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 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 grandcanonical statistics.

Featured Application: nonlinear; driven-dissipative; photonic cavity; optical bistability and dephasing.Abstract: We construct a class of variational methods for the study of open quantum systems based on Gaussian ansatzes for the quantum trajectory formalism. Gaussianity in the conjugate position and momentum quadratures is distinguished from Gaussianity in density and phase. We apply these methods to a driven-dissipative Kerr cavity where we study dephasing and the stationary states throughout the bistability regime. Computational cost proves to be similar to the Truncated Wigner Approximation (TWA) method, with at most quadratic scaling in system size. Meanwhile, strong correspondence with the numerically-exact trajectory description is maintained so that these methods contain more information on the ensemble constitution than TWA and can be more robust.

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Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finitesize scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with z ≈ 2.18 corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.