Adiabatic eigenfunction-based approach for coherent excitation transfer: An almost analytical treatment of the Fenna-Matthews-Olson complex

We suggest a 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 nonperturbatively and population relaxation using a Markovian master equation. Almost 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. Nalbach, Braun, and Thorwart, Phys. Rev. E 84, 041926 (2011)]. Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence causes only damping of oscillations and does not lead to transfer to the reaction center. Population relaxation is necessary for efficient transfer to the reaction center, 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.

Adiabatic Eigenfunction Based Approach to Coherent Transfer: Application to the Fenna-Matthews-Olson (FMO) Complex and the Role of Correlations in the Efficiency of Energy Transfer

We have recently suggested a method (Pallavi Bhattacharyya and K. L. Sebastian, Physical Review E 2013, 87, 062712) for the analysis of coherence in finite-level systems that are coupled to the surroundings and used it to study the process of energy transfer in the Fenna-Matthews-Olson (FMO) complex. The method makes use of adiabatic eigenstates of the Hamiltonian, with a subsequent transformation of the Hamiltonian into a form where the terms responsible for decoherence and population relaxation could be separated out at the lowest order. Thus one can account for decoherence nonperturbatively, and a Markovian type of master equation could be used for evaluating the population relaxation. In this paper, we apply this method to a two-level system as well as to a seven-level system. Comparisons with exact numerical results show that the method works quite well and is in good agreement with numerical calculations. The technique can be applied with ease to systems with larger numbers of levels as well. We also investigate how the presence of correlations among the bath degrees of freedom of the different bacteriochlorophyll a molecules of the FMO Complex affect the rate of energy transfer. Surprisingly, in the cases that we studied, our calculations suggest that the presence of anticorrelations, in contrast to correlations, make the excitation transfer more facile.