Ground States of Dipolar Spin–Orbit-Coupled Bose–Einstein Condensates in a Toroidal Trap

We investigate the ground-state structures of dipolar spin–orbit-coupled Bose–Einstein condensates in a toroidal trap. Combined effects of dipole–dipole interaction (DDI) and spin–orbit coupling (SOC) on the ground states of the system are discussed. A ground-state phase diagram is obtained as a function of the SOC and DDI strengths. As two new degrees of freedom, the DDI and SOC can be used to obtain the desired ground-state phases and to control the phase transition between various ground states. In particular, the system displays exotic topological structures and spin textures, such as half-quantum vortex, vortex string, vortex necklace, complex vortex lattice including giant vortex and hidden antivortex chains, different skyrmions, meron (half-skyrmion)-antimeron (half-antiskyrmion) necklace, and composite meron-antimeron lattice.