Dynamical complexity in a quantum-optical model with a simple lie-algebraic structure

The evolution of a quantum-optical system, possessing the SU(2) dynamical symmetry and consisting of an ensemble of two-level atoms that move through a single-mode high-quality cavity, is investigated. Even in the rotating-wave approximation, the system can demonstrate very complicated semiclassical dynamics that is shown to be chaotic in the sense of extreme sensitivity to initial conditions. It is shown that the respective equations of motion can be transformed to a parametrically perturbed complex Duffing equation. The homoclinic structure is found for an integrable version of the system with atoms at rest. Numerical simulation confirms that perturbations, produced by a modulation of the coupling between moving atoms and a cavity mode, provide a mechanism responsible for chaos.