Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Abstract

We consider dynamic symmetry, quantum control, and dynamic chaos of atoms moving in high-quality cavities. We review the group-theoretical approach to solve the evolution equations in the cavity quantum electrodynamics and control the quantum evolution in a micromaser device. Taking into account the photon recoil effect, we study nonlinear dynamics of the fundamental interactions between two-level atoms and a quantized cavity field. The strongly coupled atom–field system is treated as a quantum–classical hybrid with dynamically coupled quantum and classical degrees of freedom. Interaction of the purely quantum atom–field system with the classical translational atomic degree of freedom results in emergence of classical dynamic chaos from quantum electrodynamics. That chaos is shown to manifest itself in some ranges of the control parameters in the exponential sensitivity of quantum atomic variables to small variations in the initial conditions and in the appearance of dynamic atomic fractals. We discuss how to observe this effect in real experiments. Our findings establish a quantum–classical correspondence in the cavity quantum electrodynamics.