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Communications in Theoretical Physics

Study of Nonclassical Features and Quantum Dynamics in the Jaynes-Cummings Model Without RWA

Rui-hua Xie, Gong-ou Xu, Dun-huan Liu

Published Jun 15, 1997• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0253-6102/27/4/385

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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.
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.
The dynamics of the driven Jaynes-Cummings model where a two-level atom is coupled to a single mode of cavity fields and is driven by an external coherent field is investigated. We find that in this model quantum collapse and revivals of the atomic population inversion and squeezing of the cavity field can be generated from a thermal photon state. We also notice that the squeezing is very sensitive to the mean number of thermal photons initially in the cavity, but the quantum collapse and revivals are not. The influence of the amplitude of the driving field and various detuning parameters on the nonclassical effects is discussed. The result shows that one can use the external field to control nonclassical effects in the Jaynes-Cummings model.
In this paper, we study the multiphoton Jaynes-Cummings model (JCM) governed by the Milburn equation [G. J. Milburn, Phys. Rev. A 44, 5401 (1991); 47, 2415 (1993)], which models the decoherence of a quantum system as the quantum system evolves through intrinsic mechanisms beyond conventional quantum mechanics. We give an exact solution of this equation for the multiphoton Jaynes-Cummings Hamiltonian and apply it to investigate the influence of the intrinsic decoherence on nonclassical effects (atomic inversion, oscillations of the photon-number distribution, squeezing of the cavity field, and photon antibunching) in the JCM. It is shown that during the time evolution, the intrinsic decoherence in the atom-field interaction suppresses these nonclassical behaviors in the JCM.
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.
The Jaynes–Cummings model (JCM) is used to give a detailed analysis of the long-time behavior of a two-level atom interacting with a (Glauber) coherent-state field. This work is based on the earlier work of J. H. Eberly and collaborators, who drew attention to the collapse and revival of the Rabi oscillations of the atomic inversion. We use the three components S1, S2, and S3 of the pseudospin vector S to analyze the dynamics of the atom within the rotating-wave approximation and exact resonance. We show that, at the times when the revivals peak, the variables σ = |S| and η = S3/σ become independent of (1) the transition dipole moment of the atom, (2) the intensity of the coherent-state field, and (3) the (common) frequency of the atom and the field. Thus these special values of σ and η are a universal feature of the JCM that should be observed in experiments with any two-level atom in an arbitrarily intense (but resonant) coherent-state field. The derivation of the above results was facilitated by transforming into a rotating coordinate frame in which S1 = 0 so that S2 and S3 are the only dynamical variables. The two-dimensional nature of S in this frame makes it easy to visualize the dynamical changes in the atom. The dynamics of the JCM is clarified by comparison with the closely related Buck–Sukumar model. The relationship of the phenomena discussed here to photon echoes and to quench echoes (in condensed media) is pointed out.