Temporal coherence of a photon condensate: A quantum trajectory description

Abstract

In order to study the temporal coherence of a single-mode dye-cavity photon condensate, a model is developed for the dynamics which treats the condensate mode on a quantum-mechanical level. The effects of driving-dissipation and Kerr interactions on the number fluctuations are studied analytically and numerically, including the finding of a long-τ antibunching effect. Depending on the interaction strength, we quantitatively observe an exponential Schawlow-Townes-like decay or Gaussian Henry-like decay of phase correlations. The adequacy of a heuristic phasor model originating from laser physics in describing the number and phase dynamics is validated 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 grand-canonical statistics.