one population (τ2) time are shown in Fig. 2.5a

for the laser dye, rhodamine 101. The spectrum was generated by splicing together the interferograms

collected at each coherence (τ1) time delay. Fig. 2.5b shows the interferogram for τ1 = 0. We must block

E3 for each interferogram measurement (at all τ1 and τ2 times) because the relative temporal delays

(and thus the contributions of the heterodyned terms to the overall signal) of the fields are necessarily

changed during the course of a 2DES measurement. We need only block the E1 and E2 beams once for

each τ2 step, since the relative delay between Es and ELO is constant for each step. In practice, we use

a chopper to periodically block E3 and an automated shutter to block E1 and E2. We chop E3 since

we do not change the delay of the E3 beam and thus, after Fourier transformation across τ1, the scatter

from E3 appears at the zero-frequency coordinate.

The next part of the spectral interferometry procedure is performed after the data have been collected.

This part of the procedure separates the signal contributions of the remaining terms by using the

translation property of Fourier transforms

g(u− u0) = F−1[f(x)e−iu0x], (2.20)

where f(x) and g(u) are Fourier conjugate functions. This property states that a translation in one

domain is equivalent to a phase shift in the conjugate domain. The remaining heterodyne cross terms

in the data each contain a phase that depends on the relative temporal delay between the constituent

fields. When we inverse-Fourier–transform the data

F−1[Idetsub(λ)], (2.21)

the signal contributions of each term will then be shifted to different values in the conjugate domain.

In Fig. 2.6a, we show the result of the inverse Fourier transform across the wavelength domain of the

data shown in Fig. 2.5a. Fig. 2.6b shows the result for τ1 = 0. The conjugate domain is in units of

inverse wavelength which avoids the artifacts introduced if one first interpolates from wavelength units

to frequency units before Fourier transforming [24]. The inverse-wavelength units are similar to units of

time but with a different scaling. The high-amplitude feature in the center of the spectrum is due to the

remaining homodyne term, EsE∗s , and represents zero in this inverse-wavelength domain. Symmetric


Figure 2.5: Raw data of the laser dye rhodamine 101 after the first (automated) stage of spectralinterferometry. (a) The data after subtracting 12 of the homodyne and heterodyne terms of the totalsignal at the detector via the spectral interferometry algorithm. This spectrum is obtained by splicingtogether the interferograms while varying the relative temporal delay (coherence time) of the first twoexcitation fields (b) The interferogram at τ1 = 0. The spectral fringes are due to the interference of thesignal field and the LO field at the detector. The fringe spacing is proportional to the inverse of thetemporal separation of the two fields.

to either side of the homodyne term are the 12 remaining heterodyne cross-terms. The amplitude of

each term is proportional to the constituent field strength. The high-amplitude features are due to the

inverse Fourier transform of the desired cross terms

F−1[IEsELO ] ∝ F−1[As(λ)ALO(λ)cos(φs(λ)− φLO(λ))]. (2.22)

In these data, the contributions due to scattering (containing at least one of the E1, E2 and E3 fields)

are small relative to the desired cross terms because the sample is a well-behaving laser dye.

We now isolate the desired cross-term from all of the other terms by applying a Heaviside filter to

the data across the coherence-time domain, as shown in Fig. 2.6c&d. We select the term on the positive

side of the homodyne zero term; this term corresponds to the contribution of Es(λ)E∗LO(λ) by invoking

the causality principle (experimentally, the LO field arrives at the detector before the signal field thus

ts − tLO is positive).

The data of the isolated signal are then Fourier-transformed back to the wavelength domain

IEsELO = As(λ)ALO(λ)eiφs(λ)−iφLO(λ). (2.23)

We show the results for the data from rhodamine 101 in Fig. 2.7a&b.

The data are now complex because we removed the complex conjugate of IEsELO before Fourier

transforming. The final step in the spectral interferometry procedure is removing the amplitude and

phase of the LO field from the heterodyne term IEsELO . In practice, we obtain ALO(λ) by blocking the

excitation beams and thereby measuring only the homodyne intensity of the LO spectrum; the amplitude

is found by taking the square root of the intensity


Figure 2.6: The Fourier-transform part of spectral interferometry. (a) The inverse Fourier transform ofthe data shown in Fig. 2.5a along the emission-wavelength axis. The data contain the contributions of13 homodyne and heterodyne terms from the signal field, LO field, and scattered excitation-beam fields.(b) A trace of Fig. 2.6b along τ1 = 0. The highest-amplitude features correspond to terms involving Esand ELO. (c) The data after applying a Heaviside filter to isolate only the EsE

∗LO heterodyne term. (d)

The trace of the filtered data along τ1 = 0.

√ILO(λ) =

√|ELO(λ)|2 = ALO(λ). (2.24)

We obtain tLO during the procedure for 2DES as described earlier. We multiply the data by the inverse

of both these terms

IEsELO ∗ e+2π c

λtLO

ALO(λ) = IEsELO ∗ e+iφLO(λ)

ALO(λ)

= As(λ)e−iφs(λ),(2.25)

and obtain a spectrum such as the one shown in Fig. 2.7c&d for the rhodamine-101 data.

Using the spectral inteferometry algorithm, we have fully characterized the signal emission field as

well as filtered noise due to scatter in the measurements. To generate a 2DES spectrum, we Fourier-

transform along the coherence-time axis and convert the resultant frequency dimension to wavelength


Figure 2.7: The final steps of spectral interferometry. (a) The filtered data of Fig. 2.6c after Fourier-transforming back to the wavelength domain. (b) A slice of the filtered data along τ1 = 0. (c) The dataafter removing the amplitude and phase of the LO field leaving only the characteristic parameters ofthe signal field. (d) A slice along τ1 = 0 showing the amplitude As(λ) of the emitted signal field. (e)The Fourier transform of the data after spectral interferometry along the coherence-time axis producesa 2DES spectrum. Shown is the magnitude of the complex data.


units. We obtain a spectrum, as shown in Fig. 2.7f, which is a function of the emission wavelength and

the excitation wavelength.

The 2DES spectrum shown in Fig. 2.7f presents the absolute magnitude of the complex data. It

is only possible to separate the data into its real and imaginary components if the global phase of the

signal field is known. The global phase can be determined using the projection-slice theorem [39]. This

theorem states that the projection of the correct real component of the 2DES spectrum onto its emission-

wavelength axis matches the wavelength-resolved pump-probe spectrum for each τ2 time. In practice,

one first measures the pump-probe response of the sample using the same experimental apparatus as is

used for the 2DES measurements. Afterwards, one iteratively adjusts the global phase, Φg, of the 2DES

data by multiplying by a factor eiΦg until the conditions of the projection-slice theorem are satisfied.

2.7 2DES results on rhodamine 101

The proper procedure for measuring a sample using 2DES (and indeed any ultrafast spectroscopy)

involves first measuring a relatively simple, model system. The purpose of measuring a model system is

to test the entire optical setup for extraneous artifacts that may be confused for real features in more

complicated samples. We typically measure a laser dye (with a relevant absorption profile relative to the

pulse spectrum) because laser dyes are robust, well-studied and exhibit strong vibrational coherences (a

coherent superposition of vibrational degrees of freedom). We are able to gauge the properties of the

pulse (such as the temporal compression, spectral bandwidth and angular dispersion) by searching for

known features in the spectra of the model system.

We used the laser dye rhodamine 101 as a test system for the 2DES measurements of PE545. We

solvated dye crystals (Exciton Inc.) in methanol (Sigma-Aldrich) to an optical density of about 0.2 in

a fused-silica cuvette with a pathlength of 1mm. We filtered the methanol and the laser dye solution

using 0.2-µm–spacing nylon filters (VWR) before use to remove any contaminants that could scatter the

signal. We otherwise used the samples as delivered. We placed the sample in a 1-mm–pathlength flow

cell and flowed at a rate of 0.06 mL/minute. This step was not necessary to preserve the integrity of

the robust laser-dye molecules, but rather it was to match the experimental conditions of the protein

samples, as described below.

We obtained ultrashort laser pulses using the methods described previously. The compressed pulses

were nearly Gaussian-shaped with a temporal full-width half-maximum (FWHM) of about 11.7 fs and

with minimal spectral distortions as determined by an autocorrelation in pure methanol (Fig. 2.8.

Assuming Gaussian-shaped pulses, we have a spectral bandwidth of 72 THz (FWHM) centered at about

545 nm. Each excitation pulse had an energy of about 5 nJ. For the 2DES measurements, we scanned

the coherence time (τ1) from -38.4 fs to 38.4 fs in 0.15-fs steps. We scanned the population time (τ2)

from 0 fs to 200 fs in 4-fs steps.

We show representative two-dimensional electronic spectra from the measurement of rhodamine 101

in Fig. 2.9, for population times of 100 fs and 120 fs. We display the total magnitude part of the data

where phasing of the data is not applicable. The diagonal features of the spectra replicate the features

that we observe in the linear absorption spectrum, namely the main S0-to-S1 (ground singlet state to

first-excited singlet state) electronic transition at about 521 THz and the main vibrational shoulder at

about 560 THz. The features are somewhat skewed relative to the linear absorption spectrum because of

the convolution with the laser pulse spectrum (the amplitude of the signal is weighted by (µ(λ) ∗E(λ)3


Figure 2.8: Autocorrelation of the pulse used in the two-dimensional electronic spectroscopy measure-ments of PE545.

where µ(λ) is the dipole strength and E(λ) is the magnitude of the electric field and is highest at about

545 nm for this pulse). The square shape of the spectra is indicative of coherences between eigenstates of

the dye. In contrast to the multi-chromophoric phycobiliproteins, rhodamine 101 is a single chromophore

which implies that electronic coherence is absent. The coherence that we observe must be due to a

vibrational coherence between multiple vibrational eigenstates within the nuclear Hamiltonian of the

system.

We analyzed the population-time dynamics from the 2DES data of rhodamine 101 by first extracting

the total magnitude of the data at the spectral coordinates indicated in Fig. 2.9. We chose the coordi-

nates to extract the dynamics at the lower-energy diagonal peak and the cross peak feature exhibiting

downward energy transfer (depopulation of the higher-lying vibrational state of the excited electronic

state), absorption at high energy and emission at low energy. Both the time trace for the diagonal extrac-

tion and the time trace for the cross-peak extraction show strong oscillations after the high-amplitude

feature of the non-solvent response during the first 10 fs. The oscillations do not dephase during the

scan window of 200 fs. However, since the oscillation has a short period (about 30 fs) relative to the scan

window, we are able to observe six complete cycles. The number of cycles is important for accurately

determining the frequency of the mode since the resolution in the frequency domain is governed by this

quantity.

We Fourier transform the time traces and show the resultant power spectra for both the diagonal

peak and the cross peak in Fig. 2.11. Before Fourier transforming, we removed the background from

each time trace by fitting the cross-peak trace to a constant and the diagonal-peak trace to a linear

function. Removing the background limits the contribution of the non-oscillatory (0 THz) features in


Figure 2.9: Representative two-dimensional electronic spectra of the laser dye rhodamine 101, showingthe magnitude of the total signal for population (τ2) times of 100 fs and 120 fs. The crosses indicatethe diagonal time-trace extraction, [absorption, emission] = [537 ± 1 THz, 537 ± 1 THz] and cross peaktime-trace extraction points, [absorption, emission] = [575 ± 1 THz, 541 ± 1 THz]. The black lineindicates the diagonal of the spectrum (absorption frequency = emission frequency).

Figure 2.10: Time-trace extractions from the magnitude of the nonrephasing, rephasing and total partsof the signal of rhodamine 101. The extractions are at the coordinates indicated by the crosses inFig. 2.9. (a) The diagonal extraction [absorption, emission] = [537 ± 1 THz, 537 ± 1 THz]. (b) Thecross-peak extraction [absorption, emission] = [575 ± 1 THz, 541 ± 1 THz].


Figure 2.11: The power spectra of the magnitude of the total time traces of rhodamine 101 shown inFig. 2.10, for (a) the diagonal extraction and (b) the cross-peak extraction.

the power spectrum, which often overwhelm the low-frequency modes. Both the power spectrum of

the diagonal-peak trace and the power spectrum of the cross-peak trace show a strong oscillatory mode

at approximately 33 THz. These power spectra verify the observed features in the time domain and

also definitively reveal the strength of the 33-THz mode relative to any other modes (which are not

observed above the noise, if any). The 33-THz oscillation is roughly equivalent to the energy difference

between the main S0-to-S1 transition and the strongest vibrational shoulder in rhodamine 101. This

result implies that we are observing a vibrational coherence between the main transition and a higher-

energy vibrational level of the dye. Furthermore, we observe the same oscillation in the non-rephasing,

rephasing and total parts of both the diagonal peak and the cross peak; this result is expected for

vibrational coherences [94].

The autocorrelation of the laser pulse used for this measurement indicates that the temporal duration

of the pulse was about 11.7 fs. A general rule for being able to excite and measure coherences in a sample

is that the pulse duration should be at least a factor of 2 shorter than the period of the particular

coherence. The 33-THz oscillation has a period of about 30 fs; thus our measurement of this coherence

corroborates with the autocorrelation temporal value. As the power spectra show, we do not have the

spectral bandwidth to excite coherences at higher frequencies nor the temporal resolution to measure

them with the current pulse. It is useful to remember these results when we analyze the more-complicated

spectra of samples like phycobiliproteins.

2.8 2DES results on PE545

With positive results from the measurement of a laser dye, we can now confidently investigate biological

samples. We investigated the phycobiliprotein PE545 using two-dimensional electronic spectroscopy

(2DES). PE545 is a pigment-protein complex composed of two monomers. Each monomer contains

three phycoerythrobilins (PEBs) and one dihydrobiliverdin (DBV) and thus the protein contains in

total six PEBs and two DBVs as chromophores. The complex absorbs light in the green region of the


Figure 2.12: The amino-acid composition of the PE545 apoproteins from two different cryptophytespecies. The letters correspond to the particular amino acid; a green colour indicates the amino acid atthat particular site of the transcript is found in the apoprotein of both species.

visible-light spectrum, with a peak absorbance at 545 nm. The energy of the absorbed light is transferred

within the complex — mostly from the six high-energy PEBs to the two low-energy DBVs — and then

(in vivo) the energy is transferred from the DBVs to other pigement-protein complexes.

We study the intraprotein energy transfer using 2DES on isolated PE545 complexes. We obtained

samples of PE545 from two different species of cryptophyte algae. Although both cryptophyte species

contain phycobiliprotein, ’PE545’, this label is based only on the chromophore composition. The apopro-

tein (the actual protein scaffolding that holds the chromophores together) is different for each species,

as shown by the primary structure (Fig. 2.12). Through non-covalent interactions with the protein, it

is possible that the energy landscape of the chromophores is tuned differently for each species, leading

to different site energies and coupling values. This effect is evident when comparing other phycobilipro-

teins. For example, the dihydrobiliverdins (DBV bilins) in the phycobiliprotein PC645 are covalently

bound to the protein scaffolding at both ends while the DBV bilins in PE545 are covalently bound at

only one end. Despite this difference, the conformational shape of the two chromophores is the same

in both phycobiliproteins and the apoproteins themselves are remarkably similar. This result suggests

that the close proximity of the apoprotein and the bonding is altering the shape of the chromophores

and causing the nearly 100-nm–shift in the absorption peak between the two phycobiliproteins.

We obtained the samples from Tihana Mirkovic of the Department of Chemistry at the University

of Toronto. The PE545 phycobiliproteins were isolated from the cryptophyte algae Rhodomonas minuta

(strain CCMP 705) and Proteomonas sulcata strain (CCMP 344). The cells were grown in an artificial

medium (Prov 50 from NCMA) on a 12/12 hour dark-light cycle under illumination of18 mmolm2s−1 . The

cells were harvested from the growth medium by centrifugation and resuspended in a 0.1-M sodium

phosphate buffer. Importantly, this buffer was originally made for a related phycobiliprotein, PC645,

however we found that this buffer concentration (and corresponding pH) significantly reduced laser-

induced aggregation of PE545 on the inner walls of the cuvette. The proteins were extracted through

freezing and thawing (–20◦C & 4◦C) in the dark. Further purification was achieved through centrifuga-

tion and successive ammonium sulphate precipitation (40%, 55% and 80%). The samples were stored at

–20◦C. Before the 2DES measurements, we thawed the proteins and dialyzed them against a 0.025-M

phosphate buffer to remove excess ammonium sulfate. We adjusted the optical density of the samples

with the phosphate buffer. We aimed for a sample optical density of about 0.15 to reduce the possibility

of reabsorption effects when interacting with the laser pulses [109].

We filtered both the proteins and the buffer using 0.2-µm–spacing nylon filters (VWR) to remove

any contaminants. We placed the sample in a home-made flow cell. The front window of the cell was

a 0.5-mm–thick piece of UV-fused silica. We constantly flowed the samples through an ice bath using


Figure 2.13: Two-dimensional electronic spectra of the phycobiliprotein PE545 from species 705. Thereal component of the complex data are shown for two different population (τ2) times. The spectra forPE545 from species 344 appear similar.

a peristaltic pump at 0.06 mL/minute to prevent photobleaching and temperature-induced denaturing

of the samples. This cell had a sample path length of 0.5 mm. We translated the flow cell between

successive 2DES measurements to prevent light-catalyzed aggregation of the protein on the flow-cell

walls. We measured the linear absorption spectra (Varian Cary 6000i UV-Vis spectrometer with a

resolution of 1 nm) of the proteins before and after the 2DES measurements to ensure that the protein

did not denature.

For the 2DES measurements, we used the same experimental setup and pulse that we used for the

measurements of the rhodomamine-101 test sample. We scanned the coherence time (τ1) from –38.4 fs to

+38.4 fs in 0.15-fs steps. We scanned the population time (τ2) from 0 fs to 399 fs in 3-fs steps. We thus

obtained 134 spectra for each measurement for each sample — 804 spectra in total. For clarity, we show

limited numbers of the spectra to highlight key results. The spectra for both species 344 and species 705

show very similar features as a function of the population time. In Fig. 2.13 we show two representative

spectral for species 705 at population times of 66 fs and 141 fs. We show these particular population times

as one can observe an interesting cross-peak feature (the amplitude becomes negative) at the spectral

coordinates of (absorption frequency, emission frequency) = (550 THz, 519 THz), where the amplitude

becomes negative. This feature is oscillatory as a function of population time, being pronounced at some

population times and yet not visible at other times. Other than the cross peak, the spectra are very

congested with overlapping population amplitudes due to the eight constituent chromophores of PE545.

However, the overall spectra are dynamic and the shape changes in an oscillatory manner as a function

of population time.

To investigate these oscillatory dynamics further, we analyzed the absolute magnitude of the data.

