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Journal of Modern Optics

Numerical study of squeezing in the Jaynes-Cummings model with and without the rotating wave approximation

Rui‐Hua Xie, Tie-Jun Zhout, Qin Rao

Published Feb 1, 1996• 2 citations
Publisher

Abstract

Dipole squeezing in the Jaynes-Cummings model with and without the rotating wave approximation (RWA) has been numerically studied when restricted to the following initial conditions: the field in the superposition of the vacuum and one-photon state, and the atom in the ground state. Numerical results show that even if under the condition for which the RWA is considered to be valid, there is a significant effect caused by the virtual-photon field on the dipole squeezing; in the cases of sufficiently strong coupling of the atom-field interaction, the interference between the virtual-photon processes and the real-photon processes quenches the dipole squeezing.

DOI
10.1080/09500349608232746

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Dipole squeezing in the Jaynes-Cummings model with and without the rotating wave approximation (RWA) has been numerically studied when restricted to the following initial conditions: the field in the superposition of the vacuum and one-photon state, and the atom in the ground state. Numerical results show that even if under the condition for which the RWA is considered to be valid, there is a significant effect caused by the virtual-photon field on the dipole squeezing; in the cases of sufficiently strong coupling of the atom-field interaction, the interference between the virtual-photon processes and the real-photon processes quenches the dipole squeezing.
Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in the vacuum field Jaynes–Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initially prepared in the coherent state, and photon antibunching can occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (RWA). We have shown that even under the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was also studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nonclassical features disappear in the cases far from the integrable limits.
We have studied the squeezing properties of a field and atom in a two-level system. The influence of nonlinear interactions (Le. the arbitrary intensity-dependent coupling of a single-mode field to a single two-level atom, the nonlinear interaction of the field with a nonlinear Kerr-like medium) on the squeezing is discussed in detail in the rotating wave approximation (RWA). We show numerically that the effect of the virtual-photon field suppresses dipole squeezing predicted in the RWA and leads to an increased squeeze revival period; the suppressed squeezing can be revived due to the presence of the nonlinear Kerr-like medium.
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.