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Journal of Modern Optics

Effects of Atomic Coherence on Collapses and Revivals in the Binomial State of the Field

Amitabh Joshi, Ravinder Rupchand Puri

Published May 1, 1989• 50 citations
Publisher

Abstract

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.

DOI
10.1080/09500348914550671

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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 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.
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.
Collapse and revival of the Doppler-Rabi oscillations of a two-level atom moving in a cavity electromagnetic field are analyzed. The coupled atom-field dynamics are predicted accurately by numerical calculation and approximately by using the stationary phase approximation combined with the Poisson summation formula. The collapse and revival patterns are shown to be qualitatively different in the cases of moving atom and atom at rest. In particular, quantum revivals of Doppler-Rabi oscillations occur with a period determined by the Doppler shift of the atomic transition frequency. This regime of Doppler-Rabi oscillations requires that the Rabi frequency and the Doppler shift satisfy the condition Ω R ≪ Ω D . Under the inverse relation, the collapse- revival phenomenon generally does not occur. It is shown that even a small amount of atom-cavity detuning eliminates collapse-revival behavior. The analysis is performed for both coherent and thermal cavity fields.
The quantum dynamics of a system consisting of a moving two-level atom and a single-mode electromagnetic field in the standing-wave resonator is studied by using the stationary phase approximation. The conditions resulting in the emergence of the collapse — revival effect of Doppler — Rabi oscillations are analysed for the initial coherent state of the electromagnetic field in the resonator. It is shown that both the character and the possibility of this effect emergence directly depend on the initial parameters of the system: the rate of the atomic centre-of-mass motion, coupling constants of the atom with the field, the mean number of photons in the resonator. Under conditions when the collapse — revival effect is absent, the system dynamics qualitatively depends on the intial electronic state of the atom.