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Journal of Experimental and Theoretical Physics

Doppler-Rabi oscillations of a moving atom due to the roentgen interaction in a cavity

A. V. Kozlovskiĭ

Published Sep 1, 2008• 1 citation
Publisher

Abstract

The dynamics of energy exchange between an atom moving in a high-Q cavity and the cavity field is analyzed by taking into account the Roentgen interaction. A two-level atom coupled to a Fock or coherent state of an optical or microwave cavity is considered. The mean cavity photon number required for high-frequency Doppler-Rabi oscillations to occur is relatively high for both Fock-and coherent-state cavity fields and increases with the atomic transition frequency. Conditions are found when the Roentgen interaction plays a key role in the Doppler-Rabi oscillations and must be taken into account, in addition to the conventional electric field-dipole interaction.

DOI
10.1134/s1063776108090021

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The dynamics of energy exchange between an atom moving in a high-Q cavity and the cavity field is analyzed by taking into account the Roentgen interaction. A two-level atom coupled to a Fock or coherent state of an optical or microwave cavity is considered. The mean cavity photon number required for high-frequency Doppler-Rabi oscillations to occur is relatively high for both Fock-and coherent-state cavity fields and increases with the atomic transition frequency. Conditions are found when the Roentgen interaction plays a key role in the Doppler-Rabi oscillations and must be taken into account, in addition to the conventional electric field-dipole interaction.
The interaction of a two-level atom uniformly moving along a classical trajectory with a high-Q cavity quantum mode is analyzed. The dressed-state method is used to derive a recurrence formula for the transition probability of the atom with photon emission; the temporal dynamics of this probability qualitatively depends on the Doppler shift of the atomic transition frequency, on the Rabi frequency of the atom-field system, and on the detuning of the atomic transition frequency from the field mode frequency. The emission dynamics of a moving atom is very sensitive to the detuning. Rabi-type oscillations with a frequency equal to the Doppler shift can arise under certain conditions. At resonance, the emission probability of a moving atom can considerably exceed the emission probability of an atom at rest. A plane-parallel-mirror cavity and a confocal spherical-mirror cavity are considered. It is shown that the peculiarities of Doppler-Rabi oscillations must be taken into account in micromaser theory.
The interaction with a quantum mode of a high- Q cavity is considered for a two-level atom uniformly moving along the classical trajectory. The method of dressed states is employed to deduce the recursion relation for the probability of atomic transition with photon emission. It is shown that the dependence of the transition probability on the position of a moving atom in the cavity and the magnitude of this probability are qualitatively influenced by the ratio between the Doppler shift of transition frequency and the Rabi frequency of atom-field system.
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.
We discuss the dynamics of a three-level V-type atom driven simultaneously by a cavity photon and microwave field by examining the atomic population evolution. Owing to the coupling effect of the cavity photon, periodical oscillation of the population between the two upper states and the ground state takes place, which is the well-known vacuum Rabi oscillation. Meanwhile, the population exchange between the upmost level and the middle level can occur due to the driving action of the external microwave field. The general dynamic behavior is the superposition of a fast and a slow periodical oscillation under the cooperative and competitive effect of the cavity photon and the microwave field. Numerical results demonstrate that the time evolution of the population is strongly dependent on the atom–cavity coupling coefficient g and Rabi frequency ?_e that reflects the intensity of the external microwave field. By modulating the two parameters g and ?_e, a large number of population transfer behaviors can be achieved.