On Bose-Einstein condensation and superfluidity of trapped photons with coordinate-dependent mass and interactions

The condensate density profile of trapped two-dimensional gas of photons in an optical microcavity, filled by a dye solution, is analyzed taking into account a coordinate-dependent effective mass of cavity photons and photon-photon coupling parameter. The profiles for the densities of the superfluid and normal phases of trapped photons in the different regions of the system at the fixed temperature are analyzed. The radial dependencies of local mean-field phase transition temperature $T_c^0 (r)$ and local Kosterlitz-Thouless transition temperature $T_c (r)$ for trapped microcavity photons are obtained. The coordinate dependence of cavity photon effective mass and photon-photon coupling parameter is important for the mirrors of smaller radius with the high trapping frequency, which provides BEC and superfluidity for smaller critical number of photons at the same temperature. We discuss a possibility of an experimental study of the density profiles for the normal and superfluid components in the system under consideration.