Through this procedure, we avoid any artifacts due to phasing techniques of the data. In Fig. 2.14

we show the magnitude specta for species 705 at four different population times. Because the spectra

show the magnitude only, we lose some of the amplitude features that we observe in the real domain.

However, we still observe oscillatory behaviour. This behaviour can be better analyzed by extracting

time traces from the spectra at particular spectral coordinates. The crosses shown in Fig. 2.14 show the

extraction points corresponding to a diagonal peak, (absorption frequency, emission frequency) = (545


Figure 2.14: Two-dimensional electronic spectra of the phycobiliprotein PE545 (CCMP705). The mag-nitude of the complex data is shown for four different population (τ2) times. The spectra for PE545(CCMP344) appear similar. The two crosses for τ2 = 132 fs spectrum signify the spectral location wherewe extract the time traces.

THz, 544 THz), and the cross peak feature that we observed in the real domain (absorption frequency,

emission frequency) = (550 THz, 519 THz).

In Fig. 2.15 we show these time-trace extractions from the spectra for both species as a function of

the population time. The oscillatory behaviour superimposed on an exponentially decaying background

that we observed in the spectra is quite clear in the time traces. The oscillations correspond to coherences

in the sample and the background (decreasing in amplitude) corresponds to population decay. Overall,

the complex oscillations are evidently composed of multiple frequencies. In particular, a slow oscillation

(period of about 50 fs) is clear for the diagonal feature, while a fast oscillation (period of about 25 fs) is

visible in the cross-peak trace. Both of these oscillations were reproducible over three measurements for

each sample. There are also very fast oscillations from a population time of about 150 fs to 300 fs; the

period is evidently comparable to the population-time step size (3 fs) since the sharp feature indicates

under-sampling. Since they emerge only 150 fs after excitation of the sample, these oscillations are likely

due to scattered light from a distortion (such as a mote of dust) on one of the fused-silica wedges in

the 2DES apparatus. Furthermore, the oscillations are prevalent on the diagonal extraction but not the

cross-peak extraction. The energy of light does not change when it is scattered and thus it would only

appear on the diagonal of the 2D spectra where the absorption and excitation energies are equal [22].


Figure 2.15: Population dynamics in PE545. Population time traces were extracted at the two spectrallocations marked by the crosses in Fig. 2.14, corresponding to a diagonal peak (blue trace) and theobserved cross peak (green trace). Species 344 is shown in (a) and species 705 is shown in (b).


To determine the underlying frequencies of the oscillations, we Fourier transformed the time traces

to the frequency domain. This analysis also has the advantage of separating the artificial oscillations

from the real oscillations since their frequencies are quite different. We separately Fourier transformed

the rephasing, non-rephasing and total parts of the data. We excluded the first 15 fs of each trace to

avoid erroneously analyzing the artifacts due to the pulse overlap at early population times. To limit

discrepancies in the transforming process, we truncated each measurement at the same location and did

not use any filtering techniques. We fit each time trace individually to a decaying exponential function;

we subtracted this function from the data to remove the background due to population relaxation. After

zero-padding the resultant residuals, we performed the Fourier transformation numerically using a Fast

Fourier Transform algorithm. We show the results in Fig. 2.16 and Fig. 2.17.

The oscillatory behaviour present in the data is a signature of coherences within PE545. A coher-

ence represents a superposition of eigenstates of the Hamiltonian of the system which is necessarily

non-stationary in time. The oscillations may be due to a coherence of electronic states, a coherence of

vibrational states, or both. The nature of the eigenstates is an important and ongoing investigation in

photosynthetic molecules. Several studies have implicated the presence of purported electronic coher-

ences with the efficiency of energy transfer in these molecules [27, 17, 70]. In pigment-protein complexes

like PE545, vibrational coherences are likely to be observed because we are exciting bilin molecules that

have many vibrational degrees of freedom with broadband pulses. Electronic coherences are much less

conspicuous.

Distinguishing between electronic coherence and vibrational coherence is difficult with 2DES because

both phenomena exhibit similar oscillatory features in the spectra [66]. Several methods have been

developed to help uncover any unique signatures of the two processes [60, 14]. One technique — that is

particularly amenable to 2DES data analysis — compares the prevalance of oscillations in the rephasing

components versus the non-rephasing components of the spectra [93]. By this model, electronic coher-

ences would be observable only in rephasing spectra, while vibrational coherences would appear in both

rephasing and non-rephasing spectra.

The Fourier transforms show many oscillatory modes. The mode at 15 THz is the most reproducible

of all the frequencies and is well-defined in all three measurements for both species 344 and species

705. This mode corresponds to the slow oscillation that we observe in the time traces. This frequency

is observed in both the diagonal feature and the cross peak feature and is attributed to a vibrational

coherence of the chromophores. It appears that the frequency is slightly blue-shifted in species 344

relative to species 705. This effect may be due to a slight variation of the protein scaffold between

species causing the frequency of one of the modes in the bilin molecules to shift. There is also a low-

frequency component of about 6 THz evident in traces from both the diagonal and cross-peak traces.

More measurements are needed to verify the reproducibility of these transforms. However, because of

its strength relative to the noise, we can definitively observe the 15-THz mode in PE545 from both

species in the rephasing and non-rephasing spectra. Thus the 15-THz mode is assigned as a vibrational

coherence.

The frequency transforms for the cross-peak feature contain a 28-THz mode that is inseparable

from noise in the diagonal feature. This frequency corresponds to the faster oscillation observed in

the cross-peak time traces. The mode is also especially strong relative to the other modes in the

extractions from the rephasing spectra. One of our current models of the Hamiltonian of a generic PE545

protein, lists the strongest coupling between any of the chromophores in the protein at about 90 cm−1


Figure 2.16: The oscillatory modes in PE545 from species 344. The power spectra were obtained byFourier transforming the time-trace extractions of the 2DES magnitude measurements. The left columnshows the modes from the diagonal-peak extraction and the right column shows the modes from thecross-peak extraction. The data are displayed in their total form as well as deconvoluted into the inherentrephasing and non-rephasing components.


Figure 2.17: The oscillatory modes in PE545 from species 705. The power spectra were obtained byFourier transforming the time-trace extractions of the 2DES magnitude measurements. The left columnshows the modes from the diagonal-peak extraction and the right column shows the modes from thecross-peak extraction. The data are displayed in their total form as well as deconvoluted into the inherentrephasing and non-rephasing components.


[67]. The corresponding exciton absorption frequency difference is approximately 30 THz. However,

other models provide a range of 18 THz to 44 THz and thus it is evident that more experimental and

theoretical work is needed in order to accurately describe the energy landscape of the PE545 protein.

For instance, knowledge of the dephasing time of the modes will help distinguish coherences because

electronic coherences dephase within a few hundred femtoseconds while vibrational coherences can last

for picoseconds. The 28-THz mode (and many of the other modes) are well-separated in the frequency

domain and have narrow linewidths indicating a long dephasing life time. However, we can measure the

oscillations for only about 400 fs with our 2DES setup — too short to accurately measure the dephasing

times of the modes.

The other frequencies inherent to the time traces are nearer to the noise threshold which thus makes

them more difficult to distinguish. As well, the non-rephasing spectra are intriniscally weaker than the

rephasing spectra for both the diagonal-peak extraction and cross-peak extraction. We did not normalize

the non-rephasing spectra relative to the rephasing spectra, but the observation that the total spectra

are very similar to rephasing spectra implies that the non-rephasing contribution to the total signal is

minimal. Since they are then comparable to the noise threshold, the modes in the non-rephasing time

traces are difficult to analyze. Thus with these data we cannot apply the method for distinguishing

electronic coherence from vibrational coherence for the modes other than the 15-THz mode.

To gain a more quantitative understanding of PE545, we performed frequency-resolved transient-

absorption measurements. Frequency-resolved transient-absorption spectra show the differential change

in the sample population across the spectral window of the pulse and as a function of the population

time (τ2). Thus we immediately know the strength and temporal dependence of the populated states in a

sample. We collected the measurements using the same four-wave mixing optical apparatus that we used

for 2DES measurements but with the necessary adjustments to generate pump-probe signals; we blocked

two of the excitation beams and increased the energy of the remaining two beams to match the overall

power of the three beams used for the 2DES measurements. Similar to 2DES, transient-absorption

spectroscopy is a third-order measurement. The first beam now acts as the pump and contributes two

light-matter interactions, while the second beam serves as the probe with one light-matter interaction.

Since the emitted signal now overlaps with the probe laser pulse, the transient-absorption spectra are

much noisier than the 2D spectra. In addition, the filtering techniques that removed much of the scatter

in 2DES are absent for transient-absorption measurements. Despite these disadvantages, we still observe

faint oscillations in the spectra for both species 344 (Fig. 2.18a) and species 705 (2.19a). To verify the

authenticity of oscillations observed in the 2D spectra, traces were taken across the time domain of the

transient-absorption spectra for emission frequencies of 544 THz and 519 THz, corresponding to the trace

coordinates from the 2D spectra. These time traces were than transformed into the conjugate frequency

dimension and are displayed for species 344 in Fig. 2.18b&c and for species 705 in Fig. 2.19b&c .

The frequency transforms prominently display the 6 and 14 THz oscillations seen in the 2D spectra.

The 28-THz oscillation is not prominent because, as observed in the 2DES frequency transforms, this

oscillation was only evident at the cross-peak feature and the transient absorption trace integrates over

all absorption frequencies, thus averaging out the oscillation. This observation clearly illustrates the

usefulness of two-dimensional electronic spectroscopy.

The weak amplitude of the signal relative to the noise threshold prevents a thorough quantitative

investigation of the modes in PE545. As well, the maximum of 400 fs of population time that we can

observe using this optical apparatus prevents an accurate measurement of the mode dephasing times


Figure 2.18: Transient-absorption dynamics of PE545 from species 344. (a) A representative frequency-resolved transient-absorption spectrum. The dynamics occur across the spectral viewing window of thepulse and as a function of population time (τ2). (b) Power spectrum showing the oscillatory modes atthe emission frequency of 544 THz, obtained by Fourier transforming a time-trace extraction at thisfrequency. (c) Power spectrum showing the oscillatory modes at the emission frequency of 519 THz,obtained by Fourier transforming a time-trace extraction at this frequency.


Figure 2.19: Transient-absorption dynamics of PE545 from species 705. (a) A representative frequency-resolved transient-absorption spectrum. The dynamics occur across the spectral viewing window of thepulse and as a function of population time (τ2). (b) Power spectrum showing the oscillatory modes atthe emission frequency of 544 THz, obtained by Fourier transforming a time-trace extraction at thisfrequency. (c) Power spectrum showing the oscillatory modes at the emission frequency of 519 THz,obtained by Fourier transforming a time-trace extraction at this frequency.


and the picosecond dynamics that are expected to occur in the sample. To tackle these limitations,

we set out to design and build a transient-absorption spectrometer with far superior signal-to-noise

quality and with the ability to measure dynamics for nanoseconds and with femtosecond resolution. In

the next chapter, we describe the development of this spectrometer and discuss the results of its first

measurements of phycobiliproteins.

Chapter 3

Development of a

transient-absorption spectrometer

We desired a spectrometer with high temporal resolution (an instrument response of tens of femtosec-

onds), with an observation bandwidth across the visible light spectrum, and with the ability to correct

for noise in the laser. Another key aspect of the spectrometer was the ability to obtain quantitative

measurements of samples which are lacking in 2DES experiments. With this goal in mind, we devel-

oped a spectrometer measures broadband transient absorption spectra that combines fast acquisition

and balanced detection — normally obtained using single-channel detectors and lock-in amplifiers —

but with the spectral resolution of a charge-coupled device (CCD) camera. Our apparatus is similar

to one demonstrated previously [74] but we use a CCD instead of a photodiode array and we balance

the laser fluctuations. The spectrometer that we constructed has high temporal and spectral resolution,

corrects for noise, and measures the intrinisically quantitative transient absorption spectra. We describe

transient absorption measurements in the next chapter.

Another important feature of the spectrometer is its speed in acquiring data. A typical transient

absorption measurement for us (a few picoseconds in population time with a few femtoseconds step-

size totalling about 1000 time points, and with 350 averages at each time point) takes under twenty

minutes. This quick acquisition time enables multiple repetitions of the measurement without damage

to the sensitive samples. And with multiple measurements of the same sample, we are able to perform

a statistical analysis on the data (for example, the mean and standard deviation). This sort of analysis

is absolutely necessary for distinguishing small, third-order signals from artifacts and noise inherent to

the data. A sample size of one is not sufficient for a proper scientific investigation of any sample. With

multiple trials we can determine, within a given confidence, the reproducibility of the results.

The instrument suppresses noise inherent to the ultrafast laser system and extracts enhanced spectral

information from the inherently small third-order nonlinear signals. We first describe the spectrometer

in detail, including the optics and electronics behind its operation. We also quantitatively report on its

suppression of noise. We then use the spectrometer to investigate the dynamics of the phycobiliprotein

PC577, as described in the next chapter. The measurements lead to a discussion of how the coherently

generated wave packet explores the potential energy surfaces of PC577 during the first few hundreds

of femtoseconds after excitation. We observe features in the spectra both due to population decay and

coherent oscillations. Finally, we use information extracted from the spectra to identify the prevalence

52

Chapter 3. Development of a transient-absorption spectrometer 53

of dynamics on both the excited-state and ground-state potential energy surfaces.

Transient absorption spectrometers usually require two pulsed beams. One pulsed beam perturbs the

sample while the other beam monitors the transient changes in the absorption of the sample. Dynamics

of the system are then observed by incrementally delaying the second pulsed beam relative to the first.

After interacting with the sample, the probe pulses are imaged onto a CCD using a diffraction grating.

The dispersed probe pulses show the wavelength-dependence of the dynamics in the emitted third-order

signals. Our spectrometer also utilizes a third pulsed beam as a reference for correcting the intensity

fluctuations in the laser.

In this chapter we analyze the noise inherent to the laser and we describe the two main components

— the optical apparatus and the electronics for balanced detection — that form the operating basis of

the transient-absorption spectrometer.

3.1 Noise analysis

In this section we quantify the intensity fluctuations in the laser, and then we show how the spectrometer

suppresses this noise. Fig. 3.1a shows the energy output of the laser alone (before introducing other

electronics such as the CCD camera). The data represent typical fluctuations of the laser for time

periods relevant to transient absorption experiments. The noncollinear optical parametric amplifier

(NOPA) adds additional noise onto the noise inherent to the output of the regenerative amplifier. The

NOPA fluctuations correspond to an almost 2% change in intensity which is comparable to (or larger

than) the signals emitted from phycobiliproteins. Moreover, the fluctuations are oscillatory, and a Fourier

transform shows that there are indeed discrete frequencies in the noise (Fig. 3.1b). Discrete modes are

often observed in the noise of ultrafast laser systems [64, 3] and will complicate the identification and

analysis of quantitative information in the true signal. Low-frequency oscillations could be incorrectly

interpreted as sample population dynamics; high-frequency oscillations would appear to be very similar

to coherences.

The spectrometer uses two methods to suppress this noise: balanced detection and fast acquisition.

We tested the ability of the spectrometer to suppress the laser fluctuation noise and CCD electronic

noise. Fig. 3.4 shows the result of balanced detection. In Fig. 3.4a we show the spectrum of the laser

used for these analysis measurements. The spectrum was selected as its features are similar to spectra

used in measurements of samples, namely a fast-rising blue side and a slowly-falling red side. We see

that higher counts of light on the CCD suppress fluctuations most likely due to the electronic noise

inherent to the CCD camera. We extracted line-outs from three spectral regions, chosen to quantify the

contribution of noise at different intensites of light on the CCD. In Fig. 3.4b, we show the noise of the

integrated spectrum.

Balanced detection normalizes the intensity of the signals to the intensity of the laser pulses used to

probe the signals. Fig. 3.4b shows that the balanced detection methods do reduce the laser intensity

fluctuation noise in the probe beam and thus the overall signal relative to the unbalanced measurements.

However, because the signal also depends on the intensity of the pump pulses and the pointing of the

probe beam, the greater reduction of noise is obtained from the differential (between pumped and

unpumped data) itself [88]. This result is a direct outcome of the fast acquistion methods of the

spectrometer.

Acquiring data quickly has two advantages for noise suppression in the spectrometer: filtering low-


Figure 3.1: Analysis of noise in the laser. (a) Histograms showing the deviation of the pulse energy fromthe mean, over 500 000 pulses. The left panel corresponds to the output of the regenerative amplifer. Theright panel corresponds to the amplified output from the NOPA. Superimposed on both distributions isa Gaussian fit. (b) A Fourier transform of the laser intensity over time, representing noise under typicaloperating conditions. In addition to white noise, several discrete modes are noticeable over two ordersof magnitude. (c) The correlation between four consecutive laser pulses. Uncorrelated data would becircular in the x-y plane whereas these data roughly follow the diagonal — indicating high correlationand the potential to filter low-frequency noise.


Figure 3.2: The concept of balanced detection. The intensity fluctuations inherent to the laser causeartificial variations in the detected signal from the sample. Balanced detection uses a copy of the laserbeam as a reference to these fluctuations. Our setup measures the intensity of the reference beam witha photodiode and then correlates the intensity with the strength of the signal measured by the camera.The data can then be corrected for the laser fluctuations.

Figure 3.3: The effect of fast detection methods. We increased the repetition rate of the chopper andupgraded the camera to a model with faster acquisition rates. By these methods, we are integratingover the energy fluctuations of fewer laser pulses and thus filtering out the intensity drift in the laser.


Wavelength (nm) 350 KCPs (unbal.) 350 KCPs (bal.) 6000 KCPs (unbal.) 6000 KCPs (bal.)535 2.97E-4 ± 8.9E-5 3.17E-4 ± 9.6E-5 3.25E-4 ± 8.1E-5 2.01E-4 ± 9.4E-5547 5.49E-4 ± 1.94E-4 2.27E-4 ± 1.57E-4 4.27E-4 ± 2.0E-5 7.3E-5 ± 9E-6615 7.20E-4 ± 3.81E-4 7.18E-4 ± 5.84E-4 1.30E-3 ± 9E-5 6.75E-4 ± 7.3E-5integrated 1.86E-3 ± 1.4E-4 1.83E-3 ± 2.1E-4 1.49E-3 ± 5E-5 1.75E-3 ± 1.9E-4

Table 3.1: Noise suppresion through averaging. The standard deviation from the mean of the extractionpoints in 3.4a is inversely related to the number of KCPs (averages), as well as the intensity of light ona particular pixel of the CCD.

frequency noise and enabling significant averaging. Low-frequency noise will be apparent as an intensity

drift within consecutive pulses. Since the spectrometer is integrating over four consecutive pulses for

each data point, the intensity drift within those four pulses will be evident in the data. However, Fig.

