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Acta Physica Sinica (Overseas Edition)

Interaction between a moving atom and an electromagnetic wave

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

Published Oct 1, 1999• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1004-423x/8/10/003

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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.
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.
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.
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.
It is shown that the population Rabi oscillations in a lossless two-level atom, interacting with a monochromatic electromagnetic field, in general, are convergent in time. The well-known continuous oscillations take place because the restricted choosing of initial conditions, that is, when the atom is chosen on ground or excited level before the interaction, simultaneously having a definite value of momentum there. The convergence of Rabi oscillations in atomic wave-packet states is a direct consequence of the Doppler effect on optical transition rates (Rabi frequencies): it gradually leads to ``irregular'' chaotic-type distributions of momentum in ground and excited energy levels, smearing the amplitudes of Rabi oscillations. Conjointly with Rabi oscillations, the coherent accumulation of momentum on each internal energy level monotonically diminishes too.
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.
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.