Classical-field description of Bose-Einstein condensation of parallel light in a nonlinear optical cavity

We study the Bose-Einstein condensation of parallel light in a two-dimensional nonlinear optical cavity, where the massive photons are converted into photon molecules (p-molecules). We extend the classical-field method to provide a description of the two-component system, and we also derive a coupled density equation which can be used to describe the conversion relation between photons and p-molecules. Furthermore, we obtain the chemical potential of the system, and we also find that the system can transform from the mixed photon and p-molecule condensate phase into a pure p-molecule condensate phase. Additionally, we investigate the collective excitation of the system. We also discuss the problem how the spontaneous decay of an atom is influenced by both the phase transition and collective excitation of the coupling system.