3.1c shows that there is a strong correlation between four consecutive pulses [64]. This correlation implies

that low-frequency noise is only significant at time scales longer than four pulses and is thus filtered

by the fast acquistion methods of the spectrometer. Therefore there is only high-frequency noise after

filtering, some of which is attributable to noise in the camera.

High-frequency noise can be suppressed by taking more averages. This procedure takes more time,

but since our spectrometer acquires data quickly, we can take hundreds of averages at each time delay

value without the total measurement time becoming too long (which is both tedious and detrimental

to the sensitive biological samples). Our current measurements are averaged for 350 cycles, which gives

a noise threshold of 10−4. Fig. 3.4c shows that the noise suppression follows a square-root law as a

function of the number of averages. This principle implies that the returns are diminishing as we increase

the averages to more than 350; even at 6000 averages, there is not an appreciable additional reduction of

noise. In Table 3.1 we list the mean and standard deviation of the noise at these two values of averaging

for the different extraction points shown in Fig. 3.4a.

A fast chopper is also beneficial for reducing scattered light in the measurements. Dynamic scatter

is especially troublesome as our samples are in an aqueous environment with large-sized particles. Scat-

tering is dependent on the wavelength of the interacting light and the size of the scattering particle. It

is best to aim for a contrast ratio of 100:1 (with 500-nm light, we want to reduce the particle size to at

least 5 nm). In practice, we filter our samples to remove any particles larger than 200 nm in diameter.

Thus for further removal of dynamic scatter, we rely on the filtering of the chopper operating at high

speeds.

3.2 Optical apparatus

The optics upstream of the transient absorption spectrometer were similar to a design described pre-

viously [95, 107, 4]. We typically tuned the NOPA to produce pulses with an intensity maximum at

580 nm or shorter wavelengths and with minimal intensity structure from 600 nm to 700 nm (see Fig.

4.9a). The profile of these pulses is ideal for pumping the sample predominantly at high energies and

then probing the dynamics across its energetic landscape. Thus, we can use the output of the NOPA for

both the pump and probe pulses in the transient-absorption spectrometer.

Next, we compress the output of the NOPA temporally the previously described grating compressor

and a single-prism prism compressor [29, 72, 2]. This procedure minimizes second-order and third-

order dispersion in the pulses that could cause distortions to the transient-absorption features [48]. The


Figure 3.4: Noise suppression results. (a) The laser spectrum used for analyzing noise. The color gradientindicates the percent deviation of each detected wavelength from the mean over 12,000 measurements.The three points indicate single-wavelength extractions. (b) We plot the normalized intensity of theCCD signal, integrated over wavelength (red trace) and the normalized intensity of the photodiode(black trace). The integrated CCD intensity, balanced to the photodiode intensity, is shown in the bluetrace. The traces have been offset for clarity. The traces are a function of kinetic cycles, meaning thereare four measurements of the photodiode voltage for every single measurement of the spectrum on theCCD. (c) The two red lines correspond to the integrated noise intensity of all pixels of the CCD. The twoblue lines correspond to the noise at the single pixel of the CCD where the intensity is at a maximum.The lighter traces of each pair are unbalanced and the darker traces are balanced to the noise presentin the photodiode. Each trace is a function of the number of kinetic cycle pairs. We label 350 kineticcycle pairs because the data were typically measured at this value. The noise of the integrated spectrumdecreases as the square root of the number of averages. Shown are the data of one measurement undertypical operating conditions.


compressed pulse gives an instrument response function (nonresonant response of the solvent) of less

than 30 fs. With this compressed pulse, we can impulsively excite and observe any active modes in the

sample with a frequency of approximately 30 THz or less.

The compressed, broadband pulses were then input to the main part of the transient-absorption

spectrometer. We obtain three copies of the incident beam with a wedged beam-splitter; the front

reflection and back reflection (each about 0.1% of the incident beam energy since the beam is p-polarized)

are used as the probe and reference pulses, respectively; the transmitted portion is used as the pump

pulse. The collimation of the beams was adequate to scan the pump delay relative to the probe over a

range of 3800 ps with negligible changes in the pump divergence and with a resolution of 0.5 fs. In all

places before the sample, we focused and collimated the beams with protected-silver, spherical mirrors.

We kept the angle of incidence onto the spherical mirrors below 4◦ to minimize the astigmatism caused

by using them in an off-axis configuration.

We independently control the power of the pump and probe beams with an achromatic λ/2 waveplate

and a 0.7-mm-thick wire-grid polarizer pair in each arm (Fig. 3.5). We set the pump-beam power such

that the signal (∆I/I) was less than 0.05. This bleach value typically corresponded to a pump power

of 60 µW, which meant the pump pulse energy was 12 nJ/pulse. This power level is low enough that

effects such as photobleaching and multi-photon absorption are negligible.

The probe beam passes through the sample perpendicular to the surface while the pump beam passes

through at a slight angle. This configuration enabled us to isolate the probe beam and yet minimize the

time-smearing of the pump beam. We focused the probe beam onto the sample using a spherical mirror

with a shorter focal length (f = 10 cm) than the spherical mirror (f = 25 cm) used to focus the pump

beam. The focused spot size of the probe beam (16 µm beam waist) was therefore smaller than the

pump spot-size (41 µm beam waist), and thus the excitation density in the sample was fairly constant

over the spatial cross-section of the probe beam. The pump fluence was typically about 5 mJ/pulse/cm2.

Our determination of time zero (the moment when the pump and probe pulses arrive at the sample

concurrently) involved the measurement of the autocorrelation of the nonresonant response of the solvent

(water) of our samples. The precise measurement of time zero is important since the timescale of the

sample dynamics is on the order of femtoseconds. During consecutive measurements, the time zero

drifted typically a few femtoseconds due to the inaccuracy of the delay stage (Newport IMS600LM).

This drift was linear across the entire scan time window and thus we corrected the data by adjusting

time zero. We scanned typically for a few picoseconds before time zero (the probe pulse arrives at

the sample before the pump pulse) to obtain an accurate measurement of the background noise such

as scatter of the pump and fluorescence of the sample. These background spectra are averaged and

automatically subtracted from the data.

3.3 Balanced and fast detection

The transient absorption setup uses a balanced detection method to identify laser fluctuation noise in

each pulse (averaged over five consecutive pulses) and eliminate that noise automatically. This procedure

allows for a far better signal-to-noise ratio than in our previous measurements. Balanced detection is

achieved through the use of a CCD camera and a photodiode, activated and triggered with precise

timing. Below we describe each component used to adjust the timing events, and collect and display the

data. A representative schematic of the electronic components is shown in Fig. 3.6.


Figure 3.5: Schematic of the experimental apparatus for measuring transient absorption spectra. Forclarity, irises used to isolate beams and some turning mirrors are not shown. A beamsplitter (BS)generates three beams from the incident beam. The two reflected portions are used as the probe anddiagnostic beams while the transmitted portion is used as the pump beam. The diagnostic beam, whichis reflected off the beamsplitter at a slightly different angle than the probe beam, is directed into aphotodiode (PD) by a pick-off mirror (M1). The probe beam propagates through a UV-fused-silicawindow (W) to compensate for extra glass in the pump arm. Both the probe and the pump propagatethrough separate half-waveplate (λ/2) and polarizer (P) pairs for independent power adjustment. Achopper (C) blocks the pulses at a rate of 625 Hz. The path length of the pump beam is adjustedusing a retroreflector (R) mounted on a delay stage (D). A zero-degree spherical mirror (CM1) withfocal length 250 mm focuses the pump beam onto the sample while a separate mirror (CM2) with focallength of 100 mm focuses the probe beam onto the sample. The angle of incidence of the pump beamonto the sample is 4◦ from normal and the beam is blocked after traversing the sample with a beamblock (B). The probe beam is re-collimated by an achromatic lens (L1) placed after the sample. Asecond achromatic lens (L2) focuses the collimated beam into the spectrometer (G) which images thewavelength-dependent signal onto a CCD detector.


Figure 3.6: An overview of the electronics used for fast and balanced detection. The setup is designed torecord transient absorption spectra and balance the laser intensity every eight laser shots. The outputof the laser is set at 5 kHz, and the electronics downcount the pulse train to sets of eight pulses. A dataacquisition (DAQ) card serves as the central hub for controlling and monitoring the measurements. Aphotodiode reads the intensity of each laser pulse and relays the measurement to the DAQ card afterbeing enhanced by a preamplifier. Two TTL (Ch. 7 and Ch. 8) signals coming from the timing delaygenerator (TDG) of the laser are used to control the synchronization and delay of the electronics. Ch.8 is used to clock the timing of the DAQ card relative to the analog signals being received from thephotodiode. Ch. 7 drives the chopper that periodically blocks the pump pulses of the laser. A copyof Ch. 7 is selectively controlled by a delay generator before triggering the camera to measure spectra.Labview software acts as the user interface.


Figure 3.7: Possible magnitude of the photodiode signal before (a) and after (b) optimizing the timingof the CH8 TTL to have the DAQ card read the peak of the voltage generated by the laser pulse incidenton the photodiode.

The method of balanced detection requires the accurate measurement of the intensity of each laser

shot. A current preamplifier boosts the low-current output signal of the photodiode to a high-current

signal that is then converted to a voltage drop via Ohms Law. The sensitivity of this current-to-voltage

conversion is changed using the preamplifier controls while monitoring the resultant output on the

oscilloscope. It is important to first measure the output of the photodiode on the oscilloscope and then

measure the output of the preamplifier so that the signal at each stage is independently verified. As well,

the input offset of the preamplifier and the iris in front of the photodiode should be set at a level to avoid

negative voltage values at one extreme and saturation of the photodiode at the other. A typical value of

the output of the photodiode is at most a few hundred millivolts whereas the output of the preamplifier

is around 1.5 volts. The benefit of the current preamplifier is evident from its ability to adjust both the

output voltage amplitude and decay time. This allows us to shape the photodiode signal such that it is

both accurately detectable by the DAQ card and well-separated in time from adjacent signals.

The next step is to make sure that the DAQ card reads the peak of each of the photodiode output

signals to ensure the most accurate balanced detection. The idea is to have just one number to describe

the intensity of each pulse, corresponding to the peak of the light pulse. This is achieved through

calibration of the CH8 TTL signal. The CH8 TTL pulse goes to the input of the DAQ card and acts

as the clock for the DAQ card. To calibrate the timing, the TDG CH8 delay is adjusted until the

maximum voltage from the photodiode, via the DAQ card, is displayed on the computer. When this is

accomplished, we have essentially lined up the leading edge of the TTL pulse with the maximum voltage

entering the DAQ card. This calibration step maximizes ∆V of the voltage plot display on the computer

software screen (Fig. 3.7).

In the experiment a chopper will be used to periodically block the pump beam. This allows us to

see the change in signal intensity while pumping the sample versus not pumping. To enable the fastest

detection rates possible, the pump beam is chopped at a frequency of 625 Hz (half of the 1250-Hz

maximum detection rate of the camera). This chopping rate means that, in the experiment, the camera

will see laser signals with the pump unblocked (on) and laser signals with the pump blocked (off) in a

2 ms period (the chopper has changed the 5 kHz laser pulse train into on/off pulse-quartets). To have

the chopper wheel spin at 620 Hz, the CH7 TTL is input into the New Focus chopper box and the

subharmonic mode is set at 10. This device down-counts the 5 kHz input frequency of the CH7 TTL

to a 625-Hz signal. The signal is output from OUT1 as well as the Motor output to drive the chopper

wheel.

Although during the experiment the chopper is placed such that only the pump beam is chopped, at

this point it is easiest to place the chopper before the beamsplitter so that the probe beam is chopped.

This allows one to easily monitor the effect of forthcoming adjustments by observing the probe spectrum


on the camera. After calibration the chopper is placed in the pump beam. Since this is a relatively

short distance from its calibration position, the phase of the blades relative to the laser pulses is still

correct (assuming the beam is aligned perfectly so that the spot size is small and the beam is horizontally

planar, and that the chopper is placed so that the beam is incident on the outer edge of the blades).

An important objective of this transient absorption setup is the optimization of the on spectrum

versus the off spectrum. Indeed the entire idea of pump-probe is based on detecting the difference

between a signal emitted from a sample that was excited versus a sample that was not excited. Thus

this calibration step is essential for the optimization of pump on versus pump off. With the probe

beam being chopped the camera will display the spectra of the blocked pulses versus the spectra of the

unblocked pulses (to be described in greater detail below). Thus, in theory, the on spectra should be the

spectrum of the laser beam and the off spectra should be zero. Due to the inherently short timescales of

the parameters of this transient absorption setup, one will observe charge leaking into the off spectra as

well as an alteration of the amplitude features of the on spectra. These features are a symptom of two

parameters that need to be adjusted: the chopper phase and the vertical beam tilt into the spectrometer.

The chopper phase needs to be adjusted so that it is not periodically clipping the laser pulses, while

the tilt angle needs to be adjusted so that the laser is aligned onto the bottom rows of the pixels of

the CCD. Both of these adjustments allow the camera to operate at the fast speeds required while still

generating clean spectra. With the chopper in front of the beam splitter and a cuvette of methanol in

the sample position, the Labview program is set to a low number of kinetic cycle pairs. The off spectra

are observed while adjusting the phase of the chopper wheel and the vertical position of the alignment

mirror (directly before the final two irises) into the camera. The goal is to minimize the counts of signal

in the chopped off spectra while avoiding introducing any artifacts into the unchopped on spectra. It is

important to note, however, that with the fast operation speeds of the camera, there will always be some

charge leaking into the off spectra. Therefore, it is best to minimize the artifacts as much as possible.

It is helpful to scale the y-axis of the display to a low number of counts so that it is easy to observe the

change in the off spectra while adjusting the chopper phase and the vertical tilt of the beam. Both of

these parameters are coupled so it may take several iterations in order to fully optimize the on and off

spectra.

The final step of the calibration of the electronics is to optimize the triggering of the camera in order

to have its exposure coincide with the periodicity of the pulse quartets. After activation by Labview,

the camera sits in standby mode, waiting for a trigger. When the camera receives the trigger in the

form of the delayed TTL from the digital delay generator, the camera initializes and starts exposing.

The exposure coincides with the camera sending its fire pulse to trigger the DAQ card currently waiting

in standby mode. We want the first pulse of the first pulse-quartet to arrive as far after the exposure

of the camera begins in order to maximize the amount of time the DAQ card has to trigger and begin

looking for photodiode signals (Fig. 3.8).

Since the leading edge of the exposure fire serves as the trigger for the DAQ card, we want there to

be a large time delay before the first photodiode signal arrives at the DAQ card corresponding to the

first pulse that the CCD detects. However, since the chopper and the camera are frequency-controlled

independently, the small frequency mismatch between the two causes them to slowly drift out of phase.

This drift causes the camera exposure to start integrating a mix of on and off pulses instead of pulse-

quartets fully on and pulse-quartets fully off. As a result, we see a drop in the amplitude of the on spectra

and a corresponding rise from zero of the amplitude of the off spectra (3.9). So we must optimize the


Figure 3.8: CCD camera exposure/fire signal as well as the TTL signal from CH7 of the timing delaygenerator (relayed through the chopper box and delay generator) corresponding to the timing of pulses(blocked and unblocked) incident on the camera. ∆t, the time between the first exposure of the cameraand the first pulse of the first quintet, is maximized via the digital delay generator.

Figure 3.9: Representative spectra obtained with the CCD camera. In kinetic scan mode, a single cameraexposure integrates four pulse events (either blocked or unblocked) into one spectrum, cleans the chipand repeats several hundred times. When the timings are correct, the spectra should be integrations ofeither four blocked pulses or four unblocked pulses. Obtaining a spectrum with an amplitude betweenfully on and fully off indicates the exposure is integrating both on and off pulse events and the delay viathe digital delay generator should be adjusted.

time delay not just for the triggering at the beginning but also at times long after triggering using the

digital delay generator.

The digital delay generator is externally triggered by the rising edge of the 625-Hz TTL from the

chopper box. The delay generator, when working in AB output mode, manipulates the input TTL

pulse in two ways: delaying and shaping. The A value tells the delay generator how much to delay

the output TTL signal relative to the input TTL signal. This value is iteratively changed during initial

electronics calibration. The value is typically several hundreds of microseconds. The B value tells the

delay generator when to truncate the on value of the pulse and begin looking for the next input TTL

pulse. The typical setting of the B value is around 10 microseconds, although this value is not critical;

it only has to be less than 2 ms so that it doesnt miss the next TTL pulse. Note that the values of all

of the other settings (C to H) are set at zero.

The calibration procedure of the digital delay generator is to first set the kinetic cycle pairs input box

at around 500. This value implies that the camera is generating 500 on spectra and 500 off spectra in an


alternating sequence by integrating pulse-quintets for a total of 4000 laser pulses. With the Heads-Up

Display (HUD) feature activated, the Labview display screen displays the integrated spectra from kinetic

scan 1 (on spectrum 1) all the way to kinetic scan 1000 (off spectrum 500). We adjust the timing of the

Stanford Box in, usually, 10 s or 100 s increments and repeat the procedure until optimized. The goal is

to have the on and off spectra perfect at the first kinetic scan and remain perfect for as long as possible.

The maximum number of kinetic cycle pairs obtained through iterative delay timing adjustments is

usually around 350 (Fig. 3.10).

We have detailed the procedure for calibrating the electronics when the photodiode is picking-off the

zero-order diffracted beam in the grating compressor. This configuration is suitable for both the transient

absorption setup and the two-dimensional spectroscopy setup. If, however, one is only interested in

using the transient absorption setup, an alternative configuration can be used that provides a better

understanding of the calibration steps. To use this configuration, remove the photodiode from the

grating compressor and place it so that it faces the probe-arm pickoff mirror of the transient absorption

setup. In this configuration, the photodiode will measure the intensity of the back reflection of the

beamsplitter (the sample is probed with the front reflection). Since the intensity is measured after the

beam is chopped, it is much easier to optimize the phase of the chopper and consequently adjust the

delay of the triggering of the camera.

After optimizing the preamplification and CH8 TTL timing as before (Fig. 3.10a&b), one places the

chopper before the beam splitter. We want the blade of the chopper to block an entire pulse and not

block a fraction. To do this, we watch the voltage plot display and adjust the phase of the chopper

box manually. This delays the 500 Hz voltage pulses going to the chopper which then shifts the blades.

We watch on the screen to see the voltage points move to either a maximum or minimum whereupon

we know the laser pulses are not being semi-blocked. Note that we have not adjusted the Stanford box

timing yet since adjusting the chopper phase will adjust the TTL going to the digital delay generator.

