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Physical Review A

Characteristic oscillations of phase properties for pair coherent states in the two-mode Jaynes-Cummings-model dynamics

Shih-Chuan Gou

Published Oct 1, 1993• 24 citations
Publisher

Abstract

The phase properties of pair coherent states in the two-mode Jaynes-Cummings model are investigated based on the Pegg-Barnett phase formalism. The general expressions of the properties for the phase-sum operator of the two correlated fields are presented, in which the Stark shifts are considered. Analytic results are given in the strong-field approximations. It is found that the phase properties such as the variance of the phase-sum operator and the variances of the cosine and the sine of the phase-sum operator exhibit characteristic periodic oscillations in which the period is determined solely by the Stark shifts.

DOI
10.1103/physreva.48.3233

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The phase properties of pair coherent states in the two-mode Jaynes-Cummings model are investigated based on the Pegg-Barnett phase formalism. The general expressions of the properties for the phase-sum operator of the two correlated fields are presented, in which the Stark shifts are considered. Analytic results are given in the strong-field approximations. It is found that the phase properties such as the variance of the phase-sum operator and the variances of the cosine and the sine of the phase-sum operator exhibit characteristic periodic oscillations in which the period is determined solely by the Stark shifts.
It is pointed out here that quantum phase properties, as well as dynamical properties, of light exhibit a sensitivity to the relative phase between the atomic dipole and light when the atom is prepared in a coherent superposition of its states in the two-level Jaynes-Cummings model interacting with a coherent state of light. The existence of the coherent-trapping of light is demonstrated by looking not only at the variance of the light phase about the coherent state value, and the number-phase uncertainty relation, but also at the factorization of the electric-field operator, and the photon-number distribution. We find also the factorization expression of the compound state of the atom-field system. We show once more that the phase properties of light based on the phase operator formalism of Pegg-Barnett and the coherence properties of light based on the coherence theory of Glauber are complementary in description of the optical quantum coherence.
In this paper we investigate the phase and coherence properties of the field in the nonresonant Jaynes-Cummings model. We find the phase distribution to be split into four separate asymmetrically peaked functions. We also find, in the large-detuning limit, that the coherence properties of an originally coherent field occur periodically. We conclude that the phase formalism of Pegg and Barnett [Europhys. Lett. 6, 483 (1988)] and the coherence theory of Glauber [Phys. Rev. 130, 2529 (1963)] are complementary.
A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.