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When an optical emitter is strongly coupled to a vibrational bath the polarontransformation is often used to permit an accurate second-order Redfield masterequation. However, the optical transition rates in the polaron frame are notanalytic and approximations typically need to be made which result in the lossof anything other than simple additive effects of the two baths. In this paper,we derive an intuitive analytic expression for the polaron frame opticaltransition rates by means of a finite mode truncation of the vibrational bath.Using this technique, calculations of the transition rates converge for only afew modes in the truncated spectral density, and capture non-additive effectssuch as population inversion of a two-level system.

An analytic expression for the optical exciton transition rates in the polaron frame