The dynamics and stabilities of Bose-Einstein condensates in deep optical lattices

The dynamics and stabilities of Bose-Einstein condensate (BEC) trapped in a deep one-dimensional periodic optical lattices with three-body interactions are investigated. By using the tight-binding approximation, the Bloch and the Bogoliubov excitation stabilities and the dynamics of the BEC wave packet with the effects of the three-body interactions are studied. The critical conditions for occurrence of the dynamical/Landau instabilities, self-trapping/diffusion/breather of wave packet, and localized soliton are obtained analytically. The results show that the boundaries of the dynamical instability and Landau instability are modified significantly due to the presence of the three-body interactions. It is also revealed that, the initial wave packet width, the initial momentum, especially, the strength of the three-body force have strong effect on the critical conditions which are used to describe the dynamics of the wave packet. It is shown that the regions of self-trapping, diffusion, and breather for BEC wave packet in the parameter space are modified dramatically by the three-body interactions. The analytical results are confirmed by the direct numerical solutions of the discrete GPE