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Physical Review A

Generalized Jaynes-Cummings model with random telegraph noise

S. V. Lawande, Amitabh Joshi, Q. V. Lawande

Published Jul 1, 1995• 14 citations
Publisher

Abstract

The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in the atom-field coupling. The coupling coefficient is assumed to fluctuate either in phase or in frequency. The fluctuations are modeled by binary random telegraph processes. Invoking the Markovian property of the telegraph noise, we derive in these two cases an equation for the density operator averaged over the distribution of fluctuations. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.

DOI
10.1103/physreva.52.619

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The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in the atom-field coupling. The coupling coefficient is assumed to fluctuate either in phase or in frequency. The fluctuations are modeled by binary random telegraph processes. Invoking the Markovian property of the telegraph noise, we derive in these two cases an equation for the density operator averaged over the distribution of fluctuations. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic phase fluctuations in the atom-field coupling coefficient. The fluctuations are modelled by random telegraph process and an equation for the density operator averaged over the distribution of fluctuations has been obtained. The solution of this equation is used to study the resulting decoherence effects in the dynamical behaviour of the atom and the statistical properties of the field.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in atom-field coupling. The coupling coefficient is assumed to fluctuate in phase and/or in amplitude. The phase fluctuations are described by a Wiener-Levy process and the amplitude fluctuations by a colored Gaussian noise. A secular approximation and the theory of the multiplicative stochastic processes are invoked to derive the master equation for the density operator averaged over both phase and amplitude ensembles. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
In this paper, a system consisting of one atom coupled to two identical optical cavities in a stochastic interaction is investigated for the entanglement properties between the constituents by the Jaynes–Cummings model. The noise is considered to be the random phase telegraph noise and an exact solution of the model under this noise is obtained. The effects of the noise on the entanglement of the system reveal that the genuine three-partite entanglement cannot appear in the evolution of the system even in the presence of the random phase telegraph noise. The fields and the atom do not entangle with each other. However, the noise is cooperative and constructive in building a strong steady state field–field entanglement. Therefore, the separable state of the atom plays the role of a catalyst in the entanglement between the states of the cavity fields.
The entanglement dynamics in a system of the interaction of an atom with a single-mode cavity field in the presence of noise is studied by the Jaynes-Cummings model. Random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained. The obtained solution is used to investigate the entanglement dynamics of the atom-field interaction. The mutual entropy is adopted for the quantification of the entanglement in the interaction. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.