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Rotating spin–orbit coupled Bose–Einstein condensates in concentrically coupled annular traps

We study trapped 2D spin-1 Bose–Einstein condensates with isotropic spin–orbit coupling and rotation, showing rich ground state phases and phase transition results from the nontrivial interplay among spin–orbit coupling, rotation and confinement. We show that for experimentally feasible parameters and only in the presence of spin–orbit coupling, a double-ring structure for the longitudinal magnetization of the system can be formed within the minima of inner and/or outer rings. Moreover, the rotation effectively enhances the effect of the spin–orbit coupling and controls the location of atoms between both rings. Our results provide a scenario of controlling different phases of a spin–orbit coupled condensate by varying the spin–orbit coupling strength and rotation frequency, instead of using the conventional approach of changing the s-wave scattering length.