Thermalization Rate of Light in Weakly Coupled Molecular Systems

TL;DR

This paper addresses the problem of how light thermalizes in weakly coupled molecular cavities, enabling phenomena such as photon Bose-Einstein condensation. It develops a perturbative Lindblad framework by separating the low-frequency vibrational modes as a local reservoir and deriving a Lindblad thermalization term with rate $\gamma_{\rm therm}^{\alpha\beta}$ that captures tripartite exciton–vibration–photon dynamics. The rate expression shows explicit dependence on macroscopic parameters (light–matter coupling, cavity/exciton frequencies, illuminated molecule count) and the temperature-dependent vibrational occupancy, with a scaling $\gamma_{\rm therm}^{\alpha\beta} \propto 1/N_{\rm mol}$ and a cutoff $\Delta \omega_{\alpha\beta} \le \omega_{\rm MLFV}$, and recovers known planar strong-coupling results in the appropriate limit. The framework provides practical estimates from measurable quantities and clarifies the dominant phonon-emission channel for organic cavities, informing design criteria for light thermalization and polariton/photon condensation applications.

Abstract

Emission and absorption spectra of molecular films are impacted by low-frequency molecular vibrations. These vibrations define the linewidths of the absorption and emission spectral peaks, as well as the Stokes shift. In cavities that use a molecular film as an active medium, low-frequency molecular vibrations facilitate the thermalization of light, enabling the formation of Bose-Einstein condensation. In this work, I employ perturbation theory for Lindblad superoperators and derive the contribution of the low-frequency molecular vibrations to the thermalization rate of light in a weak coupling regime between light and matter. The derived thermalization rate applies for any cavity design but depends on the local microscopic properties of low-frequency molecular vibrations. I provide an estimation for the thermalization rate, which requires only knowledge of the macroscopic parameters of the system: light-matter interaction strength, resonant frequencies of the cavity and excitons, number of molecules in the illuminated area, and the linewidth temperature dependence of the 0-0 peak in the emission spectra of standalone molecular film.