Symmetry for the Nonadiabatic Transition in Floquet States

The frequency of the Rabi oscillation driven by a periodic external field varies with the parameters of the external field, e. g., frequency and amplitude, and it becomes zero at some points of the parameters, which is called coherent destruction of tunneling. This phenomenon is understood as a degeneracy of the Floquet quasienergies as a function of the parameters. We prove that the time-reversal symmetry of the external field is a necessary condition of the degeneracy. We demonstrate the gap opening in the quasienergy spectrum in asymmetrically periodically driven systems. Moreover, an adiabatic transition of the Floquet states is demonstrated and analyzed in the analogy to the Landau-Zener transition.