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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)