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Acta Physica Sinica

THE QUANTUM STATISTICAL PROPERTIES OF THE JAYNES-CUMMINGS MODEL

GU QIAO, 西北大学物理系

Published Jan 1, 1989• 0 citations
Publisher

Abstract

We derive a set of equations characterizing the quantum statistical properties of Jaynes-Cummings model, which may be used to describe overall the dynamical and statistical aspects in the interaction between a two-level atom and a single mode of the radiation field. Both interactions of a two-level atom with a vacuum field and a excited atom with a coherent field, as examples, are discussed in detail. Finally, the practicality of the above-mentionedi theoretical studies is demonstrated.

DOI
10.7498/aps.38.735

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We derive a set of equations characterizing the quantum statistical properties of Jaynes-Cummings model, which may be used to describe overall the dynamical and statistical aspects in the interaction between a two-level atom and a single mode of the radiation field. Both interactions of a two-level atom with a vacuum field and a excited atom with a coherent field, as examples, are discussed in detail. Finally, the practicality of the above-mentionedi theoretical studies is demonstrated.
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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 interaction between the pair of cold two-level atoms and the single-mode cavity field is investigated. The two-level atoms in the pair are supposed to be indistinguishable. This problem generalizes the two-photon Jaynes-Cummings model of a single two-level atom interacting with the squeezed vacuum. The model of the pair of indistinguishable two-level atoms is equivalent to the problem of the equidistant three-level radiator with equal dipole moment matrix transition elements between the adjacent energy levels. Supposing that at the initial moment the field is in the squeezed vacuum state we obtain the exact analytical solution for the atom-field state-vector. By using this solution the quantum-statistical and squeezing properties of the radiation field are investigated. The obtained results are compared with those for the single two-level atom system. We observe that in the model of the pair of cold two-level atoms the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one.