This procedure means that the camera may miss some of the first pulses of the first pulse quartet. This

loss is acceptable at this stage since we only want to make sure that we do not have any voltage points

with a magnitude between the maximum and minimum amplitude (Fig. 3.10c).

After optimization of the chopper phase, a cuvette of methanol can be placed in the sample position.

Since the leading edge of the camera exposure serves as the trigger for the DAQ card, we want there to

be a large time delay before the first photodiode signal arrives at the DAQ card corresponding to the

first light pulse that the CCD detects. We optimize this ∆T by adjusting the digital delay generatorand

viewing the voltage plot on the computer software to make sure that we do not miss the first photodiode

signal corresponding to the first pulse (Fig. 3.10). Afterwards, the on/off spectra of the camera can be

observed as the delay timing is fine-tuned to maximize the number of averages while still preserving the

time-ordering of the camera exposure and arrival of the laser pulses.

3.3.1 Summary of settings for electronics

To enable the fast detection rates needed for the transient absorption spectrometer, it is necessary to

adjust the following settings of the (Andor DU971N-FI Newton) CCD camera:

In the Setup Acquisition window: Under the Crop Mode tab, the Enable Crop Mode box should be

checked and the Crop Settings should be set at: Left = 1, Bottom = 1, Right = 1600, Top = 20. This

means that only the bottom 20 rows of pixels will be read out by the camera. Under the Setup Camera

tab, the Acquisition Mode should be Kinetic, the Triggering should be External Start and the Readout


Figure 3.10: Representative Labview display of the photodiode voltage generated from each laser pulse.(a) Possible photodiode voltage data before calibration (b) Display with ∆V maximized through CH8TTL timing (c) Display with chopper blade phase adjusted to either completely block or completelyunblock all of the pulses (d) Correct display showing complete pulse-quartets after adjusting the timingof the camera trigger via the digital delay generator.

Mode should be FVB; the Exposure Time should be 0.00100 s, the Number of Accumulations should

be 1, the Kinetic Series Length should be 1000 and the Kinetic Cycle Time should be 0.00100 s; the

vertical pixel shift should be set at a speed of 9.75 microseconds with a Normal voltage amplitude while

the horizontal pixel shift should be read at a rate of 2.5 MHz with a 1x Conventional amplifying gain.

The Stanford DG645 digital delay generator should be Externally triggered on the Leading edge of

the signal and the AB output mode should be connected to the camera.

The New Focus 3501 chopper box should be set to the 7/5 Wheel, Externally triggered on the Leading

edge of the Sync Input, and operating in H/S mode with the Harmonic set to 1 and the Subharmonic

set to 10.

The Stanford SR570 current preamplifier should be set at a Low Noise gain mode with a positive

input offset typically around 10 nA and a sensitivity around 2 µA/V.

The Thorlabs DET110 photo detector is operated with the diode in reversed-biasing mode.

DAQ Card The National Instruments PCI-6221 data acquisition (DAQ) card and the National In-

struments BNC-2110 connector block serve as the interface with the computer for signals output from

the detectors in the setup. The card functions with an internal rate of 250 kHz; the integration time

for input signals is thus approximated at 4 µs. The DAQ card operates in the following sequence: 1)

activated by computer (Labview) into a mode to wait for a trigger. 2) triggered by camera fire via PFI12

input. 3) clocked by CH8 TTL via PFI0 input. The first step is to have the computer activate the DAQ

card and then activate the camera. (Note: Labview cannot activate two devices at once). The order of

device activation matters because there is a relatively long delay between activation of each device due

to the relative slowness of Labview. Activating the DAQ card first puts the card in a standby mode

where it now looks for a trigger. (the card is always receiving the CH8 TTL clocking pulse and the

photodiode voltage pulse, but the card does not read them until it is triggered). Labview then activates

the camera and puts the camera in a standby mode where it now looks for a trigger. When the camera

receives the trigger in the form of the TTL pulse from CH7 from the timing delay generator, the camera

initializes and starts exposing (the beginning of its first exposure has already been adjusted to catch a

pulse quartet). The exposure coincides with the camera sending its fire pulse to trigger the DAQ card


currently waiting in standby mode. The DAQ card then reads the photodiode signal at its clocking rate,

set by the CH8 TTL. If we had instead activated the camera first, the camera would have found a TTL

trigger pulse, initialized, begun exposing and sent its fire signal to the DAQ card all before Labview had

time to activate the DAQ card. Thus the DAQ card would be triggered not on the first exposure scan,

but on some random scan later depending on when the DAQ card became activated.

Chapter 4

Transient absorption spectroscopy of

PC577

4.1 Background

A standard form of time-resolved optical spectroscopy is the pump-probe measurement. In general,

pump-probe studies operate under the principle of using two ultrafast pulses of light, seprated temporally,

to investigate the dynamics of a sample; the pump pulse excites the sample (starts the dynamics) and

the probe pulse monitors the dynamics. Transient absorption is a form of a pump-probe experiment that

involves monitoring the time-dependent (transient) changes in the probe transmission through a sample

[33]. Original transient absorption measurements monitored the intensity of the probe pulse over one

dimension — time — using a photodiode. Another dimension is resolved — emission wavelength — by

spectrally resolving the probe using a photodiode array or CCD.

The process is termed transient absorption because the sample interacts with different spectral com-

ponents of the probe pulse at different times after excitation with the pump pulse. The sample eventually

returns to its equilibrium configuration on the ground electronic state with vibrational levels incoher-

ently excited given by the thermalization of the sample. When we measure a standard linear absorption

spectrum, we are probing this ground-state configuration (a ground-state absorption spectrum) since we

are use a single light source as a measurement. We could even excite the sample with a pump pulse

and then wait (say microseconds) before probing the sample, and once again we would measure the

ground-state absorption since we are measuring the steady-state after all of the excite-state dynamics

have decayed to the ground state. The advantage of a transient absorption measurement is that we have

the temporal resolution to observe the dynamics that take place between the time of excitation and the

time of reaching steady-state equilibirum again.

Transient absorption measurements are different from typical linear absorption measurements because

they use ultrafast, coherent light (a laser pulse) to excite the sample and probe and the non-equilibrium

dynamics of the sample. When the sample is excited, it is no longer in an equilibrium configuration

and will exhibit dynamic behaviour. We therefore monitor the non-equilibrium dynamics as a function

of time and resonances as the excited molecule searches through phase space for a pathway back to

equilibrium.

Transient absorption spectroscopy is widely used to study the photophysics of molecules and chemical

67

Chapter 4. Transient absorption spectroscopy of PC577 68

reactions by first inducing dynamics with a strong laser pump pulse and then monitoring the dynamics

with a weaker probe pulse. The development of nearly transform-limited laser pulses within the realm of

tens of femtoseconds [30, 89] allowed researchers to investigate oscillatory behaviour of the emitted signal

in addition to ultrafast decay. This has been interpreted as the observation of wave packet dynamics,

indicating a coherent superposition of vibrational states that moves in time.

The dynamics of a wave packet on the excited-state potential-energy surface are typically classified as

either incoherent or coherent. In the incoherent regime, energy of the wave packet is quickly dissipated

to other degrees of freedom and the wave packet thermalizes; in the coherent regime the damping of the

wave packet is slow enough that it can exhibit periodic motion about the potential well [102, 111]. In

the former we expect only population decay in the emission spectrum of the wave packet as it decays to

the ground state, and in the latter we expect coherent oscillations superimposed on the decay. Transient

absorption spectroscopy with short laser pulses allows for both the creation of wave packets and the

observation of their oscillatory signatures (Fig. 4.1).

Preliminary studies of transient-absorption spectroscopy related to coherences investigated the ultra-

fast dynamics of wide-ranging samples including organic molecules in solution, [78, 79, 31, 13, 8, 83, 108],

polymers and crystals [19, 105, 110], and even elementary chemical reactions [77, 5]. A defining moment

in the history of the transient-absorpton field was when the technique was applied to the study of bi-

ological samples and coherent oscillations were observed. Femtosecond transient-absorption studies on

bacterial reaction centers [101, 41, 56], Fenna-Matthews-Olson complex [82, 81, 75], bacteriorhodopsin

[20, 7, 42] and light-harvesting complexes [12, 21] all showed the prevalence of coherence within biology.

Recent experiments using two-dimensional electronic spectroscopy have also shown coherences in

photosynthetic molecules. However, the underlying physical processes of these observed oscillations

remains uncertain, with evidence of both vibrational and electronic coherences [27, 17, 95, 70]. The

question is how to interpret the coherent oscillations. The existence of electronic coherence and its

persistence for perhaps hundreds of femtoseconds in a protein environment is indeed interesting, but its

differentiation from vibrational coherences is challenging. Over the years, several different groups have

developed or modified techniques to help unravel differences between the various types of coherences and

determine signatures that would be evident in spectroscopic data [60, 93, 14].

We seek to add to the debate by investigating the ultrafast dynamics within a photosynthetic protein,

PC577, from the cryptophyte algae Hemiselmis pacifica (CCMP 706). This pigment-protein complex

consists of eight bilin chromophores (two dihydrobiliverdins (DBVs) and six phycocyanobilins (PCBs))

covalently bonded to a protein scaffold (Fig. 4.2). PC577 acts as an auxilliary antenna for cryptophyte

algae to capture a greater spectral portion of sunlight than with just Photosysthem I and Photosystem

II alone. After absorbing a photon of sunlight, PC577 transfers the excitation energy to the common

reaction center in the photosystems. This process involves both intraprotein energy transfer — mostly

from the two high-energy DBVs to the six low-energy PCBs — and interprotein energy transfer (that

takes place in vivo) between the PCBs to another pigment-protein complex. With multi-chromophoric

complexes in general we cannot treat the individual chromophores as single states, but rather we must

consider excitons (superpositions of the chromophores) as the entities interacting with light. We chose

to study PC577 because it is an open-structure complex [106] with small electronic coupling between the

constituent chromophores, implying the excitons are highly localized on a single site. The low coupling

values also means that any coherent oscillations observed in the emission signal of PC577 would almost

certainly be due to vibrational coherence.


Figure 4.1: Transient absorption spectroscopy of a wave packet. The pump pulse excites a a coherent su-perposition of states from the minimum of the ground electronic potential-energy surface. The potentialsurfaces are shown as the energy-dependence of different nuclear configurations in the vibrational phasespace (here we show only one vibrational coordinate, in reality there are many for complex molecules).The initial nuclear configuration in the excited state is not in equilibrium with the minimum of thepotential. Analagous to a classical spring perturbed from its equilibrium, the wave packet will oscillateabout the minimum of the excited-state surface. We can stimulate emission back down to the groundstate with the probe pulse. The energetic spacing between the ground- and excited electronic state isnot constant relative to nuclear configuration and thus — depending on when we stimulate emission —the energy (and corresponding wavelength) of the interacting light will be different.


Figure 4.2: Visualization of the x-ray crystal structure of PC577. The complex is composed of eightbilin chromophores (two dihydrobiliverdins (purple) and six phycocyanobiliverdins (blue)) covalentlybound to a protein scaffold (green). The protein of PC577 has an open structure that separates thechromophores near the center.

4.2 Testing the spectrometer with cresyl violet perchlorate

We obtained an ultrafast pulse with broad bandwidth using the methods described previously for the

NOPA and pulse compression. Unlike the 2DES experiments where we can measure the autocorrelation

of the pulse, we measure the solvent response in the transient absorption setup in order to estimate the

duration of the pulse. We temporally overlap the pump and probe beam (time zero) in a cuvette filled

with the solvent of the sample (either methanol for laser dyes or buffer solution for phycobiliproteins)

and record the emitted third-order signal as we delay the pump pulse. We show a representative solvent

response measurement for the pulse used in these measurements in Fig. 4.3a. The residual angular

dispersion in the pulse is evident in the fringes. We are mostly concerned with the flat phase profile in

the center region, though, as this is where we measure the dynamics of the sample. We have a useable

bandwidth from about 550 nm to about 700 nm. Fig. 4.3b shows the integrated magnitude of the

response. The temporal duration of the pulse can be estimated as the full-width-half-maximum of this

trace — about 30 fs.

We show the linear absorption spectrum and the steady-state fluorescence spectrum of the laser

dye cresyl violet perchlorate along with the spectrum of the laser pulse in Fig. 4.4. The peak of the

absorption is at 593 nm and the peak of the fluorescence is at 620 nm. The sample was excited and

probed with the pulse spectrum shown in Fig. 4.4. The spectrum is centered at 588 nm and has enough

bandwidth to excite both the main S0-S1 transition of the dye at 593 nm and the main vibronic shoulder

at about 550 nm. The pulse also has intensity out past 700 nm to allow probing of any dynamics present

at spectral regions corresponding to the fluorescence of the molecule.


Figure 4.3: Estimating the pulse duration. (a) The solvent response to the overlap of the pump andprobe pulses showing the intensity of the constituent spectral components. (b) The integrated magnitudeof the spectrum in part (a).

Figure 4.4: The linear absorption spectrum and fluorescence spectrum of the laser dye cresyl violetperchlorate, plotted along with the spectrum of the laser pulse used for the transient absorption mea-surements.


Figure 4.5: A representative transient absorption spectrum of cresyl violet perchlorate. The amplitudeof the data corresponds to the wavelength-normalized, intensity differential of the probe light afterinteracting with the pumped sample and the unpumped sample (∆I/I). Positive features representenhanced signal emission when pumping, while blue features represent enhanced sample absorptionwhen pumping. Negative times signify the interaction of the sample with the probe pulse before thepump pulse. Coherent oscillations are visible above the background.

We show the transient absorption spectrum for cresyl violet perchlorate in Fig. 4.5. The x-axis

corresponds to the emission wavelength of the sample. The y-axis represents the time between pump

and probe interactions. Before time zero, the probe pulse arrives before the pump and thus there is

no differential in signal intensity. At time zero there is a large change in intensity with both positive

and negative features corresponding to the non-resonant response of the solvent when the pump and

probe are overlapped in time. This effect does not interfere with the true signal once the pump and

probe are no longer overlapped and thus we focus on the time points after about 50 fs. The differential

in signal intensity starts at about 7% for the highest-amplitude features after time zero and decreases

as the delay between the pump and probe is increased. The spectrum is solely positive in amplitude

indicating the transient absorption of cresyl violet perchlorate is dominated by ground state bleach and

stimulated emission. The ground state bleach and stimulated emission components of the total signal

are not distinguishable because of the small Stokes shift [44], as shown in the fluorescence spectrum.

In addition to the decay features of the intensity in the transient absorption spectrum, there are

underlying coherent oscillations present throughout the entire spectral window. We fit the data to a

unique biexponential decay function along each wavelength and subtract the decay function to investigate

the oscillations more carefully. A single exponential function did not accurately fit the decay dynamics.

This procedure removes the population decay at each wavelength and leaves the residuals containing

only the oscillatory part of the signal. These population-free data are shown in Fig. 4.7. The coherent

oscillations are quite evident with a peak-to-peak amplitude of almost 3% of the original probe amplitude

before dephasing, whereas the noise level is approximately 0.08% peak-to-peak. It is also clear that there

are superpositions of multiple frequencies, observed through the amplitude beating, present throughout


Figure 4.6: A representative line-out from a transient absorption measurement of cresyl violet at 607nm, showing the coherent oscillations over 7 ps, on a background decay due to population relaxation.

Figure 4.7: The emitted signal of cresyl violet perchlorate as a function of the pump delay time, showingthe underlying coherent oscillations as a function of frequency. The background decay features wereindependently removed at each emission wavelength.


Figure 4.8: The power spectrum of cresyl violet perchlorate taken by Fourier-transforming the timedomain of the emission signal at 607 nm. The five strongest peaks are fit to Lorentzian functions (red).

the spectral range.

Due to the high signal-to-noise ratio of the data, we were able to Fourier-transform the data along

each wavelength and observe multiple peaks in the frequency domain. The main mode, centered at

approximately 17.6 THz is well-known for cresyl violet perchlorate [99]. The frequency components are

present throughout most of the spectral range. The Fourier power spectrum was reproducible over five

measurements and the corresponding frequency spectrum of the probe is shown at the bottom of the

plot.

The high signal-to-noise ratio of the data shows the true physical, Lorenztian shape of the peaks. We

can thus extract vibrational dephasing information about the oscillations in the time domain by fitting

the main peaks in the power spectrum. As the frequencies are discrete modes and well-separated we can

fit them to separate Lorentzian functions. With the fit parameters we can then calculate the damping

constant for each frequency. This procedure is much easier than fitting in the time domain where there

would be at least eight different parameters to fit in a convoluted trace. We note that the material

response function of the sample alone is convolved with the pulse spectrum in the time domain and thus

in the frequency domain the actual modes of the sample are enhanced or suppressed depending on their

frequency [12]. Assuming our pulse spectrum is Gaussian in the time domain, the Fourier spectrum will

be multiplied by the conjugate Gaussian in the frequency domain centered at zero frequency and so the

low-frequency modes like 6.5 THz and 8 THz are enhanced artificially relative to the higher frequency

modes such as the 24-THz mode. Following this idea, any higher frequency modes may be washed out

by the noise.


4.3 Sample preparation

We obtained all biological samples from Tihana Mirkovic of the Department of Chemistry at the Uni-

versity of Toronto. The PC577 phycobiliproteins were isolated from the cryptophyte algae Hemiselmis

pacifica (strain CCMP 706). The cells were grown in an artificial medium (Prov 50 from NCMA) on a

12/12 hour dark-light cycle under illumination of18 mmolm2s−1 . The cells were harvested from the growth

medium by centrifugation and resuspended in a 0.1-M sodium phosphate buffer. The proteins were

extracted through freezing and thawing (–20◦C & 4◦C) in the dark. Further purification was achieved

through centrifugation and successive ammonium sulphate precipitation (40%, 55% and 80%). The sam-

ples were stored at –20◦C. Before the transient-absorption measurements, we thawed the proteins and

dialyzed them against a 0.025-M phosphate buffer to remove excess ammonium sulfate. We adjusted

the optical density of the samples with the phosphate buffer. We aimed for a sample optical density of

about 0.15 to reduce the possibility of reabsorption effects when interacting with the laser pulses [109].

We filtered both the protein and the buffer using 0.2-µm-spacing nylon filters (VWR) to remove any

contaminants. We placed the sample in a home-made flow cell. The front window of the cell was a 0.5-

mm-thick piece of UV-fused silica. This cell had a sample path length of 0.5 mm. To minimize protein

aggregation on the flow cell walls and to minimize the chance of photobleaching the protein, we flowed the

sample using a peristaltic pump (Cole-Parmer) at a rate of 1.05 mL/minute. The protein solution flowed

through an ice bath during the scans to prevent temperature-activated denaturation of the protein. We

translated the flow cell between successive transient absorption measurements to prevent light-catalyzed

aggregation of the protein on the flow-cell walls. We measured the linear absorption spectra (Varian

Cary 6000i UV-Vis spectrometer with a resolution of 1 nm) of the proteins before and after transient

absorption measurements to ensure that the protein did not denature. We measured the steady-state

fluorescence spectra with a Varian Eclipse fluorescence spectrometer. All steady-state and time-resolved

measurements were performed at room temperature.

