Title: Energy Transfer Mechanism Under Incoherent Light Excitation in noisy Environments: Memory Effects in Efficiency Control

Abstract: Fluctuations in the energy gap and coupling constants in and between chromophores can play important role in the absorption and energy transfer across a collection of two level systems. In a noisy environment, fluctuations can control efficiency of energy transfer through several factors, including quantum coherence. Several recent studies have investigated the impact of light-induced stationary quantum coherence on the efficiency of transferring optical excitation to a designated "trap" state, crucial for subsequent reactions such as those in photosynthesis. However, these studies have typically employed either a Markovian, or a perturbative approximation for the environment induced fluctuations. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation (QSLE). We introduce the effects of the decay of excitation (to the ground state) and the desired trapping that provides the direction of the motion of the excitation. In the presence of light-induced pumping, we establish a relation between the mean survival time, efficiency, and the correlation decay time of the bath-induced fluctuations. We find a decrease in the steady state coherence during the transition from the non-Markovian regime (characterized by small values of fluctuation strength V and inverse of bath correlation time b) to the Markovian limit (where V and b are both large), resulting in a decrease in efficiency. We recover a connection between transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.