Structural Hamiltonian chaos in the coherent parametric atom–field interaction

We consider one of the simplest semiclassical models in laser and atomic physics, a collection of two-level atoms interacting coherently with an electromagnetic standing wave in an ideal single-mode cavity within the rotating-wave approximation (RWA). In the strong-coupling limit, atoms and a cavity field constitute a strongly coupled atom–field dynamical system whose atomic and field variables oscillate in a self-consistent way with the Rabi frequency. It is proven analytically by the Melnikov method and numerically by computing maximal Lyapunov exponents and Poincaré sections that the parametric Rabi oscillations in a vibrating cavity may be chaotic in a sense of exponential sensitivity to initial conditions. Wavelet spectra computed with typical signals of the oscillations demonstrate clearly that Hamiltonian chaos in the coherent atom–field interaction with modulated coupling is structural. Structural chaos is characterized by positive values of the maximal Lyapunov exponents and regular structures which coexist in the same signal. Duration of a train of regular oscillations is defined by the period of modulation, but oscillations between successive trains are chaotic. Results of numerical experiments and estimation of the control parameters and approximations involved show that a Rydberg atom maser operating with a collection of two-level atoms inside a high-quality superconducting microwave cavity is a promising device for observing manifestations of structural Hamiltonian chaos in real experiments.