4.4 Transient absorption results of PC577

The absorption of PC577 spans over one hundred nanometers centered at 577 nm. The complex contains

two kinds of chromophores: two dihydrobiliverdin (DBV) molecules absorb at high energy values of the

absorption spectrum and six phycocyanobilin (PCB) molecules absorb at low energy values. Unlike

some other cryptophyte pigment-protein complexes, the structure of PC577 is spatially separated which

makes the center-to-center difference between the constituent chromophores relatively large. The linear

absorption and fluorescence spectra of the protein are shown in Fig. 4a&d, along with the spectrum of

the laser pulse used for the transient absorption measurements. As the same pulse was used to both

excite and probe the molecule, we optimized the features of the spectrum to be mutally beneficial for

each process. The intensity peak at 588 nm overlaps well with the peak of absorption of PC577.

In Fig. 4.9b we show one transient absorption measurement of PC577 collected at room temperature

from 0 to 2 ps. The measurements were performed five times over about a ninety-minute period. We see

a dominant negative-amplitude feature for wavelengths longer than approximately 660 nm. This feature

corresponds to excited-state absorption. A nearly zero-amplitude feature at about 650 nm separates

the excited-state absorption from the positive-amplitude features dominating the lower wavelengths of

the transient absorption spectrum. The positive-amplitude features are due to ground-state bleach and


Figure 4.9: Steady-state and dynamic spectroscopy of PC577. (a) The linear absorption spectrum ofPC577 (blue) and the laser pulse spectrum (orange) used for the transient absorption measurements.The dashed line highlights the peak of the linear absorption spectrum (b) A representative transientabsorption spectrum of PC577 measured from 0 to 4 ps in 4-fs steps (we show the first 2 ps afterexcitation). The amplitude of the data corresponds to the change in the intensity of the probe lightafter interacting with the pumped sample. Positive features represent increased signal emission whenpumping, while blue features represent enhanced sample absorption when pumping. Positive timessignify that the pump pulse arrived before the probe pulse. (c) The emission signal of PC577 showingthe underlying coherent oscillations for the first picosecond after excitation. The background decayfeatures were independently removed at each emission wavelength. A sharp node is seen around 638 nm.The oscillations on either side of this node are nearly out-of-phase relative to each other. The dashed lineindicates a biexponential fit to the node in the oscillations (d) The steady-state fluorescence spectrumof PC577 after excitation at 550 nm. The dashed line highlights the peak of the fluorescence spectrum.


Wavelength (nm) Amplitude (∆I/I) Decay (fs) Amplitude (∆I/I) Decay (ps)577 0.019 ± 0.001 640 ± 40 0.025 ± 0.001 15.16 ± 1.37620 0.007 ± 0.001 550 ± 70 0.053 ± 0.001 29.63 ± 1.80

Table 4.1: The coefficients of the biexponential fit to the population decay, extracted at 577 nm and 620nm.

Figure 4.10: Coherent oscillations at 616 nm. We display the mean (black line) and standard deviation(blue shaded area) of line-outs from five independent measurements.

stimulated emission. We see that the positive-amplitude features at different spectral ranges decay

at different rates, with the feature centered at about 580 nm decaying much quicker than the feature

centered at about 620 nm.

We fit the traces at 577 nm and 620 nm separately to biexponential decay functions to extract the

population timescales for the DBVs and the PCBs, respectively. We repeated this procedure for five

independent measurements and display the results in Table 4.1.

Oscillatory features are visible amidst the background decays throughout the spectral window. The

most prominent oscillations are centered at about 635 nm superimposed on the ground-state bleach,

and centered at about 680 nm superimposed on the excited-state absorption. We extracted a line-out at

the emission wavelength of 616 nm from each of the measurements. We plot the average and standard

deviation of these five line-outs for the first 1.5 ps after excitation in Fig. 4.10. The line-outs were linearly

shifted because a small error in the delay stage caused time zero to drift slightly between measurements

The compensation shifts ranged from 4 fs to 16 fs. We did not use any other normalization, interpolation

or scaling techniques. The coherent oscillatory features in the emission signal are quite clear amidst the

population decay feature for the first 1.5 ps. These oscillatory features are evidently composed of many

different frequency modes of comparable amplitude. We see that the small-amplitude structure in the

oscillations is reproducible.

To carefully analyze the frequency components of the oscillations we subtracted the biexponential fit

functions and plot the residuals of the data in Fig. 4.9c for the first picosecond of the measurement. The


Frequency (THz) Dephasing (ps−1)5.8 ± 0.1 3.9 ± 0.18.0 ± 0.1 3.7 ± 0.811.0 ± 1.2 3.3 ± 1.813.4 ± 3.2 5.4 ± 2.914.1 ± 0.2 1.8 ± 2.415.4 ± 0.2 4.8 ± 2.819.8 ± 0.1 1.4 ± 0.124.3 ± 0.4 6.3 ± 1.4

Table 4.2: The eight oscillatory modes with decay constants extracted from the emission wavelength of616 nm using the fitting procedure described in the text.

highest-intensity oscillations start out with a peak-to-peak amplitude of approximately 2% differential

signal. There is a distinct region around 640 nm where the amplitude of the oscillations goes to zero.

The amplitude of the oscillations blue of 640 nm have the opposite sign as the oscillations red of 640

nm. These features become more obvious when we investigate the frequency domain. In Fig. 4.11a we

plot the result of Fourier transformation across each wavelength. As suggested by the time traces, there

are multiple high-amplitude oscillation frequencies. The strongest oscillations appear at 5.8 THz and

8.0 THz, and the frequencies at 14 THz, 15 THz, 20 THz and 24 THz are also all reproducible. The

intensity of any given mode decreases to the noise threshold at around 640 nm. The intensities of the

strongest modes are about 2.5 times less on the red side of 640 nm. There is another spectral region —

from about 660 nm to 690 nm — where the intensities of the strongest modes (6.5 THz and 8 THz) are

seen to decrease to the noise threshold before becoming observable again at about 700 nm.

We focus on the 8 THz mode because it is the highest in amplitude. The complex data from the

Fourier transform contains amplitude and phase information, and in Fig. 6c we plot the result for the 8

THz mode. This plot show that the amplitude and the phase of this mode change dramatically around

640 nm. The amplitude diminishes into the noise threshold and the relative phase changes about 2.5

radians. In other words, the red and blue sides of 640 nm are about 80% out-of-phase. The other modes

show similar characteristics.

The oscillatory features in the time domain are strong enough relative to the noise to apply a fitting

technique. We first filter the time-trace data shown in Fig. 4.10 in the frequency domain by applying

a Heaviside filter from 4 THz to 30 THz. This filter eliminates the constant background and the noise

above 30 THz where we do not have the resolution to observe oscillatory modes. We fit the filtered

data in the time domain to a linear combination of eight decaying cosine functions using a nonlinear

least-squares algorithm. We chose eight functions because this was the number of clearly resolved peaks

in the frequency domain. We maximize the robustness of the fit by minimizing the least absolute value

residuals. The independent fits to each of the five line-outs all achieved a coefficient of determination

value greater than 0.95. We seeded the fit algorithm with an estimate of the frequency of the eight

peaks, but did not specify bounds. All other parameters (the amplitude, phase and decay constants) of

the fit function were seeded randomly and without bounds.


Figure 4.11: Analysis of oscillatory modes. (a) The power spectrum of PC577 from the background-subtracted transient-absorption data. Bright features correspond to high-amplitude oscillations at thatparticular emission wavelength. Shown is one of five measurements. (b) A representative power spectrumfor the oscillations at the emission wavelength of 616 nm. (c) The amplitude and phase of the 8.0 THzoscillation present in the PC577 data are plotted as a function of the signal emission wavelength. Theyare plotted on the same graph with corresponding axes for visual comparison. Both the amplitude andphase exhibit a sharp change around 638 nm. These features are signatures of excited-state wave packetsbecause 638 nm corresponds to the fluorescence maximum.


4.5 Discussion of results

4.5.1 Population dynamics

The signals emitted from typical samples in transient absorption measurements contain ground-state

bleach, stimulated emission, and excited-state absorption components. The sign of the amplitude of

ground-state bleach and stimulated emission is the same but opposite to excited-state absorption. The

physical processes behind ground-state bleach and stimulated emission are quite different as they involve

different potential energy surfaces and their relative contributions reveal distinct information about the

sample. The transient absorption spectrum of PC577 (Fig. 4.9b) consists of a strong positive-amplitude

feature in the center of the spectral probing window surrounded by negative-amplitude features on

either side. The positive-amplitude feature is composed of ground-state bleach and stimulated emission

components. In PC577, it is not possible to directly differentiate between the ground-state bleach

and excited-state stimulated emission because they share the same sign and also because the nuclear

modes in the excited state are not displaced much from the bottom of the excited-state potential energy

surface (because the Stokes shift is small) [103]. Thus, the two contributions of ground-state bleach and

stimulated emission will overlap spectrally. The problem is compounded because the broadband pump

excites chromophores over a broad spectral distribution.

The negative-amplitude features are due to absorption of the first-excited state of the chromophores

in PC577 to higher-lying states. The density of states increases dramatically after the first-excited state

in large molecules like the chromophores in PC577, and it is therefore expected that much of the transient

absorption spectrum would show these absorption events. The center of the spectral probing window

most likely contains excited-state absorption features as well, but these features are overwhelmed by

the strong oscillator strength of the ground-state absorption and the stimulated emission, and greater

laser field strength in this region (Fig. 4.9a). The ground-state bleach and stimulated emission features

become comparable in magnitude to the underlying excited-state absorption features near the edges of

the linear absorption spectrum (540 nm and 660 nm). These effects then mutally cancel and we observe

no differential intensity in the transient absorption spectrum.

A fit to each emission wavelength of the transient absorption spectra provides insight into the ultrafast

dynamics of PC577. The fit requires at least two exponential functions to accurately reproduce the

transient structure at each emission wavelength. The biexponential fit hints at the multiple processes

of population decay and energy transfer occuring within the PC577 protein. The transient absorption

spectra show a fast decay of the positive-amplitude features around 570 nm, a few hundred femtoseconds

after excitation. This spectral region corresponds to the maximum of the ground-state absorption by

the highest-energy chromophores in PC577 — the DBV chromophores — and the decay indicates the

transfer of the excitation energy from the DBVs to the lower-energy PCB chromophores. The fit in

this region gives two lifetimes of 640 ± 40 fs and 15.16 ± 1.37 ps of comparable magnitude from five

independent measurements. The 600-fs decay is due to ultrafast energy transfer. The 15-ps decay is

likely indicative of the decay to the bleach features as the chromophores relax back down to the ground

state. This timescale is only approximate as the fit is only calculated over four picoseconds.

The bulk of the ground-state absorption around 620 nm is due to the PCB chromophores. The

biexponential fit to the transient absorption data in this spectral region gives a 550 ± 70 fs and 29.63

± 1.80 ps lifetime. In contrast to the DBV lifetimes, the femtosecond component of the PCBs is very

small in amplitude relative to the picosecond component. This femtosecond component may be due to


the energy transfer between the PCBs (which are closer in energy and thus the downhill energy transfer

would be expected to be weaker), and possibly due to absorption of the PCBs to a higher-lying excited

state. The picosecond component is again an approximation of the bleach recovery time. It is longer than

the DBV lifetime possibly because of the gain in excitation energy both from the DBVs and decay from

the higher excited states, as well as being closer in energy to the ground state of the DBV chromophores.

We do not observe an amplitude increase of the PCB features with our biexponential fit, most likely

because the pulse excites the PCB and DBV chromophores simultaneously. We would expect to see an

increase (on a 600-fs timescale) with narrowband excitation of solely the DBVs.

Energy transfer within multi-chromophoric pigment-protein complexes appears to be governed by a

fast (hundreds of femtoseconds) decay from the initially excited high-energy pigments and subsequent

reorganization (tens of picoseconds) within the lower-energy pigments of the complex. For example,

the population decay times for PC577 are similar to the pigment-protein complex PC645 which also

contains DBV and PCB pigments. Previous studies have shown that in PC645, the energy transfer

from DBVs to PCBs is on a timescale of hundreds of femtoseconds, and the energy transfer from one

PCB pigment to another is on a timescale of tens of picoseconds [65, 61, 1]. Analagously, studies of the

light-harvesting structures of other organisms have shown intraprotein energy-transfer times for both

bacteriochlorophylls in chlorosomes [82] and chlorophylls in a light-harvesting complex of green plants

[32]. In vivo, one PC577 phycobiliprotein would transfer its energy to another pigment-protein complex

on a timescale that would be comparable to, but faster than the recovery of the bleach features. In intact

cryptophytes containing a pigment-protein complex similar to PC577, for example, the energy transfer

from the DBVs to the photosystems was found to be on the order of tens of picoseconds [97].

4.5.2 Coherent dynamics

Subtracting the biexponential fits from each emission wavelength of the transient absorption data removes

the population dynamics and reveals the underlying coherent dynamics (Fig. 4.9c). The oscillations are

present over much of the spectral probing window albeit with interesting amplitude and phase behavior,

to be discussed later. The maximum amplitude of the oscillations is only about a 1% change, and so the

high signal-to-noise of our spectrometer aids in observing the oscillations above the background. Fig.

4.11a shows the power spectrum as a function of emission wavelength. As expected from the oscillations

in the time domain, there are many different modes of comparable amplitude present in the frequency

domain. These modes represent superpositions of bonding degrees of freedom of the chromophores of

PC577 — often called normal modes — as long as the vibrations are harmonic in nature (the restoring

force is proportional to the displacement from equilibrium in phase space). This assumption is most

often valid. Unlike vibrational coherences observed experimentally in organic dye molecules, there are

many oscillations in photosynthetic complexes around 50 cm−1 and 100–250 cm−1 [82].

All vibrational levels strongly coupled to the electronic transition via the Franck-Condon mechanism

would be observed in the transient absorption spectra, with the number of modes given by the pulse

bandwidth overlap with the optically allowed vibronic transitions [90, 31]. While it is true that the

chromophores of PC577 have many degrees of vibrational freedom and therefore an equal number of

dimensions in their potential energy surfaces, the number of degrees of freedom that are significantly

shifted from the ground-state potential energy surface is minimal [102]. In large organic molecules,

the displacement of most of the vibrational modes are within the small-displacement regime, under the

harmonic-potential approximation. This principle limits the number of frequencies that we observe in


the spectra.

Although the coherent oscillations could be due to electronic coherences (superpositions of strongly

coupled electronic states), the open-structure of PC577 and the resultant low inter-chromophore coupling

limits this possibility. Also, the spectral dependence of the oscillations provides evidence for vibrational

coherences, to be discussed in the next section. Thus we suspect that the oscillations are vibrational

coherences.

We fit the coherent oscillations to gain insight into the dephasing information of each underlying

frequency. We see eight distinguishable peaks in the frequency domain; thus we fit each time trace to

eight exponentially-decaying cosines. At the emission wavelength of 616 nm (where the oscillations are

the strongest) we observe eight reproducible modes. The strongest-amplitude modes at 6 THz and 8

THz dephase at the same timescale of about 4 ps. Such a dephasing rate is about the median of the

other modes. Notably the 24-THz mode dephases fastest at under 1.5 ps whereas the 20 THz mode lasts

for over 6 ps. The overall vibrational dephasing results both from pure dephasing and population decay

(relaxation) of the vibrational levels involved in the coherence due to thermal equilibration with the

protein [101, 83]. It has been noted that vibrational coherences can last longer than the energy transfer

time between chromophores in some photosynthetic proteins, and thus vibrationally-active Forster theory

does not apply to the energy transfer process [102]. However there are no coherences at the wavelengths

corresponding to the DBVs. This absence is because the red side of the excited state of the DBVs

would presumably be centered in the middle of the inhomogenousely broadened bleach component of

the protein. This region would also consist of strong contributions of the PCB chromophores and would

certainly not be distinguishable from possible ground state coherences on the blue side. And, since PC577

does not have strong intermolecular coupling, the wave packet cannot be assumed to be substantially

delocalized over multiple interacting chromophores. Thus the damping of the oscillations on the blue

edge of the signal during the first few hundred femtoseconds is most likely due to population relaxation

of the vibrational modes accompanying the energy transfer.

Many of the underlying frequencies in the data of PC577 corroborate with the two-dimensional

electronic spectroscopy (2DES) data of another phycobiliprotein, PC645 (CCMP 269) from the cryp-

tophyte Chroomonas mesostigmatica [93]. PC645 contains eight chromophores: two dihydrobiliverdins,

two mesobiliverdins and four phycocyanobilins. Because of the similar composition of chromophores, we

expect PC577 and PC645 to share many of the same vibrational modes. The frequencies of 5.9 THz, 8.1

THz and 14.4 THz are statistically identical between the two datasets. In the 2DES data, the 8.1 THz

mode did not appear to dephase during the 400-fs observation window. In the current data, we observe

a dephasing lifetime of 330 fs and thus the mode would appear to not dephase over 400 fs. None of the

higher-frequency modes (33 THz, 40 THz and 50 THz) that were observed in the data of PC645 were

observed in the transient-absorption data of PC577. The absence of these frequencies is likely because

the pulse used in the transient absorption measurements is temporally longer than the pulse used in

the 2DES measurements. Vibrational coherences are only generated and measured when the pump and

probe pulses are shorter in time than the period of each vibrational mode and we were not able to resolve

any oscillatory modes greater than 30 THz.

Determining the nature of the vibrational coherences is an important but challenging task with

transient absorption data. Transient absorption measurements can probe vibrational coherences on both

the ground-state as well as the excited-state potential-energy surfaces. It is important to distinguish

between the two possibilities because coherences on the excited-state may imply that they are involved


with the energy transfer process. With a temporal δ-function pulse, and assuming that the sample

follows a Franck-Condon mechanism, the contribution of ground state coherences would diminish as the

instantaneous pump would excite the wavepacket into the excited state and then back to the ground

state before the wavepacket had time to explore the phase space of the excited state [72, 40]. Thus it

would be returned to stationary equilibrium conditions. For our short but finite-duration pulse, however,

it would be possible to see ground-state contributions to the coherences by means of resonant impulsive

Raman scattering [7]. This process happens when the pump pulse has a duration long enough to allow

the wave packet to move in the excited state so that a second interaction with the pump moves the wave

packet down to a displaced position on the ground state and we observe oscillations [20, 59].

