Exact quantum treatment of the parametric chi(3)-interaction
Gagik Yu. Kryuchkyan, Karen V. Kheruntsyan, Valeri O. Papanyan, K.G. Petrossian · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · 1995
We present an exact quantum treatment of intracavity parametric four-wave mixing accompanied by self- and cross-phase modulation effects. A steady-state solution of the Fokker-Planck equation in a generalized P-representation is found for a generated signal mode. A general expression for arbitrary moments of the signal field operators is obtained and qualitative effects caused by non-linear treatment of quantum fluctuations are discussed. The behaviour of the exact steady-state intensity, as well as of the second-order correlation function and of the photon number fluctuations of the signal mode, is studied. A sub-Poissonian photon statistic is found in the above-threshold region and a critical increase in the photon number fluctuations is shown in the transition region for the case of relatively small non-linearities. Characteristic properties of the threshold behaviour are discussed in the case of large non-linearities.