Transfer of vibrational coherence through incoherent energy transfer process in Forster limit

We study transfer of coherent nuclear oscillations between an excitation energy donor and an acceptor in a simple dimeric electronic system coupled to an unstructured thermodynamic bath and some pronounced vibrational intramolecular mode. Our focus is on the nonlinear optical response of such a system, i.e., we study both excited state energy transfer and the compensation of the so-called ground-state bleach signal. The response function formalism enables us to investigate a heterodimer with monomers coupled strongly to the bath and by a weak resonance coupling to each other (Forster rate limit). Our work is motivated by recent observation of various vibrational signatures in two-dimensional coherent spectra of energy-transferring systems including large structures with a fast energy diffusion. We find that the vibrational coherence can be transferred from donor to acceptor molecules provided the transfer rate is sufficiently fast. The ground-state bleach signal of the acceptor molecules does not show any oscillatory signatures, and oscillations in ground-state bleaching signal of the donor prevail with the amplitude, which is not decreasing with the relaxation rate.