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Annales de Physique

Phase Properties of Multiphoton Jaynes-Cummings Model

A.M. Abdel-Hafez, A.‐S. F. Obada, A. H. Essawy

Published Jan 1, 1995• 6 citations
Publisher

Abstract

The multiphoton Jaynes-Cummings model is analyzed for phase properties of a coherent field state. The phase variances tend to the values for a field with a randomly distributed phase of one-photon Jaynes-Cummings model and the off-resonant two-photon Jaynes-Cummings model. Revival of oscillations in the far off-resonant two-photon Jaynes-Cummings model occur much later. On the other hand, the variance of the on-resonant two-photon Jaynes-Cummings model variances oscillate periodically.

DOI
10.1051/anphys:199501002

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The multiphoton Jaynes-Cummings model is analyzed for phase properties of a coherent field state. The phase variances tend to the values for a field with a randomly distributed phase of one-photon Jaynes-Cummings model and the off-resonant two-photon Jaynes-Cummings model. Revival of oscillations in the far off-resonant two-photon Jaynes-Cummings model occur much later. On the other hand, the variance of the on-resonant two-photon Jaynes-Cummings model variances oscillate periodically.
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.
In this paper, we study a Jaynes-Cummings model (JCM) with phase damping, by introducing a master equation describing phase damping under the Markovian approximation. With the help of the superoperator technique, we find an analytic solution of the master equation for a nonresonant multiphoton JCM with phase damping. We investigate the influence of phase damping on nonclassical effects in the JCM, such as revivals of the atomic inversion, oscillations of the photon-number distribution, the quadrature squeezing of the cavity field, and sub-Poissonian photon statistics. It is shown that phase damping suppresses the revivals of the atomic inversion and nonclassical effects of the cavity field in the JCM.
An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.
With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.
Using the multiphoton Jaynes-Cummings model,the dynamical properties of the fidelity of quantum states in the system that consists of a two-level atom interacting with a single-mode field via multiphoton transition are studied.The frequency of the field varying with time in the form of sine is considered.The results obtained by numerical calculations show that the time-evolution behavior of the fidelities of field and system is not influenced by the frequency variation of field,but the time-evolution behavior of the fidelity of atom is modulated by the frequency variation of field.The larger the amplitude of the field frequency variance u is,the stronger modulation interaction of the field frequency variance is.When the amplitude u is larger than a fixed value,the time-evolution behavior of the fidelity of atom will display quasiperiodic oscillation behavior.Its oscillation period is in agreement with the period of frequency varying.The initial state of atom influences the time-evolution behavior of the fidelity of atom.