4.5.3 Minimum of potential-energy surface

Various techniques are available to differentiate between ground-state and excited-state oscillations.

A method for unambiguously assigning excited-state coherences is fluorescence upconversion, as the

oscillatory signals can only occur from the populated fluorescent state [47]. However, this method does

not allow the broad spectral probing window that we require for observing the wave packet dynamics. A

different method – for application in transient absorption measurements – involves intentionally adding

dispersion to the excitation pulse. Depending on the sign of the dispersion, wave-packet motion on a

particular potential-energy surface can be enhanced [6]. Our transient absorption measurements do not

rely on this method. Instead, using the formalism developed for wave packets, we provide evidence for

the vibrational coherences being predominantly on the excited-state of the PC577 chromophores.

The formalism [73] developed for coherent superpositions of vibrational modes (wave packets) is

useful for analyzing the amplitude and phase behaviour of the oscillations present in the transient

absorption data. Direct Franck-Condon excitation of the ground-state equilibrium population with

coherent, broadband light will generate a population on multiple, closely spaced vibrational levels along

different vibrational coordinates of the excited state of the molecule. This superposition of vibrational

levels is non-stationary under the Hamiltonium of the system and will lead to a wave packet that explores

the multi-dimensional phase space of the excited vibrational coordinates. The wave packet will oscillate

about the minimum of the multidimensional potential-energy surface and, based on the energy spacing

between the ground-state and excited-state surfaces, the positioning of the wave packet will be evident

in the transient absorption spectra [6]. As well, the phase of the oscillations will undergo a π-radians

shift at the global minimum of the potential-energy surface [103].

The oscillations in the PC577 transient-absorpton data are prevalent across much of the spectral

probing window but show interesting features at certain emission wavelengths. Notably, the oscillations

decrease in amplitude and abruptly change phase around the emission wavelength of 638 nm (Fig. 4.9c).

This node is also visible in the frequency domain, where we see the amplitude of the various modes

decrease around 638 nm (Fig. 4.11a). We are observing the wave packet moving about the excited-

state minimum at about 638 nm. The minimum of the excited-state potential-energy surface is where

steady-state fluorescence occurs and we see that the peak of the steady-state fluorescence is close to the

minimum of the oscillations [44]. As discussed in the next section, the slight blue-shift of the node relative

to the steady-state fluorescence peak is due to the dynamic Stokes shift. We expect that over several

picoseconds, the node of the oscillations would lead asymptotically to 640 nm where the steady-state

fluorescence peak occurs.

The phase change in the data is consistent with the formalism as well. In Fig. 4.11c we show the


Figure 4.12: The motion of a wave packet on the excited-state potential-energy surface. Excitationoccurs from a stationary equilibrium population in the minimum of the ground-state potential. Coherentbroadband excitation will excite a superposition of states (a wave packet). This wave packet will oscillatebetween the energetic turning-points on the excited-state potential with a period, T, as well as broadendue to anharmoncity of the surface. Steady-state fluorescence occurs from the minimum of the excited-state potential, although we can stimulate emission at any point. This schematic illustrates the wavepacket as a superposition of harmonics of one vibrational degree of freedom. In a real sample, the wavepacket is probably a superposition of different vibrational degrees of freedom as well.


phase profile of the strongest mode at 8 THz. There is an abrupt change of about 2.5 radians at the

emission wavelength of 638 nm. This value corresponds to about 80% of the full π-radians shift that

we expect from the wave packet formalism. Because of this dramatic shift, the oscillations on the blue

side of 638 nm are observed to be almost out of phase with the same oscillations on the red side of 638

nm (Fig. 4.9c). Closer to the edges of the spectral probing window, the phase of the oscillations is less

well-behaved probably because of the effects of residual chirp (group velocity dispersion) on the pulse

that was not fully corrected during pulse compression. The oscillations centered at 680 nm are observed

to have an artificial slope because of these effects.

We see that the amplitude of the wave packet is stronger to the blue side of the node. This observation

is consistent with the notion that the anharmonicity of the well has a sharper rise to the blue side. The

initial width of the wave packet on the excited-state potential-energy surface is given by the spectral

width of the laser pulse used to generate the wave packet and, through vibrational dephasing, relaxation

and anharmonicity over the energy surface, it broadens over time [103]. Also, the excitation of more

vibrational levels leads to greater dispersion and loss of coherence [101]. The lifetimes of the oscillations

are proportional to the harmonicity of the vibrational mode coordinate of the excited state surface, as

the anharmonicity would broaden and dampen the wavepacket [72].

Ground-state oscillations would show similar spectroscopic signatures as excited-state oscillations,

however the abrupt amplitude dip and phase shift would be centered at the emission wavelength cor-

responding to the peak of the ground-state absorption spectrum [10, 42, 58, 104, 50]. The peak of the

absorption spectrum indicates the bottom of the ground-state potential energy surface and a ground-

state wave packet would oscillate about this coordinate position. At wavelengths bluer than 577 nm in

the transient-absorption data, we see some very weak oscillations that may correspond to ground state-

oscillations. We do not, however, see any clear amplitude dip or abrupt phase change at 577 nm (the

maximum of the ground-state absorption spectrum, Fig. 4.9a). One could hypothesize that in PC577,

the ground-state oscillations will not have such a well-defined node because we have eight chromophores

with different absorption maxima that are excited simultaneously with our broadband pulse. Thus the

peak around 577 nm and 612 nm will blur any well-defined nodal point. We note, however, that the node

in the excited-state oscillations is well-defined after a few hundred femtoseconds. It is interesting that

in PC577, the ground-state oscillations are so weak relative to the excited-state oscillations; in other

biological samples like bacteriorhodopsin, it has been noted that there can be heightened contributions

from the ground-state potential to the overall signall [20].

The ground-state potential-energy surface provides additional details about the wave packets on the

excited-state potential, though. Because the excited-state wave packet is generated straight up from

the ground-state equilibrium coordinates (i.e. absorption maximum), one of its turning points should

be the wavelength corresponding to the absorption maximum. This analysis implies that we cannot

have excited-state stimulated emission at emission wavelengths lower than about the maximum of the

ground-state absorption. In the data we do see that the absolute amplitude of the oscillations drop off

sharply approaching 577 nm. This observation makes sense since our pump pulse is strongly pumping in

the blue and thus mainly exciting the DBV molecules around 577 nm. We see that we can only stimulate

light emission from this spectral region in the first few hundred femtoseconds because after that time,

the wave packet has moved via downhill energy transfer to the PCBs. It is these oscillations that are

the strongest and also represent the high-energy turning point. At the other side, we see the oscillations

extend to the emission wavelength of 650 nm even though the ground-state absorption spectrum does


not. This observation provides further evidence of stimulated emission from the excited-state potential

energy surface [23, 26].

The above picture is one-dimensional in coordinate space. To be observed experimentally, one vi-

brational mode has to be dominant [100]. The minimum potential energy surface would not necessarily

have to be the same for each vibrational mode. The signature of this possibility would be a frequency-

dependent nodal structure. Since all of the modes in our data go to zero at approximately the same

emission frequency, we are observing the global minimum of the multi-dimensional, excited-state poten-

tial energy surface. The chromophores will be transferring energy from this global minimum to another

pigment-protein complex. The protein maximizes the amount of energy transferred by configuring the

potential-energy surface so that the wave packet remains centered on the global minimum at all times.

This method avoids local minimum traps of some vibrational coordinate. Furthermore, the bottom of the

excited-state potential surface (at least 90% of where it will eventually lead) is found within hundreds of

femtoseconds. This wave-packet signature shows that the protein has found the energy surface for which

it will then transfer energy to other pigment-protein complexes in a picosecond timeframe. Essentially,

the wavepacket is prevented from moving around the congested region where there are six PCBs (which

could be inefficient over an anharmonic surface) and stays centered on a single minimum.

Because the strongest modes dephase within a few hundred femtoseconds, they are only active during

the PC577 intraprotein energy transfer. The longer-lasting modes like the 21-THz mode are active

during the timescales of interprotein energy transfer. It is interesting that there appears to be a lack of

vibrational coherences around the DBV molecules, or perhaps the excited-state potential energy surface

of these molecules are more red-shifted than the PCB molecules relative to the common ground state

of the PC577 complex. The 21-THz mode, which dephases on about the same timescale as the DBV-

to-PCB energy transfer, could be a signature of this mode belonging to DBV, and at least being active

when the DBV molecules are excited. This would imply that, at least the minimum (perhaps not the

overall shape) of the potential energy surface of the DBV molecules is shifted to the same phase-space

coordinates as the PCB molecules.

The vibrational coherences in PC577 are predominantly in the excited state of the constituent chro-

mophores. This analysis implies that intramolecular and intermolecular energy transfer occurs while

vibrational modes are active. As resonance energy transfer depends on the orientation and spatial sepa-

ration of chromophores, these oscillations could certainly affect the proximity of adjacent chromophores

and perhaps improve the overall efficiency of energy transfer.

4.5.4 Dynamic Stokes shift

The spectral and temporal resolution of the spectrometer enables us to characterize the solvation of the

PC577 pigment-protein complex upon excitation to an excited state. The Stokes shift (x nanometers) is

defined as the spectral change of the peak of fluorescence intensity relative to the peak of the ground-state

absorption. These quantities are in the steady state, though, and with ultrafast resolution, experiments

can measure the temporal change of the solvent environment. This effect is observed in the first few

hundred femtoseconds of Fig. 4.9c. By the Franck-Condon principle, the optical transition proceeds

vertically in phase space without a change to the reaction coordinates of the molecule [23]. The impulsive

excitation of the chromophores implies that the excited state finds itself in a solvent environment that

is not optimized to the new dipole configuration of the chromophore. The dynamic Stokes shift shows

that the polarity of the excited state of the chromophores is different (either more or less polar) then the


ground state. To compensate, the environment (water and protein) reorganizes its charge distribution

to minimize the energy of solvation [35].

There are many different dimensions involved with the excited-state potential-energy surface; we have

eight resolvable superpositions of vibrational coordinates, as well as a solvation, reaction coordinate [45].

The solvent reorganization is represented by a Gaussian statistical distribution of chromophores with

slightly different energies on the excited-state solvation reaction coordinate. Upon initial excitation from

the ground state, this distribution is still centered on the minimum of the ground state configuration.

The solvent reorganization changes this distribution over time and is represented by the dynamic Stokes

shift. Time-resolved fluorescence would reveal a red-shift in the fluorescence over time [47]. In transient

absorption measurements the wave packet oscillations are a window into the changing equilibrium point.

The wave packet acts as a metric for visualizing the population distribution change in time. It follows

the mean of the statistical distribution of the chromophores — all with slightly different excited-state

potential-energy surfaces. The phase change of the wave packet occurs at the mean of the distribution

which is red-shifting in time as the distribution becomes more statistically likely to be nearer the bottom

of the excited-state potential-energy surface, representing the degree of solvation.

The process of solvation is very rapid and the solvation time occurs on a timescale of hundreds

of femtoseconds to picoseconds in polar solvents like water [80]. The fast component is related to the

solvent reorganization near the solute, and the slow component is due to the solvent away from the solute

[62, 38, 80]. Nearly 80% of the dynamic Stokes shift occurs within the first 100 fs while the remainder

takes places over hundreds of picoseconds. We observe these timescales by following the window of

the wave packets. We extracted the timescales of the dynamics by fitting the node of the oscillations

at each time delay value for five independent measurements. We chose a fit function of two decaying

exponentials plus a constant. The average fit function had two lifetimes of 62 ± 5 fs and 300 ± 100 ps.

The fast component is about 75% of the total dynamic Stokes shift observed in our data, and occurs

within the first 200 fs (4.9c). The fit function can be used to determine the correlation time of the

protein environment of PC577 and thus obtain the spectral density as well.

The fit function shows that the peak of emission of the pigment-protein complex approaches the

peak of the steady-state fluorescence (Fig. 4.9c and Fig. 4.9d). The fluorescence lifetime of the complex

is orders of magnitude longer than the solvation time, and thus the sample has equilibrated to the

lowest level of the excited-state potential surface as given by Kasha’s Rule before fluorescence occurs.

It is important to note, however, that the complex must transfer energy within picoseconds of time

to adjacent complexes before fluorescence occurs on the nanosecond timescale. As the extracted decay

function shows (Fig. 4.9c0, the slower 300-ps component means that solvation is still occuring when

energy transfer takes place, albeit a very small contribution.

The shift in the node could also be due to the transfer of the excitation energy of the DBVs to the

PCBs. The DBVs, by themselves, would certainly have an excited-state minimum and so fluoresce more

to the blue than 640 nm. However Fig. 4.9b shows that the DBVs transfer their excitation energy to the

PCBs in a few hundred femtoseconds. The DBVs would not contribute to the steady-state fluorescence

over nanoseconds. It is possible, though, that we are seeing their contribution in the first few hundred

femtoseconds where we observe the nodal shift. However, most of the shift happens under 100 fs, whereas

the DBVs are excited for several hundred seconds. Thus the majority of the shift is due to solvation.


4.5.5 A higher-lying state

We observe additional features in the far-red regions of the probing window. In the transient absorption

data, the region above 660 nm is dominated by an excited-state absorption feature. The residuals of

the biexponential fit show coherent oscillations centered at about 705 nm. Residual chirp contributes to

frequency-dependent angle to the oscillations. The fit in the time domain at emission wavelength 680

nm shows that several of the same modes that were present in the mid-spectral range are also present

in the excited-state absorption region. The 6 THz, 8 THz, 20 THz and 24 THz modes are all repeatable

within the error of the measurements. It is possible that the other modes present in the middle of

the probing window are present at 705 nm and above as well, but their lower amplitude prevents their

observation above the noise. Similar to the same modes in the middle of the spectral probing window,

these red-region modes dephase quite rapidly within a few hundred femtoseconds.

The 6.5 THz and 8.5 THz modes are the strongest modes in PC577, but they were only low-amplitude

modes for PC645 in a previous two-dimensional spectroscopy study [93]. The data of PC645 indicate

that they originated from excited-state absorption pathways and thus higher-lying excited states. In

PC577, they are strongly present in the first excited state but also appear in the spectral region of the

excited-state absorption component; thus they are also present in higher-lying states.

Interestingly, the oscillations are not simply a continuation of the modes present in the middle of

the probing window, but rather decrease in amplitude and reach a mutual minimum at about 675 nm.

This spectral region coincides with the peak amplitude of the excited-state absorption feature observed

in the transient absorption measurement. If we extend the wave-packet analysis to this region, it is

likely that we are observing vibrational coherences on a higher-lying excited state. This analysis places

the minimum of this higher-lying potential state at about 675 nm. However, it would be difficult to

generate coherences on a higher-lying excited state with our pulse bandwidth and observe them over

the noise. Certainly the decrease in the amplitude of the modes between the stimulated-emission region

and the excited-state absorption region deserves more investigation. The presence of these oscillations

superimposed on the excited-state absorption features provide additional evidence that the coherences

are coupled to the excited state of the protein, and we are indeed observing a wave packet on the

excited-state potential energy surface.

Chapter 5

Transient absorption of

phycoerythrobilin-containing

complexes

5.1 Results on PE545

We also studied the ultrafast dynamics of the phycobiliprotein PE545 from two cryptophyte species using

the transient absorption spectrometer. The goal was to compare these measurements with the results

of the earlier two-dimensional electronic spectroscopy measurements and pump-probe measurements.

With the transient absorption spectrometer we gain a far better signal-to-noise ratio relative to the in

situ pump probe setup, and we obtain the capability to observe a far longer population (τ2) time for

measuring population transfer and the coherent dynamics.

We show a representative transient absorption measurement of PE545 in Fig. 5.1. The spectrum is

composed of positive-amplitude ground-state bleach and stimulated emission features. It is not possible

to directly deconvolve these features because of the overlapping absorption and emission profiles of the

eight constituent bilins. However, much of the positive-amplitude feature is present at signal emission

wavelengths of 570 nm and higher where the ground-state absorption of PE545 is minimal; thus these

features are due to stimulated emission. Interestingly the spectrum of PE545 does not show the strong

negative-amplitude excited-state absorption features that we observe in the spectra of PC577.

The transient absorption spectrum shows that the excited-state population in PE545 red-shifts from

about 545 nm and becomes centered at about 575 nm in a timescale of about a picosecond. This shift

is due to the energy transfer from the PEB chromophores to the lower-energy DBV chromophores in

PE545. The DBVs (spectral emission at about 575 nm) are initially populated because we used a

broadband pulse that was resonant with their electronic transition as well. We expect that narrowband

excitation of solely the PCBs would show a rise of the population of the DBVs within a picosecond.

We extracted a line-out of the PE545 transient absorption data at the emission wavelength of 563

nm (Fig. 5.1). The line-out highlights the exponential decay of the population in this spectral region.

A biexponential fit to the data shows that the dominant decay feature has a lifetime of about 1.3 ps.

This value is representative of the energy transfer rate from the PEBs to the DBVs in PE545.

89

Chapter 5. Transient absorption of phycoerythrobilin-containing complexes 90

Figure 5.1: A representative transient absorption spectrum of PE545 (species 705). (a) The full transientabsorption spectrum, measured from 0 to 4 ps in 4-fs steps. The amplitude of the data corresponds tothe change in the intensity of the probe light after interacting with the pumped sample. Positive featuresrepresent increased signal emission when pumping. (b) A time trace (blue dots) extracted at the emissionwavelength of 563 nm (dashed line in part (a)) with a corresponding biexponential fit function (red line).

In Fig. 5.2 we show a representative transient absorption measurement of PE545 (CCMP 705)

with the background population decay removed. We removed the background population features by

fitting each emission wavelength to independent biexponential decay functions. The residuals show

coherent oscillations although these are much than the oscillations in PC577, with a ∆I/I peak-to-peak

amplitude of 0.6% relative to 1% for PC577. The oscillations also dephase faster than PC577, becoming

indistinguishable from noise at about 1 ps. We also performed transient absorption measurements on

PE545 (CCMP344) however the lower optical density of this sample prevented analysis of the coherent

dynamics above the noise threshold.

We extracted a line-out from the residual data at the emission wavelength of 558 nm, corresponding to

the highest-amplitude coherent features. In Fig. 5.3 we show the average trace with standard deviation

for five independent measurements. The complex beating pattern of the time trace is indicative of

multiple underlying frequencies in the data and is reproducible over five measurements.

To better distinguish the underlying modes, we Fourier-transformed the average time trace and show

the power spectrum of the data in Fig. 5.4. The dominant mode in the power spectrum is centered at

about 15 THz. The power spectrum also reveals an abundance of low-frequency modes (less than 10

THz) which are the cause of the complicated structure of the oscillations in the time domain.

