Interband transitions of superlattices in arbitrary time-dependent electric fields: an analytical approach of closed-form solutions in the real space

Within a two-band tight-binding model driven by arbitrary time-dependent electric fields, we investigate the interband transitions and obtain closed-form solutions in the real space, from which we show that there are two essentially opposite evolution behaviors of the system: interband resonances and miniband localization. We also find that in weak interband coupling, as expected, the perturbative solutions are in good agreement with the exact numerical calculations.