| Bose-Einstein Condensation(BEC) is a phenomenon of macroscopic occupation in one or several quantum states by a large number of identical bosons when the temperature of system is below to a critical temperature. Although BEC-like phase transition has been observed in several physical systems, including exciton polaritions, solid quasiparticles and so on, BEC of photons has been a long sought, but elusive goal. The difficulty is that in the usual Planck blackbody configuration, which consists of an empty three-dimensional cavity, the photon is massless and its chemical potential is zero, so that the BEC of photons would seem to be impossible. However, in this paper we propose a new model in which the photon is formally equivalent a general boson having an effective mass and non-vanishing chemical potential. The result also implies a macroscopic accumulation of photons in the minimum of the modes at very low temperature.In this paper, we first theoretically investigate the BEC of photons. Especially, we investigate the excitation spectrum of weakly-interacting photon gas. Additionally, we give the famous Bogoliubov dispersion law for the elementary excitations of the system. We also investigate the influence of the BEC of photons to the decay rate and energy-level shift of an two-level atom. We find that for the atom in the BEC environment, its decay rate and energy-level shift are all temperature dependent. The investigation to these questions is important for its connection with basic quantum physics, and for its practical applications in controlling the decay rate and energy-level shift of the atom.We also propose a new photon-photon pair coupling model. In the model, there exist two possible condensate phases for the mixed gas:the photon pair condensate phase and the mixed photon-photon pair condensate phase. Using variational method, we also discuss the ground-state phase transition of the two-component system, and obtain the critical coupling line analytically. Especially, we find that the phase transition of the photons gas can be interpreted as enhanced second harmonic generation. The energy gap between the ground state and the first excited state is also investigated. Moreover, by investigating the excitation spectrum, we also illustrate the relation between superfluid and phase transition of photons and photons pairs. It is found that for the present system, in the mixed condensate phase there exist three possible superfluid states. It should be mentioned that here the mixed superfluid of photons and photon pairs is essentially a quasi-superfluid state. Furthermore, we also investigate the quantum entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement can be associated with the phase transition of the system. |
