Abstract

The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory¹ that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.² In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N² – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N² – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.²

© 1986 Optical Society of America