Photon BEC with thermo-optic interaction at dimensional crossover

Abstract

Since the advent of experiments with photon Bose–Einstein condensates (phBECs) in dye-filled microcavities in 2010, many investigations have focussed upon the emerging effective photon–photon interaction. Despite its smallness, it can be identified to stem from two physically distinct mechanisms. On the one hand, a Kerr nonlinearity of the dye medium yields a photon–photon contact interaction. On the other hand, a heating of the dye medium leads to an additional thermo-optic interaction, which is both delayed and non-local. The latter turns out to represent the leading contribution to the effective interaction for the current 2D experiments. Here we analyse theoretically how the effective photon–photon interaction increases when the system dimension is reduced from 2D to 1D. To this end, we consider an anisotropic harmonic trapping potential and determine via a variational approach how the properties of the phBEC in general, and both aforementioned interaction mechanisms in particular, change with increasing anisotropy. We find that the thermo-optic interaction strength increases at first linearly with the trap aspect ratio and later on saturates at a certain value of the trap aspect ratio. Furthermore, in the strong 1D limit the roles of both interactions get reversed as the thermo-optic interaction remains saturated and the contact Kerr interaction becomes the leading interaction mechanism. Finally, we discuss how the predicted effects can be measured experimentally.