Spinor F = 1 Bose-Einstein condensates loaded in two types of radially-periodic potentials with spin-orbit coupling* *Project supported by the National Natural Science of China (Grant Nos. 11904242 and 12004264) and the Natural Science Foundation of Hebei Province, China (Grant Nos. A2019210280 and A2019210124).

Abstract

We consider two-dimensional spinor F = 1 Bose–Einstein condensates in two types of radially-periodic potentials with spin–orbit coupling, i.e., spin-independent and spin-dependent radially-periodic potentials. For the Bose–Einstein condensates in a spin-independent radially-periodic potential, the density of each component exhibits the periodic density modulation along the azimuthal direction, which realizes the necklacelike state in the ferromagnetic Bose–Einstein condensates. As the spin-exchange interaction increases, the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose–Einstein condensates with larger spin–orbit coupling. The competition of the spin-dependent radially-periodic potential, spin–orbit coupling, and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose–Einstein condensates in a spin-dependent radially-periodic potential.