Coherent control of field-induced localization and harmonic generation in semiconductor superlattices

We consider a d-dimensional conductor (a superlattice) within the independent-electron one-band approach taking into account slow relaxation processes. Its nonperturbative response to time-periodic electric fields is studied in the nearly coherent regimes: a) dynamic (short-time) and b) kinetic (long-time). We provide a classification and analysis of field-induced dynamic localization and response through the dc/ac current and mean square displacement of electrons. We demonstrate that the overall localization increases in passing from the periodic regime through the commensurate to the incommensurate one (governed by the relation of field period and Bloch frequency) both in the dynamic and kinetic cases. Simultaneously, exceptional localization (for some particular values of field parameters or symmetries) typically retains its order in the small relaxation rate, but on the background of increasing overall localization becomes less pronounced, both in dynamic and kinetic regimes. In the dynamic regime exceptional localization is manifested through diffusion and dc response, in the kinetic - through diffusion and ac response. The commensurate case with long-range-overlap qualitatively resembles the periodic one; within nearest-neighbor approximation the commensurate regime becomes qualitatively analogous to the incommensurate one. We also obtain explicit analytic solutions for the dynamic and kinetic harmonic generation spectra. We demonstrate that in strong and smooth fields the harmonic spectrum has a plateau-like shape. In the kinetic regime all the harmonics vanish under "exceptional" localization, whereas in the dynamic regime there is no such effect. In a strong dc field there is an effect of weak ac harmonics amplification. Coherent control of induced localization and harmonic generation is discussed.