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Physical Review A

Degenerate and nondegenerate two-mode normal squeezing in a two-level atom and two-mode system

A.M. Abdel-Hafez

Published May 1, 1992• 26 citations
Publisher

Abstract

We investigate the phenomenon of degenerate and nondegenerate two-mode squeezing for a generalized Jaynes-Cummings model with a two-level atom and two modes. The effect of the relative phases between the atomic superposition state and the coherent field on normal squeezing is studied. Different values for the parameters of the atomic coherent state are taken. It is found that the nondegenerate two-mode squeezing is more effective than the one-mode degenerate type, and it recurs at later times.

DOI
10.1103/physreva.45.6610

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Journal of the Optical Society of America B•Aug 1, 1991•26 citations
We investigate the phenomenon of degenerate and nondegenerate two-mode squeezing for a generalized Jaynes-Cummings model with a two-level atom and two modes. The effect of the relative phases between the atomic superposition state and the coherent field on normal squeezing is studied. Different values for the parameters of the atomic coherent state are taken. It is found that the nondegenerate two-mode squeezing is more effective than the one-mode degenerate type, and it recurs at later times.
The nonclassical properties such as antibunching effect,violation of Cauchy-Schwarz inequality and two-mode squeezing of the pair coherent states based on a non-degenerate two-photon Jaynes-Cummings model were investigated.It is shown that these nonclassical properties can be enhanced in the case that the coefficients are chosen appropriately or the atom is selectively detected.In addition,all kinds of the nonclassical properties by using(?)-type three-level atom are more effective than that using i4-type three-level atom.
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.
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.