Vortex Lattice in the Planar Bose-Einstein Condensates with Dipolar   Interactions
  In this letter we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with the quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates. 
Jian Zhang and Hui Zhai