Coherent control of chemical reactions. II

Jennifer L. Herek FOM-Institute for Atomic and Molecular Physics [AMOLF]

Amsterdam, The Netherlandshttp://www.amolf.nlJ.Herek@amolf.nl

Control of chemical reactions

General goal: Maximize yield of desired products and suppress formation of unwanted byproducts

Lasers “Bond-selective” chemistry?

Can coherent light be used for selective bond activation and cleavage?

The concept:• Choose the light frequency to be in resonance

with the vibrational frequency of the bond to be broken

• Resonant activation of the proper vibrational mode leads to selective dissociation

Bond-selective chemistry in H + HOD

OD

OH

OD

OH

OD

OH

H2 + ODH + HOD(ν)

HD + OH

F. Crim, J. Chem. Phys. (1990) 92:6333

Excite one bond… …but soon, the entire molecule is vibrating.

Excite one bond… …but soon, the entire molecule is vibrating.

The problem: IVR

• Vibrational motion is coupled to many atoms within the molecule

• Intramolecular vibrational redistribution (IVR) leads to a loss of selective excitation and “heating” of the molecule

• Works only for small, prototype molecules

Coherent controlInterfering for the good of a chemical reaction

The difference:

• Exploits a broad range of quantum interference effects

• Many different feasible schemesFrequency domainTime domain

How is it possible that light can control a reaction?

Pulse timing controlAB + C

AC + BABC

Reactant Product

Reaction coordinateC

B

A

C

B

A

pump

C

B

A

C

B

A

dump

excitedstate

Pote

ntia

l Ene

rgy

groundstate

Tannor, D. J., Kosloff, R. & Rice, S. A. Chem. Phys. 85, 5805-5820 (1986)

• Femtosecond probing of reactions

• Femtosecond control from the transition state region

• Reaction channels

• Population control

• Channel switching

• Magnitude of depletion

• Control vs. probe

Control of dissociation pathways in NaI

Herek, J. L., Materny, A. & Zewail, A. H. Chem. Phys. Lett. 228, 15-21 (1994)

Multiple-path interference control

Excite the desired product channel via two different pathways:

Path 1Path 2

Ground state

Target state

Probability (P) of forming a product:P = P1 + P2 + P12 Interference term

depends on phase of optical fields

Brumer, P. & Shapiro, M. Chem. Phys. Lett. 126, 541-546 (1986)

Tuning the phase difference

Rice, S. A., Nature 409, 422-426 (2001)

STIRAPSTImulated Raman Adiabatic Passage

reactant

product

intermediate

Stokespump

1 >

2 >

3 >

• “Counterintuitive” pulse sequence: Stokes, then Pump• Stokes pulse creates coherent superposition of two initially

unpopulated states

• No population transfer to intermediate state; direct transfer to product

Gaubatz, U., Rudecki, P., Becker, M. Schiemann, S., Külz, M. & Bergmann, K. Chem. Phys. Lett. 149, 463 (1988)

STIRAP applied to SO2 molecules

Stokes laser on

Stokes laser off

coupling schemeenhancement

Counterintuitive pulse sequence: signature of STIRAP

transfer efficiency vs. pulse delay

Halfmann, T. & Bergmann, K. J. Chem. Phys. 104, 7068-7072 (1996)

Combining these concepts:For a given target distribution of photoproducts and the quantum mechanical equations of motion, what electric field is required to guide the temporal evolution of the system appropriately?

OCT: Optimal Control TheoryElectric field design

Hamiltonianrequired!

A. Peirce, M. Dahleh & H. Rabitz, Phys. Rev. A, 37, 4950 (1988)

OCT methodology• Forward/backward propagations of wavepackets Ψ(t) or

density matrices ρ(t) from initial to final states and vice versa

• Optimization algorithm selects best fields ε(ti)

Inherent difficulties with OCT...• Need potential energy surfaces!

