We analyze the role of coherent, non-perturbative system-bath interactions in a photosynthetic heat engine. Using the reaction-coordinate formalism to describe the vibrational phonon-environment in the engine, we analyze the efficiency around an optimal parameter regime predicted in earlier works. We show that, in the limit of high-temperature photon irradiation, the phonon-assisted population transfer between bright and dark states is suppressed due to dephasing from the photon environment, even in the Markov limit where we expect the influence of each bath to have an independent and additive affect on the dynamics. Manipulating the phonon bath properties via its spectral density enables us to identify both optimal low- and high-frequency regimes where the suppression can be removed. This suppression of transfer and its removal suggests that it is important to consider carefully the non-perturbative and cooperative effects of system-bath environments in designing artificial photosynthetic systems, and also that manipulating inter-environmental interactions could provide a new multidimensional lever by which to optimize photocells and other types of quantum device.
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