Quantum-classical correspondence in dissipative optical systems with limit cycle

Summary form only given. The situation when nonlinear interactions involve a large number of photons, N, is quite typical of many of the problems of quantum and nonlinear optics. To describe the dynamics of such quantum systems a classical approach is often used. In this theoretical work we compare classical and quantum dynamics of several dissipative quantum optical systems, which have a limit cycle in the classical limit N/spl rarr//spl infin/. In particular, we consider the dynamics of intracavity second harmonic generation (SHG) described by the Hamiltonian.