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Acta Physica Sinica

PHASE FLUCTUATIONS IN JAYNES-CUMMINGS MODEL WITH AND WITHOUT ROTATION WAVE APPROXIMATION

LI GAO-XIANG, PENG JIN-SHENG, 华中师范大学物理系,武汉430070

Published Jan 1, 1992• 1 citation
Publisher

Abstract

In this paper, we have respectively investigated the time evolution of the phase operator of radiation field in the Jaynes-Cummings model with and without RWA. We verified that the atomic Rabi oscillation leads to the phase dissipation of radiation field by analytical method, and the effect of virtual field can exhibit the quantum fluctuations of system and leads to the frequency shift of radiation field.

DOI
10.7498/aps.41.766

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In this paper, we have respectively investigated the time evolution of the phase operator of radiation field in the Jaynes-Cummings model with and without RWA. We verified that the atomic Rabi oscillation leads to the phase dissipation of radiation field by analytical method, and the effect of virtual field can exhibit the quantum fluctuations of system and leads to the frequency shift of radiation field.
In this paper, we have investigated the time evolution of the phase operator of the radiation field in the Jaynes-Cummings model with and without the rotating-wave approximation, making use of the phase formalism of Barnett and Pegg [J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)]. We verify by an analytical method that the atomic Rabi oscillation leads to phase dissipation of the radiation field, and also that the effect of the virtual-photon field can exhibit quantum fluctuations in the atom-field-coupling system and lead to a frequency shift of the radiation field.
We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes–Cummings (J–C) model. The results show that for resonant case, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.
The significance of the counter-rotating terms in the polyatomic Jaynes-Cummings model with cavity losses is demonstrated. Numerical results for the time evolution of the atomic population inversion and dipole moment for an initial Fock-state field with different photon numbers are presented for various cavity dampings. The appearance of new steady states for the population inversion and the mean-photon number under the influence of the counter-rotating terms is pointed out. Namely, as is shown, the presence of “virtual photons”, produced by the counter-rotating terms, leads to these effects.
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.