Rarely known over all range of nuclear separations necessary to describe a reaction

• Search space too large to be scanned completely

• Predicted fields difficult to reproduce accurately enough under laboratory conditions

Experimental approach“Teaching lasers to control molecules”

Learningalgorithm

Detector

Molecule

modified E(t)

pump E(t)

probe

result

Laser,pulse shaper

Objective

HamiltonianNOT required!

R. S. Judson & H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992)

The molecular view• A molecule knows its own Hamiltonian

• Given ε(t), a molecule solves rapidly!ih = HΨ∂Ψ∂t

•No prior knowledge of PESs needed

•Broadly applicable (not limited to molecular systems)•Automated pulse compression•Control of 2-photon transitions in atoms•Shaping of Rydberg wavepackets•Optimization of high-harmonic generation•Control of ultrafast semiconductor nonlinearities•Laser cooling

•Laboratory conditions accounted for automatically

Advantages

Advantage of fs lasers

Ground state

Target state

Broadband!

• allows for manipulation of many pathways to provide control over complex dynamics

• allows different control mechanisms: phase, timing, etc.

pump dumppump dumppumppump dump

Path 1Path 2

Path 1Path 2

Stokespump

Experimental realizationFeedback-driven adaptive femtosecond pulse shaping

H. Rabitz, R. de Vivie-Riedle, M. Motzkus & K.-L. Kompa, Science 288: 824-828 (2000)

Femtosecond pulse shaping

A pulse is defined by its intensity and phase in either the time or frequency domain.

( ) ( ) ( )i tE t I t e φ−= ( ) ( ) ( )iE S e ϕ ωω ω −=%

( ) ( ) ( )out inE t h t E t=fs pulses too fast

Modulation in time domain:

( ) ( ) ( )out inE H Eω ω ω=% %Modulation in frequency space:frequency disperse the pulse in space and createa spatially varying transmission and phase delay

Shaped pulse = “optical melody”

A musical score is a plot of frequency vs. time:fr

eque

ncy

time

Transform-limited pulse:chord

Shaped pulse:melody

“Ordinary” femtosecond laser pulses

“Shaped” femtosecond laser pulses

The temporal shape of the laser pulse can be changed by varying the phases between its frequency components

Acoustic analogy

-1 0 1-1

1

Ampl

itude

[A.U

.]

Time [s ]200 300 4000

1

Inte

nsity

[A.U

.]

Frequency [Hz]

2 frequencies

-1 0 1-1

1

Ampl

itude

[A.U

.]

Time [s ]200 300 4000

1

Inte

nsity

[A.U

.]

Frequency [Hz]

4 frequencies

-1 0 1-1

1

Ampl

itude

[A.U

.]

Time [s ]200 300 4000

1

Inte

nsity

[A.U

.]

Frequency [Hz]

16 frequencies

-1 0 1-1

1Am

plitu

de [A

.U.]

Time [s ]200 300 4000

1

Inte

nsity

[A.U

.]

Frequency [Hz]

Many frequencies

K.A. Nelson and J.C. Vaughan, MIT

Linear phase modulation

I(ω)φ(ω)

I(ω)

φ(ω)

“V” & quadratic phase modulation

I(ω)

φ(ω)

I(ω) φ(ω)

Cubic or periodic phase modulation

I(ω)

φ(ω)

I(ω)

φ(ω)

Methods of pulse shaping

Liquid-crystal Acousto-optic Deformable mirror

Individually-addressed pixels can vary phase or amplitude

Movable elements allow smooth phase variationModulated rf field

creates an amplitude-and phase-dependent grating

A. M. Weiner, Rev. Sci. Inst. 71, 1929 (2000)

Liquid crystal spatial light modulator

Dual stack—phase & amplitude control

State-of-the-art:2 x 640 elements = 1280 adjustable parameters!!

G. Gerber

Dual stack LC-SLM

Shaped pulses with LC-SLMs

The learning loop

Evolutionary algorithms

Survival of the fittest

o oo o

Metaphors of biological evolution

• A breeding population, in which those individuals (pulses) that are more “fit” have a higher probability of spawning offspring and passing their genetic information to succeeding generations.

