An exact solution of the master equation for the three-photon hyper-Raman process is obtained by a matrix method. Several cases of the photon statistics are considered and the appearance of photon-antibunching effect and the violation of the classical Cauchy inequality are discussed.
Exact solutions of the master equations which describe single-mode m-photon absorption and m-photon emission processes in a two-level atomic system are obtained using a density-matrix approach. Some aspects of the photon statistics, e.g., antibunching, are discussed.
An initially prepared coherent state coupled to a second-order nonlinear medium is responsible for stimulated and spontaneous hyper Raman processes. By using an intuitive approach based on perturbation theory, the Hamiltonian corresponding to the hyper Raman processes is analytically solved to obtain the temporal development of the field operators. It is true that these analytical solutions are valid for small coupling constants. However, the interesting part is that these solutions are valid for reasonably large time. Hence, the present analytical solutions are quite general and are fresh compared to those solutions under short-time approximations. By exploiting the analytical solutions of field operators for various modes, we investigate the squeezing, photon antibunching and nonclassical photon statistics for pure modes of the input coherent light responsible for hyper Raman processes. At least in one instance (stimulated hyper Raman processes for vibration phonon mode), we report the simultaneous appearance of classical (photon bunching) and nonclassical (squeezing) effects of the radiation field responsible for hyper Raman processes.
In this paper we propose the model interaction Hamiltonian which takes in-to consideration the four photon process in interaction of dressed field with 39K atoms. Using the method of elimination of virtual states, we obtain this the effective interaction Hamiltonian which describe the simultaneously generation of photon pairs. The master equation for laser field is obtain, taking into account the good cavity limits in the process of two photon generation. The steady state solution of this equation for threshold case, which takes in to account the quantum fluctuation and photon statistics, is proposed. The cross-correlation function between Stokes and anti-Stokes photon pairs is studied as function of the evolution of the system.
The photon statistic of two-photon processes is treated for the general case of two-level systems. After generalizing the generating-function method, we derived the generating function with parameter r (atomic population ratio), its partial differential equation, and equations of factoril moments as well as equations of correlation functions. Analytical solutions were obtained for various values of r. Curves of n and g(2) versus τ and r were deduced for three kinds of initial fields. Both the effect of r on photon antibunching and characteristics photon statistics for two-photon amplifiers are discussed. The photon superbunching is proposed as one of the criteria for two-photon amplification.