# Collective Modes of a Photon Bose-Einstein Condensate with Thermo-Optic Interaction

## TL;DR

This paper develops a mean-field model to analyze how thermo-optic interactions influence the collective excitations of a photon Bose-Einstein condensate, revealing dependence on thermal diffusion and a breakdown of the Kohn theorem.

## Contribution

It introduces a coupled open-dissipative Schrödinger and diffusion model to study collective modes in photon BECs with thermo-optic interactions, providing analytical results.

## Key findings

- Collective mode frequencies depend on thermal diffusion.
- Thermo-optic interaction reduces the center-of-mass oscillation frequency.
- Breakdown of the Kohn theorem is predicted.

## Abstract

Although for photon Bose-Einstein condensates the main mechanism of the observed photon-photon interaction has already been identified to be of thermo-optic nature, its influence on the condensate dynamics is still unknown. Here a mean-field description of this effect is derived, which consists of an open-dissipative Schr\"odinger equation for the condensate wave function coupled to a diffusion equation for the temperature of the dye solution. With this system at hand, the lowest-lying collective modes of a harmonically trapped photon Bose-Einstein condensate are calculated analytically via a linear stability analysis. As a result, the collective frequencies and, thus, the strength of the effective photon-photon interaction turn out to strongly depend on the thermal diffusion in the cavity mirrors. In particular, a breakdown of the Kohn theorem is predicted, i.e.~the frequency of the centre-of-mass oscillation is reduced due to the thermo-optic photon-photon interaction.