Quantum statistics of optical parametric processes with squeezed reservoirs

Quantum statistics including joint photon-number and integrated-intensity probability distributions are derived in time evolution of general optical parametric process involving processes of frequency conversion, parametric amplification and subharmonic generation taking into account losses and noise described by squeezed reservoirs. Using these tools quantum entanglement of modes is considered and the other nonclassical properties of the process under discussion are demonstrated by means of conditional probability distributions and their Fano factors, difference-number probability distributions, quantum oscillations, squeezing of vacuum fluctuations and negative values of the joint and difference wave probability quasidistributions. Nonclassical properties are illustrated for spontaneous process as well as stimulated process by means of chaotic light and squeezed vacuum field. Multimode processes are investigated in the spirit of the Mandel-Rice photocount formula.