The temporal coherence of a photon condensate: A quantum trajectory description.

A fully quantum-mechanical model is developed to describe the dynamics of a dye-cavity photonic condensate. The effects of driving-dissipation and Kerr interactions on the number fluctuations are studied analytically and numerically, including a long-$\tau$ antibunching effect. Depending on the interaction strength, we quantitatively observe an exponential Schawlow-Townes-like decay or Gaussian Henry-like decay of phase correlations. A heuristic phasor model originating from laser physics is demonstrated to be valid for the description of number and phase dynamics within the experimentally relevant parameter regime. The ratio of the first and second order coherence times is shown to be inversely proportional to the number fluctuations, with a prefactor that varies smoothly throughout the crossover between canonical and grandcanonical statistics.