Control of quantum states in nonstationary cavity QED systems

Interaction of atoms, moving through a lossless cavity, with a cavity field having a spatial structure, is treated with the aim of controlling quantum evolution of the field and atomic states. General fully-quantum analysis of the atom-field dynamics is applied for solving the finite-control problem for a micromaser device consisting of two-level atoms moving through a single-mode cavity. The semiclassical treatment of the same system shows that out of resonance between atoms and the field it may be fully uncontrollable in the sense of exponential sensitivity to initial conditions. By calculating maximal Lyapunov exponents we demonstrate dynamical chaos for a wide range of magnitudes of the detuning, the atom-field strength and the velocity of atoms which may be considered as control parameters for the micromaser.