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Physical Review A

Stochastic fluctuations in the Jaynes-Cummings model

S. V. Lawande, Amitabh Joshi

Published Aug 1, 1994• 10 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 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.

DOI
10.1103/physreva.50.1692

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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 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.
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.
A system of N identical superimposed two-level atoms (the Dicke model) interacting with one another and driven by a fluctuating laser field of finite phase and amplitude bandwidths is considered. An exact master equation for the phase-averaged reduced atomic density operator is derived using the theory of multiplicative stochastic processes. It is shown that in the absence of amplitude fluctuations, this equation admits an exact steady-state solution. The exact solution is further used to obtain and analyse the behaviour of the phase-averaged atomic observables and atomic correlation functions in the steady state. The principal results of our analysis is that the phase fluctuations tend to smooth the discontinuities in the observables and the correlation functions found in the non-fluctuating case. Further, including the amplitude fluctuations as well we derive in the high-field limit a Markovian master equation for the density operator averaged over the ensembles of both phase and amplitude fluctuations. The quantum regression theorem is used to derive and discuss exact analytical expressions for the fluorescent spectrum and the second-order intensity correlation function for a system of two interacting atoms.
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.
Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.
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.