Exact Diagonalisation of Photon Bose-Einstein Condensates with Thermo-Optic Interaction

TL;DR

This paper develops an exact diagonalisation method to analyze how thermo-optic photon-photon interactions influence the spectrum and width of photon Bose-Einstein condensates, enhancing understanding of their interaction effects.

Contribution

It introduces an exact diagonalisation approach incorporating thermal clouds to precisely study photon-photon interactions in condensates, advancing beyond variational methods.

Findings

Photon-photon interactions modify the condensate spectrum and width.

The exact diagonalisation approach captures thermal cloud effects.

Comparison with Gross-Pitaevskii shows thermal contributions are significant.

Abstract

Although photon Bose-Einstein condensates have already been used for studying many interesting effects, the precise role of the photon-photon interaction is not fully clarified up to now. In view of this, it is advantageous that these systems allow measuring both the intensity of the light leaking out of the cavity and its spectrum at the same time. Therefore, the photon-photon interaction strength can be determined once via analysing the condensate broadening and once via examining the interaction-induced modifications of the cavity modes. As the former method depends crucially on the concrete shape of the trapping potential and the spatial resolution of the used camera, interferometric methods promise more precise measurements. To this end, the present paper works out the impact of the photon-photon interaction upon the cavity modes. A quantum mechanical description of the photon-photon interaction, including the thermal cloud, builds the theoretical backbone of the method. An exact diagonalisation approach introduced here exposes how the effective photon-photon interaction modifies both the spectrum and the width of the photon gas. A comparison with a variational approach based on the Gross-Pitaevskii equation quantifies the contribution of the thermal cloud in the respective applications.