Controlled localization of interacting bosons in a disordered optical lattice

We show that tunneling and localization properties of interacting ultracold atoms in an optical lattice can be controlled by adiabatically turning on a fast oscillatory force even in the presence of disorder. Our calculations are based on the exact solution of the time-dependent Schroedinger equation, using the Floquet formalism. Implications of our findings for larger systems and the possibility of controlling the phase diagram of disordered-interacting bosonic systems are discussed.