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We analyze the non-equilibrium dynamics of a gas of interacting photons in anarray of coupled dissipative nonlinear cavities driven by a pulsed externalcoherent field. Using a mean-field approach, we show that the system exhibits aphase transition from a Mott-insulator-like to a superfluid regime. For a givensingle-photon nonlinearity, the critical value of the photon tunneling rate atwhich the phase transition occurs increases with the increasing photon lossrate. We checked the robustness of the transition by showing its insensitivityto the initial state prepared by the the pulsed excitation. We find that thesecond-order coherence of cavity emission can be used to determine the phasediagram of an optical many-body system without the need for thermalization.

Signatures of the super fluid-insulator phase transition in laser driven dissipative nonlinear cavity arrays