Exotic Quantum States in Spin-1 Bose-Einstein Condensate with Spin-Orbit Coupling in Concentric Annular Traps

We explore the exotic quantum states emerging in the ground state (GS) of a strongly-correlated spin-1 Bose-Einstein condensate confined in two-dimensional concentric annular traps with a spin-orbit coupling (SOC). In the antiferromagnetic case, the GS density manifests various patterns of distributions, including facial-makeup states, petal states, topological fissure states, multiple-half-ring states and property-distinguished vertical and horizonal stripe states. We notice a peculiar phenomenon of density-phase separation in the sense that the variations of density and phase tend to be independent. In ferromagnetic case, the GS exhibits a semi-circular or half-disk status of density embedded with vortices and anti-vortices. The spin distribution can self-arrange into an array of half-skyrmions and we also find a half-antiskyrmion fence separating vortex-antivortex pairs. Our study indicates that one can manipulate the emergence of exotic quantum states via the interplay of the SOC, interaction and potential geometry and the abundant state variations might also provide potential resources for quantum metrology.