Instability and control of a periodically driven Bose-Einstein condensate

We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes dynamically unstable when the effective intersite tunneling becomes negative. We further show how controlling the sign of the tunneling can be used to manage the dispersion of an atomic wave packet.