Rectified motion of a Bose-Einstein condensate in a horizontally vibrating shallow optical lattice

We consider a Bose-Einstein condensate, described by the Gross-Pitaevskii equation, in a horizontally vibrating shallow optical lattice. We study the dynamics of a bright soliton using the collective coordinate approximation. We show that depending on the parameters, amplitude and frequency of the vibration of the lattice, the phase space of the equation of motion for the soliton center of mass shows multi-stability. In the frequency locked regions, in which the soliton has a non-zero average velocity determined by the external frequency, the motion is quasi-periodic, and between the locked regions the soliton moves chaotically.

Bose-Einstein condensate,optical lattice,