Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the Effect of the System Dimension

In the present paper, we investigate the dynamics of a Bose-Einstein condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both analytically and numerically. We focus on the self-trapping state and the effect of the system dimension. Under the tight-binding approximation we obtain an analytical criterion for the self-trapping state of BEC using time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of the BEC cloud is obtained accordingly and verified by directly solving the discrete Gross-Pitaevskii equation (GPE) numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the lattices.