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Physical Review A

Quantum behavior of a two-level atom interacting with two modes of light in a cavity

Shih-Chuan Gou

Published Nov 1, 1989• 127 citations
Publisher

Abstract

A generalized Jaynes-Cummings model is investigated where the transition is mediated by two different modes of photons. For different types (uncorrelated and correlated) of field states, the dynamical behavior of the generalized Jaynes-Cummings model exhibits very different aspects. With the high-Q limit, the effects of cavity damping in the presence of correlated field states are also considered.

DOI
10.1103/physreva.40.5116

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A generalized Jaynes-Cummings model is investigated where the transition is mediated by two different modes of photons. For different types (uncorrelated and correlated) of field states, the dynamical behavior of the generalized Jaynes-Cummings model exhibits very different aspects. With the high-Q limit, the effects of cavity damping in the presence of correlated field states are also considered.
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A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.
We study the quantum dynamics of a two-mode two-photon Jaynes–Cummings model of a two-level atom interacting with the correlated two-mode SU(1, 1) coherent states. The collapse and revival patterns in this case are noted to be quite different from those in the case of uncorrelated coherent states and correlated pair-coherent states. As an example of the time evolution of the field statistics we show that violation of the Cauchy–Schwartz inequality by the initial field states may be nullified. We also discuss the evolution of the variance of the two-mode field quadrature operator.
The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.