Interactions in dye-microcavity photon condensates and the prospects for their observation

TL;DR

This paper develops a theoretical framework for photon Bose-Einstein condensates in dye-microcavities, highlighting their interactions and proposing experimental methods to measure these interactions with high precision.

Contribution

It derives a Gross-Pitaevskii-like equation for photon condensates considering realistic effects and suggests a novel spectroscopic approach to measure photon-photon interactions.

Findings

Equation of motion similar to Gross-Pitaevskii equation

Incoherent photoluminescence spectrum reveals Bogoliubov excitations

Proposed measurement can resolve interaction parameters two orders below current estimates

Abstract

We derive the equation of motion for a Bose-Einstein condensate of photons in a dye-microcavity system, starting from Maxwell's equations. Our theory takes into account mirror shape, Kerr-type intensity-dependent refractive index and incoherent pumping and loss. The resulting equation is remarkably similar to the Gross-Pitaevskii equation for exciton-polariton condensates, despite the different microscopic origins. We calculate the incoherent photoluminescence spectrum of the photon condensate which shows the Bogoliubov-type excitations around the mean-field at thermal equilibrium. Both open and closed-system models are presented to account for, respectively dissipation and inhomogeneities. Considering realistic parameters and experimental resolution, we estimate that by observing the angle-resolved spectrum of incoherent photoluminescence it is possible to resolve dimensionless interaction parameters of order $10^{-5}$, two orders of magnitude below current estimates. Thus we expect that this technique will lead to accurate measurements of the interactions in photon condensates.