Nonperturbative electron dynamics in crossed fields

Intense ac electric fields on semiconductor structures have been studied in photon-assisted tunneling experiments with magnetic field applied either parallel ${(B}_{\Vert })$ or perpendicular ${(B}_{\perp })$ to the interfaces. We examine here the electron dynamics in a double quantum well when intense ac electric fields F, and tilted magnetic fields are applied simultaneously. The problem is treated nonperturbatively by a time-dependent Hamiltonian in the effective mass approximation, and using a Floquet-Fourier formalism. For $B_{\Vert }=0,$ the quasienergy spectra show two types of crossings: those related to different Landau levels, and those associated to dynamic localization (DL), where the electron is confined to one of the wells, despite the non-negligible tunneling between wells. $B_{\Vert }$ couples parallel and in-plane motions producing anticrossings in the spectrum. However, since our approach is nonperturbative, we are able to explore the entire frequency range. For high frequencies $\omega ,$ we reproduce the well known results of perfect DL given by zeros of a Bessel function. We find also that the system exhibits DL at the same values of the field F, even as $B_{\Vert }\ne 0,$ suggesting a hidden dynamical symmetry in the system which we identify with different parity operations. Symmetries under general parity operations explain many of the features in the spectra, and their overall behavior under magnetic field. The return times for the electron at various values of field exhibit interesting and complex behavior which is also studied in detail. We find that smaller $\omega$ shifts the DL points to lower $eFd/ħ\omega$ ratios, and more importantly, yields poorer (less effective) localization by the field, while other states change also physical character. We analyze the explicit time evolution of the system, monitoring the elapsed time to return to a given well for each Landau level, and find non-monotonic behavior for decreasing frequencies.