We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ < 1. In the relatively strong rot...

中文翻译：

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具有自旋-轨道耦合的旋转自旋1/2 Bose-Einstein在梯度磁场中凝结

我们研究了在梯度磁场中二维自旋轨道耦合的自旋1/2玻色-爱因斯坦凝聚态（BEC）的基态相。梯度磁场，自旋轨道耦合和旋转之间的竞争导致了各种基态相位结构。在弱旋转状态下，随着梯度磁场强度的增加，BEC经历了从不稳定相到单涡流相的相变。不稳定相沿非对角线方向呈现涡流线结构。随着磁场梯度强度的增加，涡旋线的数量也随之变化。随着磁场梯度强度的进一步增加，形成沿对角线方向具有单个涡流线的单个涡流线相。