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Journal of Optics B Quantum and Semiclassical Optics

Dispersive limit of the dissipative Jaynes–Cummings model with a squeezed reservoir

V. V. Dodonov, Wagner Duarte José, Salomon Sylvain Mizrahi

Published Oct 16, 2003• 11 citations
Publisher

Abstract

We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.

DOI
10.1088/1464-4266/5/6/005

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We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.
We found analytically the exact joint Wigner function (WF) of an atom-field system described by the Jaynes-Cummings model in the dispersive limit for a given initial state. Using the solution of a master equation with a dissipative term calculated by Peixoto de Faria and Nemes (Peixoto de Faria J G and Nemes M C 1999 Phys. Rev. A 59 3918) and a general expression for the joint WF proposed by Czirják and Benedict (Czirják A and Benedict M G 1996 Quantum Semiclass. Opt. 8 975), we obtained the exact reduced atom and field WFs and analysed their time evolution. Our results show that, at the maximum entanglement times, the atom tends to a statistical mixture state represented by a spherical polar plot. Also, the atomic WF shows how fast the negative-valued part disappears as a function of dissipation constant and the strength of the field coherent state.
Time-evolution of the dispersive Jaynes–Cummings model interacting with a bosonic reservoir is considered in the presence of an initial correlation between the cavity field and reservoir. When there is at most one excitation in the whole system, the exact time-evolution can be obtained. The effects of the initial correlation on the decoherence of the two-level system and cavity field are investigated. Furthermore, the validity of the time-convolutionless quantum master equation in the second-order approximation with respect to the system-reservoir interaction is examined by means of the exact solution.
We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes-Cummings model with an intensity-dependent coupling in the dispersive approximation and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.
The full quantum theory is applied to the investigation of the entanglement between atom and field and the losses of coherence of the total system and its subsystems in the Jaynes-Cummings model with a Kerr medium.Linear entropies of the system,the atom and the field are calculated under the assumptions of dispersive atom-field interaction and initial coherent field states.The results show that the coherence loss of the atom is independent of the Kerr effect,the coherence loss of the system and that of the field are enhanced by the presence of the Kerr medium,and the entanglement between atom and field is suppressed by the medium.The time evolution of field entropy is affected by the cavity dissipation qualitatively as well as quantitatively.Only through cavity dissipation can the influence of Kerr effect on field entropy exhibit.
We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes-Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.