Due to its strength relative to the noise, we focused our analysis on the 15-THz mode. Similar to the

analysis performed for the 8 THz-mode in PC577, we extracted the amplitude and phase profile of the

15-THz mode as a function of the emission wavelength (Fig. 5.5). The data show that the amplitude of

the 15-THz mode decreases in amplitude (nodal structure) at about 575 nm. As well, the phase profile

exhibits a sharp change of close to π-radians at this wavelength. These amplitude and phase profiles

are very similar to the features observed for the 8-THz mode in PC577, but at a different emission

wavelength.


Figure 5.2: The residuals of the transient absorption data of PE545 (species 705) shown in Fig. 5.1aafter removing the background population decay. The plot displays the first picosecond after excitationwhen oscillatory dynamics are evident.

Figure 5.3: Coherent oscillations at the emission wavelength of 558 nm. We display the mean (black line)and standard deviation (blue shaded area) of line-outs from five independent measurements of PE545(species 705).


Figure 5.4: The power spectrum of the Fourier transform of the transient absorption data of PE545(species 705) extracted at 558 nm.

Figure 5.5: The amplitude (red) and phase (blue) of the 15-THz mode of the phycobiliprotein PE545(species 705) extracted from the signal emission wavelength of 558 nm.


5.2 Comparison to 2DES results

The origin of the features of the 15-THz mode in PE545 follows the same formalism as was introduced

for the analysis for PC577. The nodal structure and phase change at an emission wavelength close to

the steady-state fluorescence of the sample are both signatures of an excited-state vibrational coherence.

The steady-state fluorescence of PE545 peaks at about 586 nm. As we observed for the PC577, the nodal

structure is blue-shifted from the steady-state fluorescence maximum during the first few picoseconds

after excitation. Since we can only observe the oscillatory motion for about 1 ps, the Fourier-transform is

essentially giving us an average nodal position for only the first picosecond. Due to the dynamic Stokes

shift, we expect that the node will asymptotically red-shift to 586 nm over hundreds of picoseconds.

The 15-THz mode was also the strongest coherence that we observed with the 2DES and in situ pump

probe measurements of PE545. With those measurements, it was much more difficult to distinguish the

modes from the noise, but these current transient absorption measurements clearly show that this mode

is a pertinent component of the nonlinear signal of PE545. The 2DES analyses (comparing diagonal

peaks to cross peaks and rephasing to nonrephasing pathways) suggested that the 15-THz mode was

due to a vibrational coherence in PE545. The wave packet analysis using the transient absorption data

also indicates that this mode is due to vibrational coherence. It is quite convincing when three different,

independent ultrafast spectroscopic measurements and three different theoretical formalisms all show the

same result. The current transient absorption data provides the additional information of the coherence

being present in the excited-state potential-energy surface of PE545.

5.3 Results on PEB

For further analysis of the oscillatory modes that we observe in the phycobiliprotein PE545, we per-

formed transient absorption measurements of a mutated phycobiliprotein that only expresses a single

phycoerythrobilin chromophore (in this section we will refer to the pigment-protein complex containing

a single phycoerythrobilin as PEB). PE545 is composed of six of these bilin molecules (in addition to two

dihydrobiliverdins) and thus at least some of the oscillatory dynamics that we observe in PE545 should

be evident in measurements of PEB as well. Furthermore, because PEB only contains one chromophore,

it is now more structurally similar to a laser dye than to a multi-chromophoric pigment-protein complex.

Specifically, the one chromophore in PEB is not electronically coupled to any others and thus oscillatory

dynamics must be attributed to vibrational coherences only.

We show a representative transient absorption measurement of PEB on the short timescale (picosec-

onds) in Fig. 5.6. In contrast to the transient absorption spectra of PE545 and PC577 on the same

timescale, the population decay (or bleach recovery) of PEB is symmetric with respect to the emission

wavelength. In order words, the emission of PEB is at the same wavelength over its lifetime. This result

is reasonable because there is only one chromophore being stimulated to emit light; there are not any

other chromophores at shifted spectral coordinates that can emit light. We extracted a line-out from

this short-timescale data at the emission wavelength of 563 nm as we did for the transient absorption

data of PE545. A biexponential fit shows that the predominant decay corresponds to a lifetime of 34

ps. This value contrasts the 1-ps lifetime of the decay in PE545 at the same emission wavelength. Since

the populated phycoerythrobilin chromophore in the complex PEB does not have a lower-energy bilin to

transfer energy (no DBVs), the majority of the excitation in the phycoerythrobilin remains for a much


Figure 5.6: A representative transient-absorption spectrum of PEB — measured from 0 to 4 ps in 4-fssteps — showing coherent dynamics and population dynamics on the short timescale. The amplitude ofthe data corresponds to the change in the intensity of the probe light after interacting with the pumpedsample. Positive features represent increased signal emission when pumping.

longer period of time.

We show a representative transient absorption measurement of PEB on the long timescale (nanosec-

onds) in Fig. 5.7. Similar to the spectrum in Fig. 5.6, this long-timescale spectrum exhibits excited-state

features that decay to the ground state symmetrically. There is not any energy transfer with a corre-

sponding spectral shift of the emitted light because there is only one chromophore. This decay feature

thereby indicates the fluorescence lifetime of PEB since the only pathway for de-excitation of the bilin

is through fluorescence to the ground state. We extracted a trace at the emission wavelength of 563

nm for the long-timescale data and applied a biexponential fit function. We obtain a fit function of

f(t) = 0.023e−0.00092t + 0.0032e−0.000070t (with t in picoseconds), with a coefficient of determination of

0.998. The strongest decay component corresponds to a lifetime of about 1.1 ns.

Following the same procedure as analyses of PC577 and PE545, we fit each the transient absorption

data on the short timescale to a biexponential function independently at each wavelength. We subtracted

these fit functions and plot the residuals in Fig. 5.8. The data show oscillatory dynamics within the

first picosecond after excitation but the amplitude of the dynamics is not much greater than the noise

threshold. The strongest oscillatory features occur at about 560 nm.

We extracted the time trace at the emission wavelength of 561 (Fig. 5.9). Because we performed seven

independent measurements we are able to distinguish the reproducible dynamics from noise. Similar to

the PC577 and PE545, the complicated — yet reproducible — beating pattern in the time domain is a

signature of multiple modes of comparable magnitude in the frequency domain.

We Fourier transformed the average time trace shown in Fig. 5.9 and plot the resultant power

spectrum in Fig. 5.10. The power spectrum reveals the presence of a well-defined mode at 15 THz as

well as at least one mode at about 7 THz in the data. The width of the modes in the frequency domain

are inversely related to their dephasing times in the time domain. These 15-THz mode, which has a


Figure 5.7: A representative transient-absorption spectrum of PEB — measured from 0 to 4 ns in 25-pssteps — showing population dynamics on the long timescale. The amplitude of the data correspondsto the change in the intensity of the probe light after interacting with the pumped sample. Positivefeatures represent increased signal emission when pumping.

Figure 5.8: Representative transient absorption data of PEB after removing the background decayfeatures independently at each emission wavelength. Oscillatory dynamics are centered at the emissionwavelength of 561 nm.


Figure 5.9: Coherent oscillations at the emission wavelength of 561 nm. We display the mean (blackline) and standard deviation (blue shaded area) of line-outs from seven independent measurements ofPEB.

narrow lineshape in the power spectrum accounts for the fast oscillation that lasts for about 1 ps in the

time domain. The 7-THz mode, which has a broad lineshape profile accounts for the slow oscillation that

dephases and becomes indistinguishable from noise in a few hundred femtoseconds in the time domain.

The 15-THz mode is present in both the transient absorption data for PE545 and for PEB. Thus

we conclude that the oscillatory dynamics at this frequency in PE545 must be attributed to the six

constituent phycoerythrobilin chromophores in PE545. Furthermore, as we previously described, any

coherent oscillation in the data of PEB is a signature of vibrational coherence, and thus the 15-THz

mode in PE545 is vibrational in origin. This result corroborates with the other analyses (non-linear

pathways and the wave packet formalism) that previously also concluded that this mode was a vibrational

coherence.


Figure 5.10: The power spectrum of the Fourier transform of the transient absorption data of PEB takenfrom the average time trace extracted at 561 nm from seven measurements.

Chapter 6

Conclusion

We have detailed the analysis of the initial steps of light-harvesting in cryptophyte algae using ultrafast

spectroscopy. In particular, we have investigated the pigment-protein complexes (PE545 and PC577)

of three different species of cryptophytes using two-dimensional electronic spectroscopy and frequency-

resolved transient absorption spectroscopy. To improve the signal quality relative to noise, we developed

a transient absorption spectrometer. Through a combination of fast acquistion rates and balanced

detection, the instrument achieves high temporal resolution and broad spectral resolution. We have

described in detail the setup and experimental realization of the spectrometer as well as its capability

of suppressing noise present in ultrafast laser systems. The instrument is critical for investigating the

spectral dependence of transiently emitted non-linear optical signals.

We have described the application of the spectrometer to the study of a photosynthetic pigment-

protein complex, PC577. The complex exhibits vibrational coherence. We analyzed the wave packet

dynamics on the potential-energy surfaces. We have documented and described the evidence for the

coherent oscillations being present on the excited-state potential-energy surface of the protein. The

oscillations are coupled to the viewing window of the dynamic Stokes shift that occurs on an ultrafast

timescale. The oscillations are also found in the spectral region of excited-state absorption to a higher-

lying state of the protein. These measurements show that vibrational coherence is perhaps coupled to

the energy transfer of PC577 within their dephasing lifetime.

We also analyzed the coherent dynamics of the phycobiliprotein PE545 using both two-dimensional

spectroscopy and transient absorption spectroscopy. Both measurements — combined with third-order

pathways analysis and the wave packet formalism — strongly suggest that the dominant coherence in

PE545 is due to a vibrational superposition in the excited state of the molecule. Using PE545 as an exam-

ple, we have demonstrated experimentally several different methods to distinguish vibrational coherence

from electronic coherence. It seems likely that similar thorough analyses using multiple spectroscopic

techniques will be required to convincingly prove the nature of coherent oscillations in photosynthetic

light-harvesting complexes.

There is a need to continue to investigate not just the presence of coherent oscillations but also

their spectral dependence, amplitude, and phase. These properties will give insight into the nature of

the potential energy surfaces of the sample being studied. This idea may be useful for differentiating

between electronic and vibrational coherences in future studies. Our spectrometer is useful for analysis

of the nature of the coherences governing the signals present in photosynthetic protein samples. The

98

Chapter 6. Conclusion 99

techniques described here could also be applied to other ultrafast spectroscopies to improve the dynamic

range and quality of the data.

The main goal was to obtain quantitative data of high quality specifically describing the ultrafast

timescale (hundreds of femtoseconds to picoseconds) when both population and coherent dynamics are

active. Energy transfer is a complicated process with many possible mechanisms of realization. Pho-

tosynthetic organisms probably combine multiple energy transfer processes because in the biological

context, extreme limits are rarely relevant. Many of the current (sometimes theoretical) designs for solar

cells prove adequate when following the guidelines (chromophore placement and molecular scaffolding)

of an extreme regime, however these constructs are often only beneficial for accomplishing a single goal

in the laboratory setting. Their successful transformation to the real-world setting will require compro-

mises to satisfy other industrial, economical and environmental constraints. Photosynthetic organisms

serve as the ultimate model for light harvesting in the real world.

Bibliography

[1] A picosecond time-resolved fluorescence study on the biliprotein, phycocyanin 645. Biochim. et

Biophysica Acta (BBA) - Bioenergetics, 1059.

[2] Secuk Akturk, Xun Gu, Mark Kimmel, and Rick Trebino. Extremely simple single-prism

ultrashort-pulse compressor. Opt. Express, 14(21):10101–10108, 2006.

[3] Kevin E. H. Anderson, Samuel L. Sewall, Ryan R. Cooney, and Patanjali Kambhampati. Noise

analysis and noise reduction methods in kilohertz pump-probe experiments. Rev. Sci. Instrum.,

78:073101, 2007.

[4] Michael R. Armstrong, Peter Plachta, Evgueni A. Ponomarev, and R. J. D. Miller. Versatile

7-fs optical parametric pulse generation and compression by use of adaptive optics. Opt. Lett.,

26:1152–1154, 2001.

[5] Uri Banin, Amir Waldman, and Sanford Ruhman. Ultrafast photodissociation of i3– in solution:

Direct observation of coherent product vibrations. J. Chem. Phys., 96:2416, 1992.

[6] C J Bardeen, Q Wang, and C V Shank. Selective excitation of vibrational wave packet motion

using chirped pulses. Phys. Rev. Lett., 75:3410, 1995.

[7] C. J. Bardeen, Q. Wang, and C. V. Shank. Femtosecond chirped pulse excitation of vibrational

wave packets in ld690 and bacteriorhodopsin. J. Phys. Chem. A, 102:2759–2766, 1998.

[8] PC Becker, HL Fragnito, JY Bigot, CH Brito Cruz, RL Fork, and CV Shank. Femtosecond photon

echoes from molecules in solution. Phys. Rev. Lett., 63:505–507, 1989.

[9] Robert W. Boyd. Nonlinear Optics. Academic Press, 2003.

[10] Markus Braun, Constanze Sobotta, Regina Dur, Horst Pulvermacher, and Stephan Malkmus.

Analysis of wave packet motion in frequency and time domain: oxazine 1. J. Phys. Chem. A,

110:9793–9800, 2006.

[11] Neil A Campbell and Jane B Reece. Biology, (2005)., volume 98. Benjamin Cumming’s Publishing

Company., 1984.

[12] M. Chachisvilis, T. Pullerits, M. R. Jones, C. N. Hunter, and V. Sundstrom. Vibrational dynamics

in the light-harvesting complexes of the photosynthetic bacterium Rhodobacter sphaeroides. Chem.

Phys. Lett., 224:345–351, 1994.

100

Bibliography 101

[13] J. Chesnoy and A. Mokhtari. Resonant impulsive-stimulated raman scattering on malachite green.

Phys. Rev. A, 38(7):3566–3576, 1988.

[14] Niklas Christensson, Franz Milota, Jurgen Hauer, Jaroslaw Sperling, O. Bixner, Alexandra

Nemeth, and Harald F. Kauffmann. High frequency vibrational modulations in two-dimensional

electronic spectra and their resemblance to electronic coherence signatures. J. Phys. Chem. B,

115:5383–5391, 2011.

[15] Richard J Cogdell, Andrew Gall, and Jurgen Kohler. The architecture and function of the light-

harvesting apparatus of purple bacteria: from single molecules to in vivo membranes. Quarterly

reviews of biophysics, 39(03):227–324, 2006.

[16] Elisabetta Collini, Carles Curutchet, Tihana Mirkovic, and Gregory D Scholes. Electronic Energy

Transfer in Photosynthetic Antenna Systems. Springer, 2009.

[17] Elisabetta Collini, Cathy Y Wong, Krystyna E Wilk, Paul M G Curmi, Paul Brumer, and Gre-

gory D Scholes. Coherently wired light-harvesting in photosynthetic marine algae at ambient

temperature. Nature, 463(7281):644–7, 2010.

[18] George W Crabtree and Nathan S Lewis. Solar energy conversion. Physics today, 60(3):37–42,

2007.

[19] S. De Silvestri, J. G. Fujimoto, E. P. Ippen, E. B. Gamble, L. R. Williams, and K. A. Nelson. Fem-

tosecond time-resolved measurements of optic phonon dephasing by impulsive stimulated raman

scattering in alpha-perylene crystals from 20 to 300 k. Chem. Phys. Lett., 116:146, 1985.

[20] SL Dexheimer, Q Wang, LA Peteanu, WT Pollard, RA Mathies, and CV Shank. Femtosecond

impulsive excitation of nonstationary vibrational states in bacteriorhodopsin. Chem. Phys. Lett.,

188(1):61–66, 1992.

[21] William M Diffey, Bradley J Homoelle, Maurice D Edington, and Warren F Beck. Excited-state

vibrational coherence and anisotropy decay in the bacteriochlorophyll a dimer protein b820. J.

Phys. Chem. B, 102(15):2776–2786, 1998.

[22] Rayomond Dinshaw. Spectroscopic investigations of the photophysics of cryptophyte light-

harvesting. Master’s thesis, University of Toronto, Toronto, 2012.

[23] J. Dobler, W. Zinth, and W. Kaiser. Excited-state reaction dynamics of bacteriorhodopsin studied

by femtosecond spectroscopy. Chem. Phys. Lett., 144(2):215, 1988.

[24] Christophe Dorrer, Nadia Belabus, Jean-Pierre Likforman, and Manuel Joffre. Spectral resolution

and sampling issues in fourier-transform spectral interferometry. J. Opt. Soc. Am. B, 17(10):1795–

1802, 2000.

[25] Alexander B. Doust, Krystyna E. Wilk, Paul M G Curmi, and Gregory D. Scholes. The photo-

physics of cryptophyte light-harvesting. J. Photochem. Photobio. A, 184:1–17, 2006.

[26] Juan Du, Takahiro Teramoto, Kazuaki Nakata, Eiji Tokunaga, and Takayoshi Kobayashi. Real-

time vibrational dynamics in chlorophyll a studied with a few-cycle pulse laser. Biophys. J.,

101(4):995 – 1003, 2011.

Bibliography 102

[27] Gregory S Engel, Tessa R Calhoun, Elizabeth L Read, Tae-Kyu Ahn, Tomas Mancal, Yuan-Chung

Cheng, Robert E Blankenship, and Graham R Fleming. Evidence for wavelike energy transfer

through quantum coherence in photosynthetic systems. Nature, 446(7137):782–6, 2007.

[28] Paul G Falkowski, Miriam E Katz, Andrew H Knoll, Antonietta Quigg, John A Raven, Os-

car Schofield, and FJR Taylor. The evolution of modern eukaryotic phytoplankton. Science,

305(5682):354–360, 2004.

[29] R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank. Compression of optical pulses to six

femtoseconds by using cubic phase compensation. Opt. Lett., 12(7):483–485, 1987.

[30] R. L. Fork, B. I. Greene, and C. V. Shank. Generation of optical pulses shorter than 0.1 psec by

colliding pulse mode locking. Appl. Phys. Lett., 38:671, 1981.

[31] H. L. Fragnito, J.-Y. Bigot, P. C. Becker, and C. V. Shank. Evolution of the vibronic absorption

spectrum in a molecule following impulsive excitation with a 6 fs optical pulse. Chem. Phys. Lett.,

160(2):101–104, 1989.

[32] Claudiu C Gradinaru, Andy A Pascal, Frank van Mourik, Bruno Robert, Peter Horton, Rienk van

Grondelle, and Herbert van Amerongen. Ultrafast evolution of the excited states in the chloro-

phyll a/b complex cp29 from green plants studied by energy-selective pump-probe spectroscopy.

