Changes in Floquet-state structure at avoided crossings: Delocalization and harmonic generation

Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identified: one type leads only to temporary changes (as a function of driving field strength) in Floquet state structure while the second type can lead to permanent delocalization of the Floquet states. Radiation spectra from these latter states show a significant increase in high harmonic generation as the system passes through the avoided crossing.