Dynamical Control in a Quasi-periodically Modulated Optical Lattice

We investigate quantum tunneling phenomena for an optical lattice subjected to a bichromatic ac force. We show that incommensurability of the frequencies leads to super Bloch oscillation. We propose directed super Bloch oscillation for the quasi periodically driven optical lattice. We study the dynamical localization and photon assisted tunneling for a periodical and quasi-periodical ac force.