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Communications in Theoretical Physics

A Possible Generalization of Jaynes–Cummings Model with Degenerate Spectrum

Wu Qiang, Fan Hong-Yi

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We propose a generalized Jaynes–Cummings model (JCM) for three two-level atoms and three-mode radiation field with the interaction being . This model is characteristic of possessing partly degenerate spectrum. Some transition process of this system is calculated.
DOI
10.1088/0253-6102/13/1/113

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One of the simplest models for the interactions between an atom and a quantized electromagnetic field is known as the Jaynes-Cummings model GCM) [1]. In this model, the atom is assumed to have two levels, and the electromagnetic field is a single mode. For the past several years, we have investigated the model for the singlephoton, the two-photon, and the multi-photon cases. First, we studied the characteristic functions and their time behaviors for a simple JCM[Z] using the density matrix approach, and then, by using the Heisenberg equation method, we exmined the degenerate two-photon JCM[31, where the operator differential equations and their solutions are obtained. We further studied the cases of the non-degenerate two-photon JCM[4] and the mUlti-photon JCM[51. Moreover, the atomic spectrum for mUlti-photon JCM[61 and the field spectrum for multiphoton JCM[71 were explored, and these spectra were presented in the 3-dimensional pictures. We also solved the degenerate two-photon JCM with Stark-shifts [8] , and further we just published the results of the non-degeneratetwo-photon JCM with Stark-shifts[91. In this paper, we show a derivaition of the product operator alZ ( t ) = al ( t ) az ( t ). We explicitly use the idea of the constant motion operator. Since the derivations are quite complicated and it is not streightword, we showed them in detail here. The present paper is organized as follows. In section II, we show the effective non-degenerate Hamiltonians and the constant of motion operators. In section Ill, the second-order differential equation for a product operator alZ ( t ) = al ( t ) az ( t) of Mode 1 and Mode 2, will
The Jaynes-Cummings model describing the interaction of a single linearly- polarized mode of the quantized electromagnetic field with an isolated two- level atom is generalized to the case of atomic levels degenerate in the projections of the angular momenta on the quantization axis, which is a usual case in the experiments. This generalization, like the original model, obtains the explicit solution. The model is applied to calculate the dependence of the atomic level populations on the angle between the polarization of cavity field mode and that of the laser excitation pulse in the experiment with one-atom micromaser.
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