Localization and delocalization of an electron in biased and unbiased quantum wells driven by a mono- and bichromatic laser field

Localization (delocalization) of an electron driven by laser in a biased quantum well is considered. The initially trapped electron can be delocalized by the field if the bias energy is close but not equal to an integer number of a photon energy. When the bias energy is exactly equal to an integer number of photon quanta, dynamical localization occurs. A general analytical solution for a population difference is obtained. When the electron is driven by a bichromatic field, localization regions are strongly dependent on the field incommensurability. The topology of localization exhibits stable and unstable regions originating from nonanalytical behavior of the population with respect to the small incommensurability. This phenomenon resembles phasetransition instabilities in the solid state. A low-frequency spectrum of electron oscillations consists of a low-frequency mode and split lines. We also show frequency controlling of the time evolution of an electron dipole moment on a phase shift between the two lasers. The low frequency can be increased or decreased, or it oscillates with the phase shift depending on the laser intensity.