Abstract

We utilize the novel non-Markovian quantum jump (NMQJ) approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory decoherence rates can have negative regions, a signature of non-Markovian behavior and of the revival of coherences. This can lead to non-Markovian population beatings for a dimer system at room temperature. We show that strong exciton-phonon coupling to low frequency modes can considerably modify transport properties. We observe increased exciton transport, which can be seen as an extension of recent environment-assisted quantum transport concepts to the non-Markovian regime. Within the NMQJ method, the Fenna-Matthew-Olson protein is investigated as a prototype for larger photosynthetic complexes.

Highlights

  • The initial step in photosynthesis is the excitonic transport of the energy captured from photons to a reaction center.[1]

  • The exciton transfer dynamics has been studied utilizing the Förster theory in the limit of weak intermolecular coupling[3] or Redfield master equations in the limit of weak exciton-phonon coupling.[4]. The latter approach describes the transport as dissipative dynamics for the reduced excitonic density matrix

  • The first is equivalent to the chronological ordering prescription while the second corresponds to a partial ordering prescription of the time ordering in a system-bath cumulant expansion.[7,12,13]

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Summary

INTRODUCTION

The initial step in photosynthesis is the excitonic transport of the energy captured from photons to a reaction center.[1]. A Markovian master equation in Lindblad form can be simulated by means of the Monte Carlo wave function methodMCWF.[28] This numerical technique relies on the property that density matrix evolution is equivalent to an averaging of wave function trajectories, each of which is interrupted by stochastic, discontinuous quantum jumps. We employ the non-Markovian quantum jumpNMQJapproach, recently developed by Piilo et al.[29,30] This method is a generalization of the MCWF to the case of NM dynamics derived from a TCL approach. We find that in the NM regime transport can be enhanced compared to purely Markovian dynamics and thereby provide an extension to the recent environment-assisted quantum transportENAQTconcept.[33–35] These effects are pronounced in situations when the main phonon-mode frequencies are much smaller thani.e., “off-resonant” toa particular system transition frequency. V–VII, we analyze dimer systems and the FMO complex

MASTER EQUATION
SPECTRAL DENSITY AND TIME-DEPENDENT RATES
NON-MARKOVIAN QUANTUM JUMPS
POPULATION BEATINGS IN A DIMER SYSTEM
TRANSPORT IN THE NON-MARKOVIAN REGIME
FENNA–MATTHEWS–OLSON COMPLEX
VIII. CONCLUSION
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