The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties

Abstract

In this paper, we investigate various dynamical properties of the Jaynes–Cummings (JC) model beyond the rotating wave approximation (RWA). We first show that in the absence of the RWA, the JC Hamiltonian can be transformed into an intensity-dependent Hamiltonian. Corrections produced by the counter-rotating terms (CRTs) appear in the first order as the intensity-dependent detuning, i.e. the dynamical Stark shift and in the second order as the intensity-dependent atom–field coupling. Then, by determining the atom–field wavefunction evolution, we study the effects of CRTs on various dynamical properties of the JC model, including the atomic population inversion, atomic dipole squeezing, atomic entropy squeezing, photon counting statistics, quadrature field squeezing, field entropy squeezing and quantum phase properties of the cavity field.