Nonlinear dynamics of the fundamental interaction between a two-level
atom and a quantized radiation field in a high-quality cavity is studied.
We consider the strongly coupled atom-field system as a quantum-classical
hybrid with coupled quantum and classical degrees of freedom modelling
quantum evolution to be disturbed by interaction with environment. We
derive a set of the Hamilton-Scrodinger equations for the atom-field probability
amplitudes and the translational atomic variables and treat this
infinite-dimensional nonlinear dynamical system theoretically and numerically
with Fock, coherent, and thermal quantum-field states and with different internal
atomic states. We find manifestations of Hamiltonian dynamical chaos computing
the Rabi oscillations, atomic trajectories, Poincare sections, and Lyapunov
exponents. Fractal-like structures are found in the dependence of the time
of exit of atoms off the cavity on the initial atomic momentum.
Tiny interplay between all the degrees of freedom is responsible for
dynamical trapping of atoms even in a very short microcavity. Correlations between the atomic
Rabi oscillations and its motion may cause the Doppler-Rabi resonance, deep
Rabi oscillations practically with an arbitrarily large atom-field detuning
under the definite condition imposed on the initial atomic momentum, its recoil
frequency, and the detuning. Gedanken experiments are proposed to detect
manifestations of atomic Fock, coherent, and thermal fractals in cavity
quantum electrodynamics.
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