The Degenerate Parametric OscillatorIII: Phase-Space Analysis Outside the Small-Noise Limit

Abstract

The small-noise limit has received a great deal of attention in quantum optics, and not without good reason. Until quite recently, in cases of experimental interest, the system size expansion has always been well justified. In the case of the laser, for example, its validity is governed by the saturation photon number n _sat = γ _h (γ↑ + γ↓)/8g²; for the degenerate parametric oscillator by the threshold pump photon number n^thr _p = (κ/g)². Each of these numbers is determined by the ratio of a dissipation rate and a fundamental coupling constant. When the dissipation rate dominates, the ratio is large; n _sat and n^thr _p are typically on the order of 108 (see the final paragraph of Sect. 7.1.4 and Eq. 10.17).