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

TL;DR

This paper derives an analytical expression for optical transition rates in the polaron frame, enabling accurate and convergent calculations with few vibrational modes, capturing complex effects like population inversion.

Contribution

It introduces a finite mode truncation method to obtain an analytic expression for polaron frame optical transition rates, improving computational efficiency and accuracy.

Findings

Transition rates converge with few vibrational modes.

Captures non-additive effects such as population inversion.

Provides an intuitive analytic expression for complex systems.

Abstract

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.