Excitation Transfer in Photosynthetic Pigment Protein...

Excitation Transfer in Photosynthetic Pigment Protein Complexes

Tomáš Mančal

Faculty of Mathematics and Physics Charles University, Prague

Ke Karlovu 5, 121 16 Prague 2, Czech Republic

Open questions on energy transport & conversionin nanoscale quantum systems

Marseille, November 16th 2018

Outline

• Photosynthetic light-harvesting: a brief introduction

• Does in make sense to distinguish between the quantum and the classical?: a brief history of a controversy

• What is quantum on photosynthetic energy transfer? (This question is related to thermodynamics behavior)

Quantum-coherent weakly driven thermal machines can be simulated classically

Talk right after me:Luis. A. CorreaQuantum-coherent weakly driven thermal machines can be simulated classically

Photosynthesis

Photosynthesis: Biology, Chemistry or Physics?

6 CO2 + 12 H2O → C6H12O6 + 6 O2 + 6 H2O

A school definition

A row of complicated physical, chemicaland biological processes

Interesting for physicists: primary processes in photosynthesisPhoton captureExcitation energy transfer towards reaction centerElectron transfer in reaction centerTransfer of protons across cellular membrane

Photosynthesis done not just by plants, but also by bacteria

Photosynthetic Antennae

Photosynthesis always occurs on membranes

Photosynthetic bacterium

Invaginations on the innercellular wall

Two separatedaquatic environments

reaction center

various light harvesting antennae


Scheuring et al. The EMBO J. 20 (2001) 3029

Sun light = a rather sparse source of energy

Antenna

Reactioncenter


• Highly organized structure

• Fixed spatial relations between individual pigments

• Very few types of buildingblocks

• Protein play major role in establishing structure andmodulating electronic properties

• Photon capture

• Energy transfer

• Electron transfer

• Proton transfer

• ATP production

• Other cellular processes including carbon fixation and oxygen production

Physics

Chemistry

Biology

Timescale difference!

Place of Photosynthesis in Natural Sciences

Quantum/Classical Controversy in Photosynthetic Research

Brief (Biased) History of the Controversy

2005 – Brixner et. al, Nature 434 (2005) 625optical/near IR analogues of coherent NMR experiments on Photosyntheticsystems - Coherent 2D Electronic Spectroscopy (2DES)

2006 – Pisliakov et. al, J. Chem. Phys. 124 (2006) 234505prediction of oscillations in 2DES due to electronic coherence; dephasing timespredicted for Fenna-Matthews-Olson (FMO) complex

2007 – Engel et. al, Nature 446 (2007) 782detection of the predicted oscillations - much longer than expected life-timesclaims: oscillations = electronic coherence; electronic coherence importantfor the efficiency of energy transfer in photosynthesis; perhaps photosyntheticsystems are actually quantum computers

2008 and onMany theoretical papers on quantumness of photosynthesisClaims: quantum entanglement is the cause of the efficiency;

entanglement survives unusually long etc.


Essential claim of the new theoretical papers:• Now we formulate quantum theory of energy transfer (before it was described classically)• Quantum means coherent, coherent means entanglement• Coherence enables efficient energy transfer in space• Coherent motion induced not only by laser light, but also by natural (sunlight) illumination

Some counter arguments• Coherent does not mean necessarily quantum

o There is a classical coherence: W. H. Miller, J. Chem. Phys. 136 (2012) 210901o Coherent states of light are actually as classical as it gets: Any quantum optics book

• Coherent dynamics of photosynthetic (Frenkel) excitons is classicalo They can be mapped on a system of harmonic oscillators

S. Mukamel, J. Chem. Phys. 132 (2010) 241105,J. S. Briggs and A. Eisfeld, Phys. Rev. E 83 (2011) 051911

o Only the thermodynamic downhill preference in energy transfer is a genuinely quantum effect: T. Mancal, J. Phys. Chem. B, 117 (2013) 11282

• Sunlight does not induce any time-dependent coherence (photon is not a bullet)o One must not mix statistical interpretation of quantum mechanics with what is “actually” going on: T. Mančal and L. Valkunas, New J. Phys. 12 (2010) 065044


Quantum theory of photosynthesis• It is so old that there are textbooks on it

van Amerongen, Valkunas, van Grondelle, Photosynthetic excitons, World Scientific, 2000

May & Kuehn, Charge and Energy Transfer Dynamics in Molecular Systems, Wiley-VCH, 2000

for comparison

• Plenio, Engel (eds.) Quantum Effects in Biological Systems, (2014) does literally not containa single equation not found in the two books above

S. Mukamel, J. Phys. Chem. A 117 (2013) 10563Comment on “Coherence and Uncertainty in Nanostructured Organic Photovoltaics”In summary, exciton coherence and localization are well established concepts dating backto the 1970s that are constantly being rediscovered and recast with a different terminology, earlier in biological light harvesting and now in photovoltaics. There is nothing particularly surprising in the recent biological or photovoltaic experiments that require paradigm change.

The Quantum and The Classical

- certainly not the theorists: only quantum mechanics is used, nothing else

Who cares if photosynthesis is quantum or classical?

