ar X iv : q ua nt - p h / 99 02 07 0 v 1 2 3 Fe b 19 99 Statistics of the single mode light in the χ ( 3 ) transparent medium

Statistics of the single mode light in the χ Abstract The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated,namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Plank equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics. Inroduction Four-wave-mixing processes (FWM) are of particular interest for the study of nonclassical states of the light as predicted by Yuen and Shapiro [1] and observed by Slusher et al. [2]. The quantum theory of FWM is based on two general approaches. The first is the Effective Hamiltonian Approach (EHA) when a nonlinear medium is described by a c-number coupling constant in an effective Hamiltonian of interaction. The starting point of the second approach is the master equation for the field obtained by adiabatic elimination of the atomic variables. EHA has been used to consider the time evolution of the number of optical systems [3]. Loudon et al have developed the quantum theory of propagation of the light and examined squeezing produced by self-phase modulation in fiber and in the nonlinear Saqnac interferometer with the help *