Spin–orbit-coupled spin-1 Bose–Einstein condensates confined in radially periodic potential* *Project supported by the Scientific and Technologial Innovation Program of the Higher Education Institutions in Shanxi Province, China (Grant Nos. 2019L0813, 2019L0785, and 2019L0808).

Abstract

We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radially periodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.