Hamiltonian Formulation of Thermo-Optic Photon-Photon Interaction in Photon BECs*

Since the discovery of photon Bose-Einstein condensates in 2010 [1] this phenomenon has been studied extensively. At its core, this system consists of a dye solution filling the microcavity in which the photons are trapped. Due to cyclic absorption and re-emission processes of photons, the dye leads to a thermalisation of the photon gas at room temperature and finally to its Bose-Einstein condensation. Because of a non-ideal quantum efficiency, those cycles yield in addition a heating of the dye solution, which results in an effective photon-photon interaction [2].

In this talk, we focus on the Hamiltonian description of the effective photon-photon interaction, which allows to include the thermal cloud into the description. By utilising an Exact Diagonalisation approach, we work out how the effective photon-photon interaction modifies the spectrum of the photon gas. As a second case study, we apply our theory to the dimensional crossover from 2D to 1D [3]. In this scenario, we especially focus on the contribution of the thermal cloud and a subsequent comparison with from the Gross-Pitaevskii theory.

[1] J. Klaers, et al., Nature 468, 545 (2010) 

[2] E. Stein, et al., New J. Phys. 21, 103044 (2019)

[3] E. Stein, et al., New J. Phys., in press (2022)