Quantum Coherent Photosynthesis

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Quantum Coherent Photosynthesis Alexandra
Olaya-Castro, Chiu Fan Lee and Neil F.
Johnson Department of Physics, University of
Oxford June 2005
Goal To gain qualitative and quantitative
understanding of the role that quantum
correlations play in the excitation transfer in
light-harvesting complexes.
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Schematic of a light-harvesting complex
(Taken from T. Ritz, et al. Chem. Phys. Chem. 3,
243 (2002)
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Key features

• High efficiency the excitation is transferred to
  the reaction center within 100 ps and with a
  quantum yield of 95.
• This organization has a photoprotective function.
  For instance, excess of energy that is not used
  in an RC to induce electron transfer, is
  transferred back to LH1.

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What would happen in the coherent limit?

• Under what circumstances coherence between
  electronic states actually accelerates energy
  transfer?
• How does the transfer time and the efficiency
  depend on whether the excitation is initially
  localized in one of the donors or delocalized
  among few of them?

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A toy model spin-star network with dipole-dipole
interaction (only one excitation)
Donors
Reaction centre
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Dynamics Quantum jump approach
Preserved number of excitations
Subspace of one excitation
Non-unitary evolution conditioned on no-jump
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Features characterizing a quantum coherent
photosynthetic unit

• Excitation lifetime (t) average time to have the
  (first) jump in the reaction center, given that
  the excitation was initially in the donors.
• Efficiency (?) probability that the excitation
  is used in charge separation in the RC.
• Forward-transfer time (Tf) average time to have
  the (first) jump in the reaction center, given
  that the excitation was initially in the donors.
• Distribution of entanglement how much are the
  donors entagled with the RC and how much are they
  intrinsically entangled.

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Definitions
Probability of no-jump
Density of probability of having a jump of any
type
w(t?0)?dP(t?0)/dt
CPSUs main features
Lifetime
Efficiency
Transfer time
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Excitation initially in the donor subsystem
Efficiency depends on the symmetry and degree of
entanglement of the initial state
Symmetric-entangled states lead to an increase in
the efficiency
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Density of probabilities of having jumps
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Efficiency and transfer-forward time
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Distribution of entanglement and efficiency
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Lifetime and probability of no-jump
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Equivalent system

• It is possible to map the M1 two-level systems
  to an effective 21 system

From the RC perspective
Population
PRC (t)2PRC(t)M
Quantum correlations
From the donors perspective
E12(t)2 ? Sum Eij(t)M
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A more realistic model Transfer between LH-I and
RC in Purple Bacteria
g
J
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Symmetric states
Asymmetric states
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Summary and future work

• In the symmetric and resonant case ? is
  proportional to N, where N is the number of
  donors among which the excitation is
  symmetrically delocalized. Hence, coherence in
  the initial state yields higher efficiencies.
  This is a consequence of the nature of the
  interaction among donors. For fixed dissipation
  and charge separation rates, higher efficiencies
  are obtained when the interaction is restricted
  to nearest neighbours.
• As expected, the life time t is shorter for
  initial states with more donors entangled.
  Transfer time is shorter or equal than t,
  depending on N. This is comparable to what
  happens in the incoherent case.
• The efficiency is related with the time-average
  distribution of entanglement. Increased
  efficiencies imply and increase in the
  entanglement between donors and reaction centre.
• These results could be observed in natural
  light-harvesting complexes at 70 K
• For the future robustness with respect to static
  and dynamic disorder, for example fluctuations in
  individual energies and in the coupling strength
  among donors and between donors and reaction
  centre