- certainly not the experimentalists: they know it is quantum

+ future quantum technologists

The question of Quantum vs. Classical photosynthesis is not a purely academic one.It is very practical:

Should we expect some counter intuitive, hard to imagine and hard to understand behavior in photosynthetic antennae?

Quantum Photosynthesis

What is Quantum in Photosynthesis

Classical picture of photosynthetic antenna?

T. Mancal, J. Phys. Chem. B 117 (2013) 11282

-

Lorentz theory of absorption (1910)

+

Electrically neutral atom (molecule)

xy

zElectron is displaced by interaction with light

-+

displacementincoming field

polarization

wave vector

r

k

e




Classical equations for electronic displacement

• Identification of electronic oscillator amplitude with electronic (optical) coherence• Perfect mapping of Schrödinger equation for excitons on a set of oscillators

Pointed out by MukamelStudied in detail by Briggs and Eisfeld

Equation of motion for a set of (classical) harmonic oscillators coupled to a reservoir

Amplitude of n-th oscillatorCoupling between oscillators

Modulation of frequency by bath




slow

We can take this away

Canonical quasi-equilibrium establishes here

Classical equations do not show any preference for downhill transfer

(Correct) thermodynamic behavior is the only uniquely quantum featureof Frenkel exciton energy transfer

g

1e2e

3e

Entanglement and Thermodynamics

In J. Phys. Chem. B 117 (2013) 11282 – derivation by analogy

Here – derivation of classical oscillator equations from quantum mechanical equations for excitons in photosynthetic antenna

Schrödinger equation

Decomposition into pointer states

Crucial property of the bath states relative to pointer states

Bath states


This is where the „observer“ is

Classical bath that does not entangle with the quantum mechanical system

Interaction picture with respect to the bath

Bath induced fluctuations


Bath can now be eliminated

Modulation throughexpectation value

One strange term


Global phase and its elimination

Global phase does notplay any role in physics


System-bath interaction – operator on system Hilbert space only!


Frenkel exciton Hamiltonian

Harmonic bath

State decomposition into collective excited states


Equations identical to the classical equations for oscilátor amplitudes

Bath introduced real valued transition frequency fluctuations

In a true quantum case,there is an operator here!

In the absence of system-bath entanglement, quantum system of excitons behaves entirely classically

Conclusions

• Coherent component of photosynthetic energy transfer can be perfectly mapped onto a classical system of oscillators

• Thermodynamic behavior (trapping) is a uniquely quantum feature of photosynthetic antennae

• Trapping is enabled by system-bath entanglement

Acknowledgement

Funding from Czech Science Foundation (GACR)

Neuron fund – private fund for support of basic science

Postdoc and PhD positions open

gments

Research groupJoachim SeibtPavel Malý Sayeh RajabiVladislav Sláma

Thank you for your attention

Open Quantum Systems from Wavefunction Perspective

Open (Quantum) Systems

• Quantum theory is a universal theory• Only the whole Universe can be considered ”isolated”• Microscopic systems can be considered isolated for in a limited time interval after a state preparation• We need quasi-isolated systems to test quantum theory

All things that exist are open quantum systems

Classical world emerges from the quantum world in the process of decoherence

• Features natural to quantum world (such as entanglement) seemingly disappear• It is those very features that make the classical world emerge• On a fundamental level everything remains quantum

Density Matrix vs. Wavefunction

Bath

System

State vector(a.k.a. wavefunction)

Statistical operator(a.k.a. density matrix)

Description of the combined system

Expectation values of the system quantities

Reduced density matrix

Some basis on bath

No reduced wavefunction is possible!

Can We Live without Density Matrix?

YES and NO

In some fields of chemistry (and physics) they never use (reduced) density matrix (see e.g. text book derivationsof excited state life time)

Methodology is well developed

Working with reduced density matrix is very convenient.Expectation values, i.e. analoguess or sections of reduced DMhave to be calculated anyway

We would loose „master equations“

Advantages of Wavefunction Formalism

1. We never loose sight of the bath

Basis states of the system

Probability amplitudes for the system „Relative“ state of the bath

Existence of „relative“ states of the bath goes to the heart of quantum mechanics• System and bath entangle with each other!

Relative bath states ARE states• no problem (not even philosophical) in talking about them• On the contrary – „relative“ density matrices of the bath ARE NOT states

Beware of spectroscopic speak!!!


2. Decoherence and dephasing are not confounded in wavefunction formalism

Ensemble and quantum mechanical averaging are cleanly separated

Decoherence – results from quantum mechanical averaging

Dephasing – results from ensemble averaging

)


3. Clear and concise way of speaking about the state of the system

In interpretations of quantum mechanics, which tend to be based on “classical terms” (classical observations) only, you are not allowed to speakabout certain things:

Where was the particle between measurements?What is a momentum of a particle?

These are inherently „density matrix“ questions.They assume there IS a particle without the rest of the Universe.

Keep thinking about the (complete) state!

Excitation Transfer in Photosynthetic Pigment Protein...

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