Accurate control of a Bose-Einstein condensate by managing the atomic interaction

We exploit the variation of the atomic interaction in order to move ultra-cold atoms across an AC-driven periodic lattice. By breaking relevant symmetries, a gathering of atoms is achieved. Accurate control of the gathered atoms positions can be demonstrated via the control of the atomic localization process. The localization process is analyzed with the help of the nonlinear Floquet states where the Landau-Zener tunneling between states is observed and controlled. Transport effects in the presence of disorder are discussed.