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Physica Scripta

Two-photon Jaynes–Cummings model in Kerr-like media

N. Patargias, Vasileios Bartzis, A. D. Jannussis

Published Nov 1, 1995• 3 citations
Publisher

Abstract

In the present paper are found the solution of a model-Hamiltonian that describes the three-level two cavity mode Jaynes–Cummings model in Kerr-like media (nondegenerate case). Finally we calculate atom level populations as well as squeezing for the quadrature components of the cavity modes and of the total field.
DOI
10.1088/0031-8949/52/5/011

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An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.
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.
The cavity field spectra for various initial fields of a nondegenerate two-photon Jaynes-Cummings Model are investigated. It is shown that the two-peak structure due to the resonant interaction between a single two-level atom and two different mode fields inside a high-Q cavity persists for coherent and thermal cases. Moreover, coherent sidebands appear for a coherent field whose widths are governed by the field statistics. However, squeezed vacuum fields exhibit rather different features showing the classical resonance fluorescence spectra at large n\ifmmode\bar\else\textasciimacron\fi{} (even in two-photon transitions).
The dynamics of the Q-function for a two-level system coupled to one-cavity mode (Jaynes-Cummings model) in the presence of a Kerr-like medium is investigated. Starting the field mode in a coherent state and the atom in its upper state, the Q-function splits into distinct distribution functions as in the case of the Jaynes-Cummings model. In addition to this splitting the Kerr medium introduces an additional rotation and broadening of the counter-rotating contributions to the Q-function. It is further shown that the discrete superpositions of coherent states produced by the Kerr medium split into additional peaks is due to atomic coupling.
We present the dynamics of nondegenerate as well as degenerate two-photon processes in a three-level Rydberg atom interacting with the eigenmodes of an ideal cavity. For large one-photon detuning, the results are compared with those obtained from an effective Hamiltonian and are found to be mostly different. However, for atom–field interaction times that are comparable with that in the two-photon micromaser experiment, the two models give similar results. We also discuss the time evolution of squeezing in the individual fields in the non-degenerate case. If the two modes are of frequencies ωf + ɛ and ωf − ɛ with ɛ ≪ ωf, the radiation field can be represented by a wave of frequency ωf with amplitudes modulated at ɛ. We find squeezing in the dynamical evolution of these amplitudes.