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Journal of Russian Laser Research

Effects of atomic motion in a standing-wave laser field on the Rabi oscillations

Leonid E. Kon’kov, Sergey V. Prants

Published Jul 1, 2009• 2 citations
Publisher
DOI
10.1007/s10946-009-9080-3

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We present an in-depth study on the behavior of an atomic wave packet which is placed in a standing wave cavity prepared in various states of light. We extract a simple classical oscillator model out of the dynamics of the quantum system. We quantitatively resolve the states of the spatially reorganized wave packet by the dressed state spatial probability distribution functions we developed. We also report a novel type of the “quantum collapse and revival” behavior of the Rabi nutation which is originated from the effect of the quantized atomic center-of-mass motion on the atomic internal motion.
A group-theoretical approach is applied to study the behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is described quantum mechanically in terms of the SU (2) group parameters. The evolution operator is found in an explicit way after solving a single ODE for one of the group parameters. The translational motion in a standing wave is governed by the classical Hamilton equations which are coupled to the SU (2) group equations. It is shown that the full set of equations may be chaotic in some ranges of the control parameters and initial conditions. It means physically that there are regimes of motion with chaotic center-of-mass motion and irregular internal dynamics. It is established that the chaotic regime is specified by the character of oscillations of the group parameter characterizing the mean interaction energy between the atom and the laser field. It is shown that the effect of chaotic walking can be observed in a real experiment with cold atoms crossing a standing-wave laser field.
We consider dissipative dynamics of atoms in a strong standing laser wave and find a nonlinear dynamical effect of synchronization between center-of-mass motion and internal Rabi oscillations. The synchronization manifests itself in the phase space as limit cycles, which may have different periods and riddled basins of attraction. The effect can be detected in fluorescence spectra of atoms as equidistant sideband frequencies with the space between adjacent peaks to be inversely proportional to the value of the period of the respective limit cycle. With increasing intensity of the laser field, we numerically observe cascades of bifurcations that eventually end up in settling a strange chaotic attractor. A broadband noise is shown to destroy a fine structure of the bifurcation scenario, but prominent features of period-1 and period-3 limit cycles survive under a weak noise. The character of the atomic motion is analyzed with the help of the friction force whose zeroes are attractor or repellor points in the velocity space. We find ranges of the laser parameters where the atomic motion resembles a random but deterministic walking of atoms erratically jumping between different wells of the optical potential. Such a random walking is shown to be fractal.