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Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects

We study the nature of the energy transfer process within a pair of coupled two-level systems (donor and acceptor) subject to interactions with the surrounding environment. Going beyond a standard weak-coupling approach, we derive a master equation within the polaron representation that allows for investigation of both weak and strong system-bath couplings, as well as reliable interpolation between these two limits. With this theory, we are then able to explore both coherent and incoherent regimes of energy transfer within the donor-acceptor pair. We elucidate how the degree of correlation in the donor and acceptor fluctuations, the donor-acceptor energy mismatch, and the range of the environment frequency distribution impact upon the energy transfer dynamics. In the resonant case (no energy mismatch) we describe in detail how a crossover from coherent to incoherent transfer dynamics occurs with increasing temperature [A. Nazir, Phys. Rev. Lett. 103, 146404 (2009)], and we also explore how fluctuation correlations are able to protect coherence in the energy transfer process. We show that a strict crossover criterion is harder to define when off-resonance, though we find qualitatively similar population dynamics to the resonant case with increasing temperature, while the amplitude of coherent population oscillations also becomes suppressed with growing site energy mismatch.