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

Abstract

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 and the hierarchical equations of motion (HEOM) formalisms into a double hierarchy of density matrix equations. 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 N-photon Fock state input induces 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 analyze the absorption probability in the opposite long pulses (narrow bandwidth) regime. We then 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 equations.

Coupled charge and energy transfer dynamics in light harvesting complexes from a hybrid hierarchical equations of motion approach

“…27,51,52 In this section, we describe how Zwanzig projection can be used to construct a hybrid HEOM/QME method in which radiative and electron transfer processes are treated with perturbation theory while preserving the high accuracy of the EET dynamics afforded by HEOM. Similar approaches have been used to derive hybrid HEOM methods to describe radiative processes in EET in protein-pigment complexes, 19,23,70 but these have not included charge transfer processes. The approach taken here combines some of the ideas for describing radiative processes in Ref.…”

Emulating Quantum Entangled Biphoton Spectroscopy Using Classical Light Pulses

“…We now prove the equivalence explicitly by analyzing the signals using an input-output formulation of quantum nonlinear spectroscopy. This approach is based on a perturbative expansion of the signal observables in the Heisenberg picture, distinct from the more common approach of perturbing the combined system plus field density matrix in the interaction picture. , The input-output formulation simplifies the theoretical analysis by focusing on the signal observables and using standard results from the input-output formalism of quantum optics. − …”

“…a pr,out ( t ) is the output field operator of the probe field. This output field operator is the result of time-evolving the input field operator in the Heisenberg picture with the combined matter and field Hamiltonian, and thus it mixes the field and matter degrees of freedom . The time domain field operator a ( t ) is related to the frequency domain field operator a (ω) by the Fourier relation a ( t ) = 1 2 π ∫ d ω normale − i ω t a ( ω ) Therefore, a ( t ) also satisfies the bosonic commutation relations …”

“…However, it is important to recognize that despite this similarity, there is also a difference in the overall dynamics of the reduced matter system, since the ground-excited state coherence is identically zero under a single photon Fock state excitation and nonzero under a coherent state excitation. 23 Combining the equivalence between signals from biphotons and single photon Fock states and the equivalence between signals from single photon Fock states and single photon coherent states, we can then establish a class of QLS experiments that can be performed by using only classical light. We now begin the formal analysis.…”

“…Regardless of the difference in the collective matter state, we show here that the two-point correlation signals of the output light are the same. In a different context of a single molecule system, it has been shown , that a single photon Fock state and a coherent state containing one photon on average give rise to the same excited state dynamics in the molecule. However, it is important to recognize that despite this similarity, there is also a difference in the overall dynamics of the reduced matter system, since the ground-excited state coherence is identically zero under a single photon Fock state excitation and nonzero under a coherent state excitation …”