Dimensional Crossover of Photon Bose-Einstein Condensates

In recent years the phenomenon of equilibrium Bose-Einstein condensation (BEC) of photons has been studied extensively also within the realm of non-equilibrium condensation. At its core this system consists of a dye solution filling the microcavity in which the photons are trapped. Due to cyclic absorption and reemission 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 [1]. This talk focuses on the theoretical description of a dimensional crossover from a two-dimensional photon BEC to a one-dimensional photon gas. To this end we extend the semiclassical mean-field equations for a photon BEC [2] by including the matter degrees of freedom. Our special focus lies on the effect of the retarded photon-photon interaction on the dimensional crossover, which we study for a anisotropic box potential. Finally, we characterise the steady state of the resulting one-dimensional photon gas.\\ [1] Kl\"ars et al., Appl. Phys. B \textbf{105}, 17 (2011)\\ [2] Stein et al., New J. Phys. \textbf{21}, 103044 (2019)