  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.
