Analytical Treatment of Coherent Excitation Transfer in FMO Complex

TL;DR

This paper introduces a new analytical method for studying coherence and energy transfer in the FMO complex, separating decoherence and relaxation effects, and demonstrating excellent agreement with numerical results.

Contribution

The paper presents a novel analytical approach using adiabatic states to treat decoherence and relaxation separately in light-harvesting complexes.

Findings

Decoherence causes damping but not transfer to the reaction centre.

Population relaxation is essential for efficient energy transfer.

Method agrees well with exact numerical simulations.

Abstract

We suggest a new method of studying coherence in finite level systems coupled to the environment and use it for the Hamiltonian that has been used to describe the light-harvesting pigment-protein complex. The method works with the adiabatic states and transforms the Hamiltonian to a form in which the terms responsible for decoherence and population relaxation are separated out. Decoherence is then accounted for non-perturbatively, and population relaxation using a Markovian master equation. Analytical results can be obtained for the seven level system and the calculations are very simple for systems with more levels. We apply the treatment to the seven level system and the results are in excellent agreement with the exact numerical results of Nalbach et al. (P. Nalbach, D. Braun, and M. Thorwart, Physical Review E, 84, 041926 (2011)). Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence only causes damping of oscillations, and does not lead to transfer to the reaction centre. Population relaxation is necessary for efficient transfer to the reaction centre, in agreement with earlier findings. Our results show that the transformation to the adiabatic basis followed by a Redfield type of approach leads to results in good agreement with exact simulation.