  When an optical emitter is strongly coupled to a vibrational bath the polaron
transformation is often used to permit an accurate second-order Redfield master
equation. However, the optical transition rates in the polaron frame are not
analytic and approximations typically need to be made which result in the loss
of anything other than simple additive effects of the two baths. In this paper,
we derive an intuitive analytic expression for the polaron frame optical
transition rates by means of a finite mode truncation of the vibrational bath.
Using this technique, calculations of the transition rates converge for only a
few modes in the truncated spectral density, and capture non-additive effects
such as population inversion of a two-level system.
