Group-theoretical approach to study atomic motion in a laser field

TL;DR

This paper employs a group-theoretical framework to analyze the coupled internal and external dynamics of two-level atoms in a standing-wave laser field, revealing conditions for chaotic atomic motion and potential experimental observation.

Contribution

It introduces a novel group-theoretical method to explicitly solve atomic dynamics in a laser field, linking quantum internal states with classical motion and identifying chaos regimes.

Findings

Chaotic regimes depend on control parameters and initial conditions.

Explicit solutions for the evolution operator are derived.

Chaotic walking can be observed experimentally with cold atoms.

Abstract

Group-theoretical approach is applied to study 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.