Chaos in Radiative Interactions

Toshihiko Ohno

トシヒコ オオノ, Toshihiko Ohno

Leonid E. Kon’kov, Sergey V. Prants

With the help of Lyapunov exponents different routes to quantum chaos are demonstrated numerically in two semiclassical models of the interaction of N two-level atoms with their own radiation field in a resonant cavity. The usual transition to chaos is observed when varying the external control parameter b which describes the interaction of the atomic ensemble with the field. After reaching its critical value b approximately equal to 1 the system becomes more and more chaotic as b increases. As the second control parameter a (the dimensionless individual Rabi frequency) increases the system undergoes transitions to chaos by a completely different way. We observe a complex sequence of order-to-chaos transitions that resembles those for the classical Lorenz attractor.

R. H. Graham

Peter W. Milonni

Leonid E. Kon’kov, Sergey V. Prants

The dynamical-group approach is developed and applied to investigate the problems of controllability and quantum chaos in two fundamental models of the matter–radiation interaction. It provides a new insight into the dynamics of nonstationary quantum process of the interaction between two-level atoms and a single-mode radiation field without and with the feedback. A sequence of transitions from the quasiperiodicity to chaos has been numerically observed for two-level atoms interacting with a self-consistently generated radiation field. The unitary irreducible representations of the SU(2) group of dynamical symmetry in a noncanonical parametrization is constructed, allowing one to use the results for describing the time evolution of any driven quantum system with the underlying SU(2) symmetry.