Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states

Kavli Affiliate: K. Birgitta Whaley

| First 5 Authors: Liwen Ko, Robert L. Cook, K. Birgitta Whaley, ,

| Summary:

We develop a method to simulate the excitonic dynamics of realistic
photosynthetic light harvesting systems including non-Markovian coupling to
phonon degrees of freedom, under excitation by N-photon Fock state pulses. This
method combines the input-output formalism and the hierarchical equations of
motion (HEOM) formalism into a double hierarchy of coupled linear equations in
density matrices. We show analytically that, under weak field excitation
relevant to natural photosynthesis conditions, an N-photon Fock state input and
a corresponding coherent state input give rise to equal density matrices in the
excited manifold. However, an important difference is that an N-photon Fock
state input has no off-diagonal coherence between the ground and excited
subspaces, in contrast with the coherences created by a coherent state input.
We derive expressions for the probability to absorb a single Fock state photon,
with or without the influence of phonons. For short pulses (or equivalently,
wide bandwidth pulses), we show that the absorption probability has a universal
behavior that depends only upon a system-dependent effective energy spread
parameter {Delta} and an exciton-light coupling constant {Gamma}. This holds
for a broad range of chromophore systems and for a variety of pulse shapes. We
also analyse the absorption probability in the opposite long pulses (narrow
bandwidth) regime. We also derive an expression for the long time emission rate
in the presence of phonons and use it to study the difference between
collective versus independent emission. Finally, we present a numerical
simulation for the LHCII monomer (14-mer) system under single photon excitation
that illustrates the use of the double hierarchy for calculation of Fock state
excitation of a light harvesting system including chromophore coupling to a
non-Markovian phonon bath.

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