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arXiv:1306.1319

Analytical Treatment of Coherent Excitation Transfer in FMO Complex

Pallavi Bhattacharyya, Kizhakeyil L. Sebastian

Published Jun 6, 2013• 0 citations
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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.

DOI
10.48550/arxiv.1306.1319

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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.
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.
Two chlorophylls of the FMO complex, the light-harvesting complex of the green sulfur bacteria, are modeled as two coupled qubits, each surrounded by one spin-bath simulating the environment. The dynamics of the system at a non-zero temperature provide exact analytical expressions for the transition probability and the coherence. It is shown that the decoherence-inducing interaction with the environment enhances the electronic energy transfer. Also the correlations in terms of entanglement and nonlocality are quantitatively studied, sensitively differing when introducing a decay term to resemble both chlorophylls being in their ground states. It is proved that nonlocality is a stronger form of correlation than entanglement.
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
We have developed a simple and physically clear picture of adiabatic rapid passage (ARP) in molecules in solution by careful examination of all the conditions needed for ARP. The relaxation effects were considered in the framework of the Landau-Zener model for random crossing of levels. The model enables us to include into consideration non-Markovian Gaussian-correlated noise. It explains all the numerical results obtained in the first paper of the series [B. D. Fainberg and V. A. Gorbunov, J. Chem. Phys. 117, 7222 (2002)], in particular, that for positive chirp pulse excitation relaxation favors more efficient population transfer with respect to the relaxation-free system with frozen nuclear motion. We also relate parameters of non-Markovian Gaussian-correlated noise with irreversible dephasing time of an optical transition by calculating the photon echo signal attenuation.
Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna–Matthews–Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e. memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling (recoupling) method, which is turn off (on) the couplings, and also Solovay–Kitaev techniques to decompose Hamiltonian and Lindbladians into efficient elementary gates on an NMR simulator. Finally, we design the quantum circuits for the unitary and nonunitary part due to the system-environment interactions of the open system dynamics.
The influence of excited-state absorption (ESA) and two-exciton processes on a coherent population transfer with intense ultrashort chirped pulses in molecular systems in solution has been studied. A unified treatment of adiabatic rapid passage (ARP) in such systems has been developed using a three-state electronic system with relaxation treated as a diffusion on electronic potential energy surfaces. We have shown that ESA has a profound effect on coherent population transfer in large molecules that necessitates a more accurate interpretation of experimental data. A simple and physically clear model for ARP in molecules with three electronic states in solution has been developed by extending the Landau-Zener calculations putting in a third level to random crossing of levels. A method for quantum control of two-exciton states in molecular complexes has been proposed. 1.