We investigate the combined effects of spin-orbit coupling and rotation on the topological vortical phase transition in $F=2$ Bose-Einstein condensates. We find that the spin-orbit coupling can precisely manipulate the canonical atom current which is generated in the opposite direction of the gauge atom current and causes both a continuous and a discontinuous canonical angular momentum. We apply the canonical angular momentum and magnetization to reveal the emergence of novel topological excitations, such as the Anderson-Toulouse vortex as well as the vortex–dipole lattice. Especially, strong spin-orbit coupling can induce two perpendicular vortex chains. We also find that both the first-order and the second-order phase transition can be characterized by the canonical angular momentum and the magnetization. Differently from the spin singlet-pairing interaction, the spin-exchange interaction can adjust the canonical angular momentum and control the phase transition well. The topological vortical phase transition in an $F=2$ cold-atom system is compatible with the current experiment and can be detected by the spin polarization procedure.

中文翻译：

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自旋轨道耦合控制自旋 2 旋转玻色-爱因斯坦凝聚中的拓扑涡旋相变

我们研究了自旋轨道耦合和旋转对拓扑涡旋相变的综合影响 $F=2$玻色-爱因斯坦凝聚。我们发现自旋轨道耦合可以精确地操纵规范原子流，该规范原子流在规范原子流的相反方向上产生，并导致连续和不连续的规范角动量。我们应用典型角动量和磁化强度来揭示新拓扑激发的出现，例如安德森-图卢兹涡旋以及涡旋-偶极子晶格。特别是，强自旋轨道耦合可以诱发两个垂直的涡链。我们还发现，一阶和二阶相变都可以用正则角动量和磁化强度来表征。与自旋单线态配对相互作用不同，自旋交换相互作用可以调节正则角动量并很好地控制相变。$F=2$ 冷原子系统与当前实验兼容，可以通过自旋极化程序进行检测。