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Journal of Experimental and Theoretical Physics Letters

Doppler-Rabi oscillations of a two-level atom moving in a cavity

A. V. Kozlovskiĭ

Published Apr 1, 2001• 2 citations
Publisher

Abstract

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.

DOI
10.1134/1.1378111

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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.
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 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 dynamics of interaction of an electromagnetic field with a two-level atom uniformly moving in an open resonator is analysed. The probability of the radiative transition of an excited atom to a lower state is studied as a function of the slope of its trajectory relative to the resonator axis and of the detuning of the atomic transition frequency from the resonator mode frequency. The study was performed in the case of strong coupling by the method of dressed states. The complicated dependences of the transition probability on the detuning and the slope of the atomic trajectory are analysed for small angles (~1°) for typical experimental conditions. It is shown that under certain conditions, a field can be efficiently excited in the resonator by atoms whose transition frequency considerably differs from the field-mode frequency when the detuning is not close to the Doppler shift.
We study the dynamics of a ∨-type three-level atom in the cavity employing the dressed state of the system. We consider a ∨-type three-level atom initially in a different state that interacts with two mode photons in a closed cavity. The initial state of the atom and Rabi frequency have a significant effect on the population exchange between excited and ground levels. The numerical results show that the atom-field coupling strength determines the fast and slow periodic oscillation of the probability between the upper and ground states. The highest probability of finding it in the upper and ground states is determined by the initial state conditions of the atom. In general, the initial state conditions of the atom and the atom-field coupling strength have a significant effect on population transfer between the upper and ground states of a ∨-type three-level 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.