Transition to dynamic chaos in the interaction of a two-level atom in a cavity with its own radiation field

An analytic symmetry approach is proposed and applied to nonlinear Hamiltonian dynamics of the self-consistent interaction of a two-level atom in a high-Q cavity with its own radiation field. A numerical investigation is reported of a transition from quasiperiodic to deterministically chaotic oscillations in a system of this kind which has classical and quantum degrees of freedom. This occurs when the control parameter Ω, which is the constant of the atom – field interaction, is increased. The largest Lyapunov exponent (which is a measure of the degree of chaos of a system) is used to demonstrate an alternation of the order – chaos transitions with increase in Ω. The power spectra and the phase portraits obtained for different ranges of Ω confirm the predicted path of the appearance of dynamic chaos in the fundamental model of quantum electronics.