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Journal of Modern Optics

Effects of a Moving Mass Centre on Atomic Dynamics in Locally Inhomogeneous Quantized Cavity Field

Xiaoguang Wang, Chang-Pu Sun

Published Mar 1, 1995• 15 citations
Publisher

Abstract

By invoking an exactly solvable model as the generalization of the Jaynes-Cummings model, the influence of spatial motion of atomic centre on the dynamics of a single-mode cavity-two-level atom system are studied for various initial conditions. These investigations show that the Doppler effect exercised by the motion of atom in a locally inhomogeneous cavity field can lead to the phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.

DOI
10.1080/09500349514550491

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By invoking an exactly solvable model as the generalization of the Jaynes-Cummings model, the influence of spatial motion of atomic centre on the dynamics of a single-mode cavity-two-level atom system are studied for various initial conditions. These investigations show that the Doppler effect exercised by the motion of atom in a locally inhomogeneous cavity field can lead to the phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.
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.
A single two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field. When the atom's centre-of-mass motion is in a coherent state, we show that the atomic inversion exhibits collapses and revivals. Whereas in the Jaynes-Cummings model this behaviour occurs due to the discrete nature of the light field, in our case the behaviour is due to the discrete nature of the vibrational trap states. The Q -function for the external motion is also calculated and shown to break into two peaks in the collapse region. Finally the parameter ranges under which the collapses and revivals can be observed are discussed, as well as the possibility of an experiment.
A generalized approach of the Born-Oppenheimer approximation is developed to analytically deal with the influence exercised by the spatial motion of atom's mass-center on a two-level atom in an optical ring cavity with a quantized single-mode electromagnetic field. The explicit expressions of tunneling rate are obtained for various cases, such as that with initial coherent state and thermal equilibrium state at finite temperature. Therefore, the studies for Doppler and recoil effects of the spatial motion on the scheme controlling atomic tunneling should be reconsidered in terms of the initial momentum of atom's mass center.