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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.