Modulational Instability of Dipolar Bose-Einstein Condensates in Optical Lattices with Three-Body Interactions

Motivated by the recent experiment [Nature 530 (2016) 194] in which a stable droplet in a dipolar quantum gas has been created by the interaction-induced instability, we focus on the modulation instability of an optically-trapped dipolar Bose-Einstein condensate with three-body interaction. Within the mean-field level, we analytically solve the discrete cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction loaded into a deep optical lattice and show how combined effects of the three-body interaction and dipole-dipole interaction on the condition of modulational instability. Our results show that the interplay of the three-body interaction and dipole-dipole interaction can dramatically change the modulation instability condition compared with the ordinary Gross-Pitaevskii equation. We believe that the predicted results in this work can be useful for the future possible experiment of loading a Bose-Einstein condensate of Dy-164 atoms with strong magnetic dipole-dipole interaction into an optical lattice.