Ground states of a distinct spin–orbit-coupled spin-1 Bose–Einstein Condensate in a toroidal trap

This study delves into the influence of a new type of spin–orbit coupling(SOC) on spin-1 Bose–Einstein condensates(BECs) in quasi-two-dimensional annular regions. The unconventional characteristics of the annular potential trap coupled with innovative artificial gauge field bring about a diverse array of phase diagrams for the ground state behavior of the BECs. In the antiferromagnetic state, we observe a distinct petal-like phase structure with components exhibiting novel density and phase distributions. In the ferromagnetic state, the spin-1 BECs exhibit rich asymmetric states which showcase a new type of vortex-molecule structure with multiple winding numbers in the huge hole. Many other novel breaking structures have also been discovered by modulating the strength of the nonlinear interaction. We contribute the different ground states of distinct spin–orbit couplings to the different symmetries.