Dynamics of Phase Coherence Onset in Bose Condensates of Photons by Incoherent Phonon Emission

Recent experiments with photons equilibrating inside a dye medium in a cavity have raised the question of whether Bose condensation can occur in a system with only incoherent interaction with phonons in a bath but without particle-particle interaction. Analytical calculations analogous to those done for a system with particle-particle interactions indicate that a system of bosons interacting only with incoherent phonons can indeed undergo Bose condensation and furthermore can exhibit spontaneous amplification of quantum coherence. We review the basic theory for these calculations.