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arXiv:1705.00738

An Almost Analytical Approach to Simulating 2D Electronic Spectra

Pallavi Bhattacharyya, Nandini Ananth

Published May 1, 2017• 1 citation
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Abstract

We introduce an almost analytical method to simulate 2D electronic spectra as a double Fourier transform of the the non-linear response function (NRF) corresponding to a particular optical pulse sequence. We employ a unitary transformation to represent the total system Hamiltonian in a stationary basis that allows us to separate contributions from decoherence and phonon-mediated population relaxation to the NRF. Previously, one of us demonstrated the use of an analytic, cumulant expansion approach to calculate the decoherence term. Here, we extend this idea to obtain an accurate expression for the population relaxation term, a significant improvement over standard quantum master equation-based approximations. We numerically demonstrate the accuracy of our method by computing the photon echo spectrum of a two-level system coupled to a thermal bath, and we highlight the mechanistic insights obtained from our simulation.

DOI
10.48550/arxiv.1705.00738

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We introduce an almost analytical method to simulate 2D electronic spectra as a double Fourier transform of the the non-linear response function (NRF) corresponding to a particular optical pulse sequence. We employ a unitary transformation to represent the total system Hamiltonian in a stationary basis that allows us to separate contributions from decoherence and phonon-mediated population relaxation to the NRF. Previously, one of us demonstrated the use of an analytic, cumulant expansion approach to calculate the decoherence term. Here, we extend this idea to obtain an accurate expression for the population relaxation term, a significant improvement over standard quantum master equation-based approximations. We numerically demonstrate the accuracy of our method by computing the photon echo spectrum of a two-level system coupled to a thermal bath, and we highlight the mechanistic insights obtained from our simulation.
Two-dimensional (2D) photon-echo spectra of a single subunit of the Fenna-Matthews-Olson (FMO) bacteriochlorophyll trimer of Chlorobium tepidum are simulated, employing the equation-of-motion phase-matching approach (EOM-PMA). We consider a slightly extended version of the previously proposed Frenkel exciton model, which explicitly accounts for exciton coherences in the secular approximation. The study is motivated by a recent experiment reporting long-lived coherent oscillations in 2D transients [Engel et al., Nature 446, 782 (2007)] and aims primarily at accurate simulations of the spectroscopic signals, with the focus on oscillations of 2D peak intensities with population time. The EOM-PMA accurately accounts for finite pulse durations as well as pulse-overlap effects and does not invoke approximations apart from the weak-field limit for a given material system. The population relaxation parameters of the exciton model are taken from the literature. The effects of various dephasing mechanisms on coherence lifetimes are thoroughly studied. It is found that the experimentally detected multiple frequencies in peak oscillations cannot be reproduced by the employed FMO model, which calls for the development of a more sophisticated exciton model of the FMO complex.
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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.