We consider the topological defects and spin structures of spin-1 Bose–Einstein condensates with spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant ...

中文翻译：

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自旋-轨道耦合偶极自旋1 Bose-Einstein凝聚体的拓扑缺陷

我们考虑了旋转自旋加四次陷阱中具有自旋-轨道耦合（SOC）和偶极-偶极相互作用（DDI）的自旋1 Bose-Einstein冷凝物的拓扑缺陷和自旋结构。分析了SOC，DDI和旋转对系统基态相位的综合影响。我们的结果表明，对于固定的旋转频率，可以通过调整SOC和DDI的大小来实现结构相变。根据SOC和DDI强度给出了基态相位图。结果表明，该系统展现出丰富的量子相，包括具有孤立密度峰（DPs）的涡流串相，具有DPs的三角（正方形）涡流晶格相，棋盘相和带隐藏涡旋和反涡旋的条纹相。对于给定的SOC和DDI强度，