Biochemistry, 37(4):1143–1149, 1998.

[33] B.D. Guenther, editor. Chemical applications of lasers — Pump and probe studies of femtosecond

kinetics. Elsevier, 2005.

[34] Serap Gunes, Helmut Neugebauer, and Niyazi Serdar Sariciftci. Conjugated polymer-based organic

solar cells. Chemical reviews, 107(4):1324–1338, 2007.

[35] M. L. Horng, J. A. Gardecki, A. Papazyan, and M. Maroncelli. Subpicosecond measurements of

polar solvation dynamics: coumarin 153 revisited. J. Phys. Chem, 99:17311–17337, 1995.

[36] John D. Hybl, Allison Albrecht Ferro, and David M. Jonas. Two-dimensional fourier transform

electronic spectroscopy. J. Chem. Phys., 115(14):6606–6622, 2001.

[37] Jeong-Hyeok Im, Chang-Ryul Lee, Jin-Wook Lee, Sang-Won Park, and Nam-Gyu Park. 6.5%

efficient perovskite quantum-dot-sensitized solar cell. Nanoscale, 3(10):4088–4093, 2011.

[38] R. Jimenez, G. R. Fleming, P. V. Kumar, and M. Maroncelli. Femtosecond solvation dynamics of

water. Nature, 369:471–473, 1994.

[39] David M Jonas. Two-dimensional femtosecond spectroscopy. Ann. Rev. Phys. Chem., 54:425–63,

2003.

[40] David M. Jonas and Graham R. Fleming. Vibrationally abrupt pulses in pump-probe spectroscopy,

page 225. Chemistry for the 21st Century. Blackwell Scientific Publications, Oxford, 1995.

[41] David M Jonas, Matthew J Lang, Yutaka Nagasawa, Taiha Joo, and Graham R Fleming. Pump-

probe polarization anisotropy study of femtosecond energy transfer within the photosynthetic

reaction center of rhodobacter sphaeroides r26. J. Phys. Chem., 100(30):12660–12673, 1996.

Bibliography 103

[42] Anat Kahan, Omer Nahmias, Noga Friedman, Mordechai Sheves, and Sanford Ruhman. Following

photoinduced dynamics in bacteriorhodopsin with 7-fs impulsive vibrational spectroscopy. J. Am.

Chem. Soc., 129:537–546, 2007.

[43] Prashant V Kamat. Quantum dot solar cells. the next big thing in photovoltaics. The Journal of

Physical Chemistry Letters, 4(6):908–918, 2013.

[44] Hideaki Kano, Takashi Saito, and Takayoshi Kobayashi. Observation of herzberg-teller-type wave

packet motion in porphyrin j-aggregates studied by sub-5-fs spectroscopy. J. Phys. Chem. A, 2001.

[45] Chul Hoon Kim and Taiha Joo. Coherent excited state intramolecular proton transfer probed by

time-solved fluorescence. Phys. Chem. Chem. Phys., 11:10266–10269, 2009.

[46] Hui-Seon Kim, Jin-Wook Lee, Natalia Yantara, Pablo P Boix, Sneha A Kulkarni, Subodh G

Mhaisalkar, Michael Gratzel, and Nam-Gyu Park. High efficiency solid state sensitized solar cell

based on submicrometer rutile tio2 nanorod and ch3nh3pbi3 perovskite sensitizer. Nano letters,

2013.

[47] So Young Kim, Myeongkee Park, Kyoung Chul Ko, Jin Yong Lee, and Taiha Joo. Coherent nuclear

wave packets generated by ultrafast intramolecular charge-transfer reaction. J. Phys. Chem. Lett.,

3:2761–2766, 2012.

[48] Victor I Klimov and Duncan W McBranch. Femtosecond high-sensitivity, chirp-free transient

absorption spectroscopy using kilohertz lasers. Opt. Lett., 23:277, 1997.

[49] Akihiro Kojima, Kenjiro Teshima, Yasuo Shirai, and Tsutomu Miyasaka. Organometal halide

perovskites as visible-light sensitizers for photovoltaic cells. Journal of the American Chemical

Society, 131(17):6050–6051, 2009.

[50] Jan Philip Kraack, Tiago Buckup, Norbert Hampp, and Marcus Motzkus. Ground- and excited-

state vibrational coherence dynamics in bacteriorhodopsin probed with degenerate four-wave-

mixing experiments. ChemPhysChem, 12:1851–1859, 2011.

[51] Brent P Krueger, Gregory D Scholes, and Graham R Fleming. Calculation of couplings and energy-

transfer pathways between the pigments of lh2 by the ab initio transition density cube method.

The Journal of Physical Chemistry B, 102(27):5378–5386, 1998.

[52] AWD Larkum. Limitations and prospects of natural photosynthesis for bioenergy production.

Current opinion in biotechnology, 21(3):271–276, 2010.

[53] Michael M Lee, Joel Teuscher, Tsutomu Miyasaka, Takurou N Murakami, and Henry J Snaith.

Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science,

338(6107):643–647, 2012.

[54] L. Lepetit, G. Cheriaux, and M. Joffre. Linear techniques of phase measurement by femtosecond

spectral interferometry for application in spectroscopy. J. Opt. Soc. Am. B, 12(12):2467–2474,

1995.

[55] Kristin L M Lewis and Jennifer P Ogilvie. Probing photosynthetic energy and charge transfer with

two-dimensional electronic spectroscopy. J. Phys. Chem. Lett., 3:503–510, 2012.

Bibliography 104

[56] Su Lin, Aileen KW Taguchi, and Neal W Woodbury. Excitation wavelength dependence of energy

transfer and charge separation in reaction centers from rhodobacter sphaeroides: evidence for

adiabatic electron transfer. J. Phys. Chem., 100(42):17067–17078, 1996.

[57] Robert Livingston. Intermolecular transfer of electronic excitation. The Journal of Physical Chem-

istry, 61(7):860–864, 1957.

[58] Larry Luer, Christophe Gadermaier, Jared Crochet, Tobias Hertel, Daniele Brida, and Guglielmo

Lanzani. Coherent phonon dynamics in semiconducting carbon nanotubes: a quantitative study

of electron-phonon coupling. Phys. Rev. Lett., 102:127401, 2009.

[59] Stephan Malkmus, Regina Durr, Constanze Sobotta, Horst Pulvermacher, Wolfgang Zinth, and

Markus Braun. Chirp dependence of wave packet motion in oxazine 1. J. Phys. Chem. A,

109:10488–10492, 2005.

[60] Tomas Mancal and Leonas Valkunas. Exciton dynamics in photosynthetic complexes: excitation

by coherent and incoherent light. New Journal of Physics, 12:065044, 2010.

[61] A. Marin, Alexander B. Doust, Gregory D. Scholes, Krystyna E. Wilk, Paul M G Curmi, IH van

Stokkum, and R. van Grondelle. Flow of excitation energy in the cryptophyte light-harvesting

antenna phycocyanin 645. Biophysical Journal, 101(4):1004–1013, 2011.

[62] Mark Maroncelli and Graham R Fleming. Picosecond solvation dynamics of coumarin 153: The

importance of molecular aspects of solvation. J. Chem. Phys., 86:6221, 1987.

[63] Volkhard May and Oliver Kuhn. Charge and Energy Transfer Dynamics in Molecular Systems.

Wiley-VCH, 2004.

[64] U Megerle, I Pugliesi, C Schriever, C F Sailer, and E Riedle. Sub-50fs broadband absorption

spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on

solid ground. Appl. Phys. B, 96:215–231, 2009.

[65] Tihana Mirkovic, Alexander B. Doust, Jeongho Kim, Krystyna E. Wilk, Carles Curutchet,

Benedetta Mennucci, Roberto Cammi, Paul M G Curmi, and Gregory D. Scholes. Ultrafast light

harvesting dynamics in the cryptophyte phyocyanin 645. Photochem. Photobiol. Sci., 6:964–975,

2007.

[66] Alexandra Nemeth, Franz Milota, Tomas Mancal, Vladimir Lukes, Jurgen Hauer, Harald F. Kauff-

mann, and Jaroslaw Sperling. Vibrational wave packet induced oscillations in two-dimensional

electronic spectra. i. experiments. J. Chem. Phys., 132:184514, 2010.

[67] Vladimir I Novoderezhkin, Alexander B Doust, Carles Curutchet, Gregory D Scholes, and Rienk

van Grondelle. Excitation dynamics in phycoerythrin 545: modeling of steady-state spectra and

transient absorption with modified redfield theory. Biophysical journal, 99(2):344–352, 2010.

[68] Alexandra Olaya-Castro and Gregory D Scholes. Energy transfer from forster–dexter theory to

quantum coherent light-harvesting. International Reviews in Physical Chemistry, 30(1):49–77,

2011.

Bibliography 105

[69] Brian Oregan and Michael Graatzel. A low-cost, high-efficiency solar cell based on dye-sensitized.

Nature, 353:24, 1991.

[70] Gitt Panitchayangkoon, Dugan Hayes, Kelly A. Fransted, Justin R. Caram, Elad Harel, Jianzhong

Wen, Robert E. Blankenship, and Gregory S Engel. Long-lived quantum coherence in photosyn-

thetic complexes at physiological temperature. Proc. Natl. Acad. Sci. U.S.A., 107:12766–12770,

2010.

[71] VPS Perera, PKDDP Pitigala, PVV Jayaweera, KMP Bandaranayake, and K Tennakone. Dye-

sensitized solid-state photovoltaic cells based on dye multilayer-semiconductor nanostructures. The

Journal of Physical Chemistry B, 107(50):13758–13761, 2003.

[72] W. T. Pollard, H. L. Fragnito, Bigot J.-Y., C. V. Shank, and Richard A. Mathies. Quantum-

mechanical theory for 6 fs dynamic absorption spectroscopy and its application to nile blue. Chem.

Phys. Lett., 168(3,4):239–245, 1990.

[73] W. Thomas Pollard, Susan L. Dexheimer, Qing Wang, Linda A. Peteanu, Charles V. Shank,

and Richard A. Mathies. Theory of dynamic absorption spectroscopy of nonstationary states. 4.

application fo 12-fs resonant impulsive raman spectroscopy of bacteriorhodopsin. J. Phys. Chem.,

96:6147–6158, 1992.

[74] Dario Polli, Larry Luer, and Giulio Cerullo. High-time-resolution pump-probe system with broad-

band detection for the study of time-domain vibrational dynamics. Rev. Sci. Instr., 78:103108,

2007.

[75] VI Prokhorenko, AR Holzwarth, FR Nowak, and TJ Aartsma. Growing-in of optical coherence in

the fmo antenna complexes §. J. Phys. Chem. B, 106(38):9923–9933, 2002.

[76] Thomas Renger. Theory of excitation energy transfer: from structure to function. Photosynthesis

research, 102(2-3):471–485, 2009.

[77] Todd S. Rose, Mark J. Rosker, and Ahmed H. Zewail. Femtosecond realtime observation of wave

packet oscillations (resonance) in dissociation reactions. J. Chem. Phys., 88:6672, 1988.

[78] M. J. Rosker, F. W. Wise, and C. L. Tang. Femtosecond relaxation dynamics of large molecules.

Phys. Rev. Lett., 57:321, 1986.

[79] S. Ruhman, A. G. Joly, and Keith A. Nelson. Time-resolved observations of coherent molecular

vibrational motion and the general occurrence of impulsive stimulated scattering. J. Chem. Phys.,

86:6563, 1987.

[80] Anunay Samanta. Dynamic stokes shift and excitation wavelength dependent fluorescence of dipo-

lar molecules in room temperature ionic liquids. J. Phys. Chem. B, 110:13704–13716, 2006.

[81] Sergei Savikhin, Daniel R. Buck, and Walter S. Struve. Oscillating anisotropies in a bacteriochloro-

phyll protein: Evidence for quantum beating between exciton levels. Chem. Phys., 223:303–312,

1997.

[82] Sergei Savikhin, Yinwen Zhu, Lin Su, Robert E. Blankenship, and Walter S. Struve. Femtosec-

ond spectroscopy of chlorosome antennas from the green photosynthetic bacterium Chloroflexus

aurantiacus. J. Phys. Chem., 98:10322–10334, 1994.

Bibliography 106

[83] N.F. Scherer, L. D. Ziegler, and G. R. Fleming. Heterodyned-detected time-domain measurement

of i2 predissociation and vibrational dynamics in solution. J. Chem. Phys., 96(7):5544, 1992.

[84] Gregory D Scholes. Long-range resonance energy transfer in molecular systems. Annual review of

physical chemistry, 54(1):57–87, 2003.

[85] Gregory D Scholes. Quantum-coherent electronic energy transfer: Did nature think of it first? J.

Phys. Chem. Lett., 1(1):2–8, 2010.

[86] Gregory D Scholes and Graham R Fleming. Energy transfer and photosynthetic light harvesting.

Adv. Chem. Phys., 132:57–130, 2005.

[87] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro, and R. van Grondelle. Lessons

from nature about solar light harvesting. Nature Chemistry, 3:763–774, 2011.

[88] C Schriever, S Lochbrunner, E Riedle, and D J Nesbitt. Ultrasensitive ultraviolet-visible 20fs

absorption spectroscopy of low vapor pressure molecules in the gas phase. Rev. Sci. Instrum.,

79:013107, 2008.

[89] D. E. Spence, P. N. Kean, and W. Sibbett. 60-fsec pulse generation from a self-mode-locked

ti:sapphire laser. Opt. Lett., 16:42, 1991.

[90] Gerhard Stock and Wolfgang Domcke. Detection of ultrafast molecular-excited-state dynamics

with time- and frequency-resolved pump-probe spectroscopy. Phys. Rev. A, 45:3032, 1992.

[91] J Strumpfer, Melih Sener, and Klaus Schulten. How quantum coherence assists photosynthetic

light-harvesting. The journal of physical chemistry letters, 3(4):536–542, 2012.

[92] Villy Sundstrom, Tonu Pullerits, and R. van Grondelle. Photosynthetic light-harvesting: recon-

ciling dynamics and structure of purple bacterial lh2 reveals function of photosynthetic unit. J.

Phys. Chem. B, 103(13):2327–2346, 1999.

[93] Daniel B. Turner, Rayomond Dinshaw, Kyung-Koo Lee, Michael S. Belsley, Krystyna E. Wilk,

Paul M G Curmi, and Gregory D. Scholes. Quantitative investigations of quantum coherence for

a light-harvesting protein at conditions simulating photosynthesis. Phys. Chem. Chem. Phys.,

14:4857–4874, 2012.

[94] Daniel B Turner, Katherine W Stone, Kenan Gundogdu, and Keith A Nelson. Invited article:

The coherent optical laser beam recombination technique (colbert) spectrometer: coherent multi-

dimensional spectroscopy made easier. Rev. Sci. Instr., 82(8):081301, 2011.

[95] Daniel B. Turner, Krystyna E Wilk, Paul M G Curmi, and Gregory D. Scholes. Comparison

of electronic and vibrational coherence measured by two-dimensional electronic spectroscopy. J.

Phys. Chem. Lett., 2:1904–1911, 2011.

[96] B. Wieb van der Meer. Forster theory. 2012.

[97] Chantal D. van der Weij-De Wit, Alexander B. Doust, Ivo H. M. van Stokkum, Jan P. Dekker,

Krystyna E. Wilk, Paul M G Curmi, Gregory D. Scholes, and R. van Grondelle. How energy funnels

from the phycoerythrin antenna complex to photosystem i and photosystem ii in cryptophyte

rhodomonas cs24 cells. J. Phys. Chem. B, 100:25066–25073, 2006.

Bibliography 107

[98] Rienk van Grondelle and Vladimir I. Novoderezhkin. Spectroscopy and dynamics of excitation

transfer and trapping in purple bacteria. 2009.

[99] E. Vogel, A. Gbureck, and W. Kiefer. Vibrational spectroscopic studies on the dyes cresyl violet

and coumarin 152. J. Mol. Structure, 550-551:177–190, 2000.

[100] Marten H. Vos, Michael R. Jones, C. Neil Hunter, Jacques Breton, Jean-Christophe Lambry, and

Jean-Louis Martin. Coherent dynamics during the primary electron-transfer reaction in membrane-

bound reaction centers of Rhodobacter sphaeroides. Biochemistry, 33:6750–6757, 1994.

[101] Marten H. Vos, Jean-Christophe Lambry, Steven J. Robles, Douglas C. Youvan, Jacques Breton,

and Jean-Louis Martin. Direct observation of vibrational coherence in bacterial reaction centers

using femtosecond absorption spectroscopy. Proc. Natl. Acad. Sci. USA, 88:8885–8889, 1991.

[102] Marten H. Vos and Jean-Louis Martin. Femtosecond processes in proteins. Biochim. Biophys Acta,

1411:1–20, 1999.

[103] Marten H. Vos, Fabrice Rappaport, Jean-Christophe Lambry, Jacques Breton, and Jean-Louis

Martin. Visulization of coherent nuclear motion in a membrane protein by femtosecond spec-

troscopy. Nature, 363:320–325, 1993.

[104] Amir Wand, Shimshon Kallush, Ofir Shoshanim, Oshrat Bismuth, Ronnie Kosloff, and Sanford

Ruhman. Chirp effects on impulsive vibrational spectroscopy: a multimode perspective. Phys.

Chem. Chem. Phys, 12:2149, 2010.

[105] AM Weiner, DE Leaird, Gary P Wiederrecht, and Keith A Nelson. Femtosecond pulse sequences

used for optical manipulation of molecular motion. Science, 247(4948):1317–1319, 1990.

[106] D. E. Wemmer, G. J. Wedemayer, and A. N. Glazer. J. Biol. Chem., 268:1658–1669, 1993.

[107] T. Wilhelm, J. Piel, and E. Riedle. Sub-20-fs pulses tunable across the visible from a blue-pumped

single-pass noncollinear parametric converter. Opt. Lett., 22(19):1494–1497, 1997.

[108] Yi Jing Yan and Shaul Mukamel. Femtosecond pump-probe spectroscopy of polyatomic molecules

in condensed phases. Phys. Rev. A, 41(11):6485, 1990.

[109] Michael K. Yetzbacher, Nadia Belabus, Katherine A. Kitney, and David M. Jonas. Propagation,

beam geometry, and detection distortions of peak shapes in two-dimensional fourier transform

spectra. J. Chem. Phys., 126:044511, 2007.

[110] HJ Zeiger, J Vidal, TK Cheng, EP Ippen, G Dresselhaus, and MS Dresselhaus. Theory for

displacive excitation of coherent phonons. Phys. Rev. B, 45(2):768, 1992.

[111] Ahmed H. Zewail. Femtochemistry: atomic-scale dynamics of the chemical bond. J. Phys. Chem.

A, 104:5660–5694, 2000.

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