Efficient Excitation Energy Transfer in Light-Harvesting

Systems

吴建澜

Physics DepartmentZhejiang University

Outline

• Transfer efficiency optimization

interplay of quantum coherence and environment-induced dissipation

• Introduction

solar energy conversion

photosynthesis and light harvesting

multi-dimensional spectroscopy

• Quantum kinetic network

quantum-classical comparison

non-trivial quantum effects

trapping-free subspace

Solar Energy Conversionpower from sun to earth /consumed by human: 1.2 x 105 / ~15 TW

Crabtree and Lewis, Physics Today, March 37 2007

solar energy consumption

180 x 10-3 TW10.7 x 10-3 TW

key issues

efficiency; cost; storage; distribution; stability; …

photosynthesis ~1%; light-harvesting in the early stage ~100%

Photovoltaics

Efficiency

Cost

Storage, distribution, and stability

Photosynthesis

2nCO2 + 2nDH2 2(CH2O)n+ 2nDOh

~1%

有氧光合作用

Calvin Cycle

3 CO2 + 9 ATP + 6 NADPH + 6 H+ → C3H6O3-phosphate + 9 ADP + 8 Pi + 6 NADP+ + 3 H2O

Light reactions

~100%

High plants

Pigment-Protein Complex

PS II (photosystem II)

Purple Bacteria

K. McLuskey et al.: Biochemistry40, 8713 (2001).

http://thegardenpondblog.org.uk/2008/11/30/pink-pond/

LH II

James Allen & coworkers, Photosynth. Res., 75 49 (2003)

Green Sulfur Bacteria

Sarovar, et. al. Nature Phys. 6 462 (2010)

Artificial Antenna-Reaction-Center Complex

Light harvesting

Quantum coherence ?

~100%efficiency

Pigment

D

A

Excitation energy transfer

D* A D

EET

A*

Forster rate:

incoherent

dIIJk ADhop )()(~ 2

Fermi golden rule

Quantum coherence?

Multi-Dimensional Spectroscopy Setup

http://engelgroup.uchicago.edu/research/laserspectroscopy.html

Quantum coherence

Multi-Dimensional Spectroscopy

http://www.chemphys.lu.se/research/techniques/2Dspec/

cross peaks and asymmetry environments

diagonal peaks

2D Feynman diagram

M. C. Asplund, M. T. Zanni, and R. M. Hochstrasser, PNAS 2000

Mukamel, Non-linear optical spectroscopy

t T

FMO Spectroscopy

Engel, …, and Fleming, Nature 2007

FMO Spectroscopy

Engel group, PNAS 2010

BathLight-Harvesting

System HS

R C

ΓGround

State

tk

dk

Theoretical Framework of Energy Transfer

trapping

dissipation

decay

two irreversible population depletion channels: trapping and decay

dissipation: population redistribution and decoherence

system Hamiltonian leads to an coherent oscillation

)(][)( )( tLLLLtLt disspdecaytrapsys

J. S. Cao and R. J. Silbey J. Phys. Chem. A, 113, 13825 (2009)

efficient

inefficient

Average trapping time

Transfer efficiency

tk dk

Transfer efficiency and dissipation

11 tkq d

)]0()[(Tr 1 dissptrapsys LLLt

Transfer efficiency can be optimized by dissipation

2nd order expansion: Lindblad, Redfield, Generalized Bloch-Redfield (GBR), …;

Haken-Strobl: classical white noise

)( ),( ),(Tr )(0 b III

t

I VtVdt

branching ratio of trapping process

Bath System

dissipation

*

Hierarchic: Kubo, Tanimura, Ishizaki; Y. J. Yan, Q. Shi, R. X. Xu, …

Classical white noise

Haken-Strobl

)()( tHHtH

0)( tH )()0()( , tHtH nmnm

iiimi

mSB aagmmH )( ||system-bath interaction

Microscopic model

)()( tt mnmn pure dephasing

extremely high-temperature limit

SBBStot HHHH

Example: Two-site system

Jtk

12

*

light

trap (reaction center)

Haken-Strobl bath

3.35

3.4

3.5

3.5

4

4

4

5

5

5

6

6

8

8

0

1

2

3

4

5

Γ

0 2 4 6 8tk

3,1 Jwitht

*

2tk

tk

* t

pure dephasing rate

right panel

optimization

Brixner T., et. al. Nature 434 625 (2005)

Tight-Binding Model of FMO

Engel group, PNAS 2010

quantum chemical calculationdipole-dipole interaction

fitting spectroscopy

*Γ )cm( 1−

<t>

ps)

(initial site: 1

initial site: 6

q

)cm( 1−*Γ

initial site: 1

initial site: 6

secular Redfield

exact result

(a) (b)

FMO: Optimization over dephasing rate

An intermediate pure dephasing rate minimizes the trapping time

J. L. Wu, F. Liu, Y. Shen, J. S. Cao and R. J. Silbey, N. J. P. 12 105012 (2010)

1ps 1 tk

(Lindblad)

Haken-Strobl model

GBR Equation

)0( 2)( 22

DDJ

Debye spectral density

Generalized Bloch-Redfield (GBR) equation

non-Markovian memory

)]( ,[)]( ,[)()()(

)]( ,[)()()(

. ;

0 ;

tftiftgLLtg

tgQitLLt

mi

imr

iimitrapsysim

i mimmtrapsys

)( ; tg imauxiliary field

if bath correlation function can be written as

J. S. Cao J. Chem. Phys., 107, 3204 (1997)

J. L. Wu, F. Liu, Y. Shen, J. S. Cao and R. J. Silbey, N. J. P. 12 105012 (2010)

λ )cm( 1−

<t>

ps)

(

initial site: 1

initial site: 6(a)<t>

ps)

(

λ )cm( 1−

(b)

Optimal Bath Coupling Strength

K 300Tfs 50/1 D

initial site: 6

J. L. Wu, F. Liu, Y. Shen, J. S. Cao and R. J. Silbey, N. J. P. 12 105012 (2010)

bath characterization (spectral density)

)0( 2)( 22

DDJ

Reorganization energy

More Optimal Conditions

J. L. Wu, F. Liu, Y. Shen, J. S. Cao and R. J. Silbey, N. J. P. 12 105012 (2010)

Temperature1/ Relaxation Time

initial site: 1

Spatial correlation

More: spatial arrangement of system; energy displacement; static disorder; etc.

-1cm 35 fs 50/1 D

K 300T-1cm 35

K 300Tfs 50/1 D

Jtk

12

*

light

trap (reaction center)

Haken-Strobl bath

2'2

2

21

'||2

)()(~

J

dffJk AD

Mechanism based on framework of quantum dynamics

incoherent explanation

Forster Interpretation

Conclusions

Quantum kinetic network

classical hopping and multi-body nonlocal quantum coherenceIn progress for general spectral density

Optimization is generic for excitation energy transfer networks

independent of bath spectral density and basis set selection

behaves in various variables: reorganization energy, bath relaxation time, temperature, spatial correlation, detuning, …

mechanism lies on the trapping-free subspacedependent on the initial condition

flux network can be used to distinguish the quantum coherence contribution

Acknowledgement

Prof. Robert J. SilbeyProf. Jianshu Cao

Visiting students at MIT

Fan Liu Young Shen

Students Ph.D. student (collaborator) Jian Ma （马健）Master student Zhuoran Huang （黄卓然）Undergrad. students Zhoufei Tang （唐舟飞） Xiaobin Lu （芦晓斌）Zhihao Gong （龚志浩） Chuanyu Zhao （赵传寓）

jianlanwu@zju.edu.cn