F\"orster resonance energy transfer with transient coherent effects

Abstract

We formulate the weak intramolecular coupling F\"orster resonance energy transfer theory in a form suitable for calculating ultrafast nonlinear response of molecular systems. We introduce a formally exact time-dependent factorization of the molecular statistical operator into the system and bath components. Combining this factorization with unperturbed environment evolution, we generalize the traditional F\"orster master equation for the state population probabilities into a complete master equation for the system's reduced statistical operator. The traditional F\"orster theory applies in the limit where the intermolecular coupling is weak, and the system-bath coupling is strong. Our technique of derivation explicitly leads to a time non-local F\"orster type master equation, which remains valid also in the limit of vanishing system-bath coupling. The theory predicts a rapid initial coherent evolution of populations arising from a transient initial coherence-dependent term, which induces a slippage of the initial condition that persists during subsequent rate-controlled transfer. Comparison with exact numerical results confirms the clear improvement of the present generalization over earlier formulations of the F\"orster theory and delineates its range of validity.