Quantum fluctuations in unstable dissipative systems

We show how quantum instability is displayed in the von Neumann entropy and in the Wigner function. For this purpose, an intracavity second-harmonic generation close to the Hopf bifurcation range is studied. We examine the role of dissipation in unstable dynamics and the formation of the quantum states of the cavity modes, and discuss contrast ensemble behavior with that of individual realization on the basis of a quantum-jump simulation method. Namely, it is found that the Wigner functions for fundamental and second-harmonic modes prepared initially in a vacuum state acquire the three-hump structure due to phase symmetry breaking in the bifurcation range. The time evolution of coherent states leads to long-lived swing of the system between two side humps in a phase space.