Excitation energy transfer with initial system-bath correlations for coherent initial conditions in a toy donor-acceptor model

Abstract

A theory of coherent resonant energy transfer with initial system-bath correlations [Qin et al., Phys. Rev. A 99, 032111 (2019)] is extended for a coherent initial system condition, which is a linear superposition of donor and acceptor excitations, and is more general and actual in many respects. The nonequilibrium bath state, containing initial system-bath correlations, is expanded in powers of coupling strength within the polaron formalism of second-order time-convolutionless quantum master equation. Detailed expressions for both homogeneous and inhomogeneous terms are derived and calculations are performed under the assumption of super-Ohmic spectral densities where the case of common bath modes is also included. Numerical results indicate that, for certain initial system conditions, the nonequilibrium due to the initial system-bath correlations brings about larger amplitude of population oscillation. And the initial system condition is of crucial importance in determining whether the initial system-bath correlations would play a significant role in the transfer dynamics. We identify a sensitive window in which the transfer dynamics is especially vulnerable to the bath such that there exists a greatly obvious difference between the dynamics with and without initial correlations. Besides, the system-bath coupling strength, the evolution time, and the nature of common bath modes are also shown to contribute to these effects. Rate equations based on F\orster-Dexter energy transfer theory are derived for comparison.