Quantum-classical transition of photon correlations of two coupled cavities

We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates periodically in time. Coupling between the cavities leads to synchronization of the oscillations and classical correlations between the cavities. In the quantum limit, there are quantum correlations due to entanglement. The quantum correlations persist even when the cavities are far off resonance with each other, in stark contrast with the classical case. We also find that the quantum and classical limits are connected by an intermediate regime of almost no correlations. Our results can be extended to a wide variety of quantum models.