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Quantum Electronics

Dependence of emergence of the collapse and revival effect of Doppler — Rabi osciallations on the initial state of the moving-atom — electromagnetic-field system

A. V. Kozlovskiĭ

Published May 26, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qe2010v040n03abeh014270

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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.
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.
Dynamics of a two-level atom moving in an electromagnetic field is studied. The atomic motion gives rise to a momentum-dependent detuning which holds back the atomic transition, and leads to a momentum-dependent Rabi oscillation which causes an overlapping among different Rabi oscillations. When the field is in a Fock state, the atomic population and the mean momentum of the atom exhibit damping oscillation, the damping rate is related to the momentum distribution; the collapse-revival phenomena of the atomic population and the mean momentum will occur if the atomic momentum has some special distribution. When the field is in a superposition state, the collapse-revival phenomena are modified by the atomic momentum distribution and disappear for the wider atomic momentum wavepackets. We also find that each atomic level will split into two sublevels with the same energy difference when the field is in a Fock state and the atom has a definite momentum.
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 dynamics of a degenerate two-mode electromagnetic field coupled to a single two-level atom is investigated both analytically and numerically. New quantum effects are discussed concerning the time dependence of the photon number and of its fluctuations, assuming that at t = 0 one of the modes is coherent and the other is empty. The field dynamics are dominated by oscillatory net exchanges of a large number of photons between the two modes, displaying amplitude decay. Over a longer time scale, revivals and collapses in the field populations take place. The time scales of these phenomena are much larger than those of the atomic Rabi oscillations decay. Moreover, the system attains a highly non-classical regime in which the field intensity in each mode is subjected to strong fluctuations even for a large initial number of photons in the coherent mode. Various correlations between atomic and field dynamics are pointed out, and the physical origin of the new quantum effects is briefly discussed. Finally, using our fully quantized calculations, we comment on the validity of the atomic homodyne detection proposed by Wilkens and Meystre.