Noise-induced dynamical localization and delocalization

We investigate the effect of a two-level jump process or random telegraph noise on a square wave driven tight-binding lattice. In the absence of the noise, the system is known to exhibit dynamical localization for specific ratios of the amplitude and the frequency of the drive. We obtain an exact expression for the probability propagator to study the stability of dynamical localization against telegraph noise. Our analysis shows that in the presence of noise, a proper tuning of the noise parameters destroys dynamical localization of the clean limit in one case, while it induces dynamical localization in an otherwise delocalized phase of the clean model. Numerical results help verify the analytical findings. A study of the dynamics of entanglement entropy from an initially half-filled state offers complementary perspective.