Joint probability distributions and entanglement in optical parametric processes

Joint photon-number and integrated-intensity probability distributions are used for description of time evolution of optical parametric process including processes of frequency conversion, parametric amplification and subharmonic generation taking into account losses and noise. Using these tools quantum entanglement of modes based on the separability criteria is considered and 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 wave probability quasidistributions in time evolution. Sub-Poissonian and sub-shot-noise properties are illustrated for spontaneous process and stimulated process by means of chaotic light and squeezed light. Also the multimode processes are investigated in the spirit of the Mandel-Rice photocount formula. The description is applied to interpretation of experimental data.