Nonlinear multiphoton resonances in quantum wells

Abstract

The periodically driven particle in a box serves as a starting point for the qualitative analysis of nonintegrable systems, and as a simple model of semiconductor quantum wells exposed to intense far-infrared radiation. Classically, the phase space contains chaotic low-momentum trajectories, bounded by a sharp transition to regular motion for high momenta. The quantized system contains invariant states which localize upon classical invariant surfaces. We model the time evolution of the ground state (in the classical system, an ensemble of low-momentum trajectories) under various driving amplitudes and frequencies. Whereas the dynamics of the classical system are governed by the presence of KAM tori, the quantized system also displays sharp, nonperturbative resonances at particular driving parameters. These resonances correspond to the mixing of Floquet states at avoided crossings in the quasienergy spectrum. This form of transport should survive when many-body effects, dissipation, and the continuum are taken into account.