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Chinese Physics

Interaction of a two-level atom with fine structure moving in an electromagnetic field

Jingtao Zhang, Chen Zhao-yang, Xu Zhi-Zhan

Published Jan 1, 2000• 0 citations
Publisher

Abstract

Dynamics of a moving two-level atom with fine structure interacting with an electromagnetic field is studied. The fine structure increases the damping rate induced by the atomic momentum distribution. When the field is in a Fock state, the Rabi oscillation becomes very complicated; when the field is in a superposition state, the collapse-revival phenomenon disappears for the wider atomic wavepackets. In the presence of the fine structure, each atomic level splits into three sublevels when the field is in a Fock state and the atom has a definite momentum.

DOI
10.1088/1009-1963/9/1/005

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Dynamics of a moving two-level atom with fine structure interacting with an electromagnetic field is studied. The fine structure increases the damping rate induced by the atomic momentum distribution. When the field is in a Fock state, the Rabi oscillation becomes very complicated; when the field is in a superposition state, the collapse-revival phenomenon disappears for the wider atomic wavepackets. In the presence of the fine structure, each atomic level splits into three sublevels when the field is in a Fock state and the atom has a definite momentum.
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.
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.
We have studied the effects of the fine structure of energy levels on the dynamics of the atom and light field. A significant influence is exhibited in the collapse-revival behavior of atomic inversion, the light squeezing, the phase of the field, and the antibunching of a light beam. When the energy difference between the doublet is large (\ensuremath{\Delta}\ensuremath{\ge}20g, where g is the coupling constant), the dynamics of the atomic inversion becomes identical to that of the usual Jaynes-Cummings model, as expected. However, the fine-structure effects on the phase and the antibunching of the light field exist in a much larger range. In particular, for a strong field, the normally ordered variance of the photon-number operator exhibits complicated collapse and revival patterns and the light displays strong antibunching in each revival envelope. Numerical calculations also show that this model does not produce significant squeezing due to the influence of the fine structure. \textcopyright{} 1996 The American Physical Society.
Interaction of a lossless two-level atom with a monochromatic (classical) field of radiation is considered, as the atom initially possesses a translational state with a number of equidistant and discrete momenta. It is shown that the Rabi oscillations in such an atom evolve as a sequence of collapses and revivals, if the coupling wave deeply saturates the optical transition. Between revivals, the populations undergo subrevivals. Approximate analytical formulae are obtained taking the initial momentum distribution in the form of two shifted Gaussians or a Besselian. A possible experimental realization of such revivals is 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.