Intrinsic decoherence effects on quantum dynamics of the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation

Abstract

In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz