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Journal of Modern Optics

Quantum Electrodynamics of a Rydberg Atom Making Two-photon Transitions in the Binomial State of the Field in a Lossless Cavity

Amitabh Joshi, Ravinder Rupchand Puri

Published Feb 1, 1989• 23 citations
Publisher

Abstract

The dynamic and statistical properties of a system of an effective two-level atom making two-photon transitions in the binomial state of the field in a lossless cavity are discussed. The binomial state enables the study of the development of the phenomenon of collapses and revivals of the Rabi oscillations as the field state is changed from a pure number state to a coherent state. This is because the binomial state, which is a pure number state in one limit, develops into a coherent state as some parameters are changed appropriately. The effect of Stark shifts arising due to the transitions to virtual levels are also investigated.

DOI
10.1080/09500348914550261

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The dynamic and statistical properties of a system of an effective two-level atom making two-photon transitions in the binomial state of the field in a lossless cavity are discussed. The binomial state enables the study of the development of the phenomenon of collapses and revivals of the Rabi oscillations as the field state is changed from a pure number state to a coherent state. This is because the binomial state, which is a pure number state in one limit, develops into a coherent state as some parameters are changed appropriately. The effect of Stark shifts arising due to the transitions to virtual levels are also investigated.
The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.
It is shown that a single atom making two-photon transitions in an ideal cavity (Q = ∞) in the presence of an initial coherent state field will, as expected, continue to show the collapses and revivals of atomic inversion and the intensity–intensity correlation of the field; however, these collapses and revivals are both compact and regular, in contrast to the one-photon case. This is because, although the several Rabi frequencies involved are incommensurate, for the two-photon case, unlike for the one-photon problem, they become commensurate in the limit of intense field. We derive analytic expressions for the atomic inversion and the intensity–intensity correlation in the case of direct, as well as homodyned, detection of the intracavity field. The effects of the Stark shift are discussed.
The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.
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.