Localization and hybridization across an effective mobility edge in periodically driven speckle potentials

Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and blocks transport through the lattice. A time-periodic drive, when applied to a lattice with uncorrelated disorder, typically increases (as compared to the stationary states) localization length of the appearing Floquet states. We go beyond the uncorrelated disorder limit and address the experimentally relevant case of speckle potentials in which spatial correlations in on-site disorder are present. These correlations are responsible for the creation of an effective mobility edge in the spectrum of the stationary lattice Hamiltonian. We find that a slow driving leads to resonant hybridization of the Floquet states across the edge; i.e., it increases the width of the states in the localized band and decreases it for the states in the quasi-extended band. By increasing the drive amplitude, we observe homogenization of the bands so that finally all Floquet states become weakly localized and sparse