One of the striking features of rotating atomic Bose-Einstein condensates (BECs) is the formation of vortices above a critical angular velocity. In a symmetric BEC, multiple vortices arrange in a characteristic triangular pattern. This triangular vortex lattice minimizes the free energy of the BEC. While the initial experiments considered atoms with local interactions, more recently, dipolar BECs with significant electric or magnetic dipole moment have received much attention from both theoretical and experimental studies. The dipole-dipole interaction (DDI) crucially affects the ground-state properties, stability, and dynamics of the gas. Furthermore, they offer a route for studying many-body quantum effects, such as a superfluid-to-crystal quantum phase transition, supersolids or even topological quantum phases.
In a quasi-2D rotating dipolar BEC, the emergence of vortex depends on the s-wave contact interaction strength, the polarization angle and the rotational frequency. When the rotational speed increases, many vortices will appear and arrange in patterns. In literature, several transitions of vortex lattice structure have been predicted, involving triangular lattice, rectangle lattice and square lattice.
Recently, CSRC researcher Yongyong Cai, together with Yongjun Yuan, Matthias Rosenkranz, Weizhu Bao and Han Pu, employed a quasi-2D dipolar Gross-Pitaevskii model for arbitrary DDI polarization, and studied how the s-wave contact interaction strength and the polarization angle affect the critical rotational frequency with both attractive and repulsive DDI strengths. Focusing on the regime with many vortices, they were able to discern characteristic vortex patterns that occur as the polarization changes from predominantly perpendicular to parallel. It was found that the critical rotational frequency for single vortex depends mainly on the effective 2D contact interaction strength. For fast rotation, when the polarization angle changes from perpendicular to parallel to the condensate plane, a structural phase transition in the vortex lattice geometry from triangle to square is observed for positive DDI, but not for negative DDI. However, there is no simplified theory to illustrate the lattice structure transition and the DDI in rotating BEC requires further studies. The highly accurate numerical simulations provided insights for next step research on rotating dipolar BECs.
 Y. Cai, M. Rosenkranz, Z. Lei, and W. Bao, Phys. Rev. A 82, 043623 (2010).
 Y. Cai,Y. Yuan, M. Rosenkranz, H. Pu, and W. Bao, Phys. Rev. A 98, 023610 (2018).