• Genetic makeup of the offspring is a mixture (characterized by a crossover rate) of the genetic makeup of the parents.

• Genetic material is occasionally altered by mutation, thereby generating offspring that can be more or less “fit” than they would have been otherwise.

• Cloning is possible.

Evolutionary operators

Multiple-point crossover

Single-point crossover

Double-point crossover

Intermediary recombination

Recombination

Mutation

Cloning

Evolutionary algorithm example

First Generation

Parameter 1

1.The first generation evenly samples the parameter space. From this we select the parents for the next generation.

2.The second generation is concentrated around the first set of parents, and from this we select the next set of parents.

3.Successive generations converge on the optimal solution.

Second Generation

Para

met

er 2

The learning curve

The learning loop

Examples of closed-loop experiments

• Fluorescence spectrum manipulation (Wilson 1997)

• Molecular fragmentation selectivity (Gerber 1998, Levis 2001, Woste 2003)

• Atomic excitation tailoring (Bucksbaum 1999)

• High-harmonic X-ray tailoring (Murnane & Kapteyn 2000)

• Ultrafast optical switching (Keller 2000)

• Molecular rearrangement selectivity (Levis &Rabitz 2001)

• Chemical discrimination in mixtures (Gerber 2001)

• Distortion-free transmission through optical fibers (Omenetto 2001)

• Vibrational excitation tailoring in polymers (Motzkus 2002)

• Decoherence management (Walmsley 2002)

• Energy transfer in photosynthesis (Herek & Motzkus 2002)

So far, more than 40 systems successfully controlled

Changing the pulse shape changes the product ratio

Simultaneous but selective absorption of two different molecules using shaped femtosecond pulses:

Control of energy flow in light harvesting

The LH2 light harvesting antenna from Rps. acidophila

0 -2

B8 0 0

B8 5 0

400 450 500 550 600 650 700 750 800 850 900 950Wave length, nm

CarotenoidS2

BChlQy

BChlQx

0 -1 0 -0

B8 0 0 / B8 5 00 -2

B8 0 0

B8 5 0

400 450 500 550 600 650 700 750 800 850 900 950Wave length, nm

CarotenoidS2

BChlQy

BChlQx

0 -1 0 -0

B8 0 0 / B8 5 0

Energy transfer

Energyloss

DonorCar

AcceptorBChl

Two competing channels:internal conversion vs. energy transfer

Can we control the IC/ET branching ratio?

Experimental setup

Car BChl

Sn

S2

S1

S0

Qy

g

ETIC

excλ510 nm

prλ580 nm

prλ880 nm

Excitation Probe Rotatingsample

Feed-backImproved

shape

whitelightgen.

shaperΦ λ, )A((λ)

ETIC

nc-OPA

=510nm=30fs

λ∆τ0

IF

Evolutionary algorithm

“Blind” optimization (64 parameters)Target: maximize ratio of IC/ET signals

0 5 10 15 20 25 30 35

1,0

1,1

1,2

1,3

1,4

Car/B

Chl r

atio

(rel

ativ

e to

TL)

Generation

TL

IC/E

T ra

tio (r

elat

ive

to T

L) “best” individual result

What is the pulse shape?Unshaped pulse Shaped pulse

1500 fs

IC ETIC ET

40 fs

Time

490

530

Wav

elen

gth,

nm

Reducing the complexity: restricted optimization

Sinusoidal phase mask in FREQUENCY DOMAIN:

φ(pix) = a*sin(b*pix + c)

Only 3 parameters:a: modulation depth b: frequencyc: phase offset

a

2π/b

c

pix(λ)

Time, ps

a: length of pulse trainb: inter-pulse separationc: carrier phase pattern

Result in TIME DOMAIN: pulse train

Restricted optimization (3 parameters)Target: maximize ratio of IC/ET signals

0 5 10 15 20 25 30 350,6

0,8

1,0

1,2

1,4

1,6

1,8

∆∆O

D (re

lativ

e to

TL)

Generation0 5 10 15 20 25 30 35

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

Car/B

Chl r

atio

(rel

ativ

e to

TL)

Generation

ratio Car

BChl

TL

TL

IC/E

T ra

tio (r

elat

ive

to T

L)

IC

ET

-1

0

1

Pul

se e

nvel

ope

and

Elec

tric

field

-1

0

1

Pha

se (r

ad)

0 5000 10000 15000 20000

Time, a.u.0 5 10 15 20 25 30

-1

0

1

Pixel number

Effect of the phaseShifting the offset parameter (c) changes the phase pattern of the excitation pulse

Optimized vs. π-shifted-optimized pulsesPhase offset of optimal mask pattern shifted by half a period

-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0

02468

Time, ps-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0

02468

phas

e (r

ad)

Time, ps

I(t)

optimized pulses π-shifted-optimized pulses

Result: No change in pulse envelope, energy or spectrumDifferent phase pattern between subpulses

Energy flow depends on the carrier phase

Evidence of coherent control

Ο π 2π 3π0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

IC

ET

Flow

(rel

ativ

e to

π p

hase

shi

fted)

Shift of optimized phase parameter

Nature 417, 533 (2002)

Histogram of successive optimizations

Spectroscopy by coherent control

0 50 100 150 200 250 300

5155 cm-1

num

ber o

f res

ults

4

3

2

1

0

active mode, cm-1

The carotenoid loss channel

Promoting modes for carotenoid internal conversion:

CC stretch~1100, 1500 cm-1

symmetric (ag)

CCC bend~120-180 cm-1

asymmetric (bu)

S (1A )0 g -

S (1B )2 u +

S (2A )1 g -

tuning ~ a g

ener

gy

coupling ~ b u

Resonant coupling to bending mode promotes internal conversion via conical intersection(stretch)

(bend)

0 100 200 300 400

∆A

(a.u

.)

Time Delay (fs)

800 1000 1200 1400 1600 1800

1155

1508

Frequency (cm-1)

Time delay (fs)0 100 200 300 400

11501508

Frequency (cm-1)

G. Cerullo, Politechnico di Milano

What is the control mechanism?

• Couple to specific molecular motion(155 cm-1 bending mode)

• Manipulate quantum interferences (coherent control)

Vibrational mode matching

Coherent Impulsive Raman Scattering

BChl

S2

S 1

S0

hotS0shap

ed p

ump

Φ(ω) ω

02πCar

Reducing the complexity: Model systems

LH2

• Biological complexes (wild-type, mutants)function

• Biomimetic molecular assembliesreactivity

caroteno-porphyrin dyad

• Isolated moleculesmotion

porphryincarotenoid

A new spectroscopic tool for reducing biological complexity

Blind optimizations:Identify functionally important motion

Restricted parameter space:Test simple pulse shapes correlated to• shapes of potential energy surfaces• specific vibrational modes

Control knobs:

∆t

• Wavelength• Spectral amplitude• Temporal envelope• Phase• Polarization

Challenges and opportunitiesInversion: Can we extract microscopic information of the molecular system by analysis of the optimized laser field?

• Parametrization. Test/catalogue the effects of simple pulse shapes

Finessed quantum mechanical manipulations may provide a unique source of data on intramolecular forces

Develop coherent control “rules of thumb”

• Analyze relevant electric field shapes to obtain information about the temporal evolution of the system

Recent review articles:Walmsley, I. & Rabitz, H. Quantum physics under control.Physics Today (Aug 2003) 43-49

Brixner T., Damrauer N. H. & Gerber G. Femtosecond quantum control. Adv. Atom. Mol. Opt. Phys. 46, 1-54 (2001)

Rice, S. Interfering for the good of a chemical reaction. Nature 409, 422-426 (2001)

Rabitz, H., deVivie-Riedle, R., Motzkus, M. & Kompa, K.-L. Whither the future of controlling quantum phenomena?Science 288, 824-828 (2000)

A fun website:http://www.physik.uni-wuerzburg.de/femto-welt/