AI 中文总结
研究环形捕获几何结构中玻色 - 爱因斯坦凝聚体非线性旋转下涡旋晶格构型变化，发现强度增加会致结构转变，确定相关参数范围，研究对集体激发谱影响及多量子化涡旋稳定性，揭示违反科恩定理等现象。
AI 中文摘要
我们通过数值研究了依赖密度的规范势对限制在环形捕获几何结构中的玻色 - 爱因斯坦凝聚体诱导非线性旋转的影响。通过关注由此产生的涡旋晶格构型，我们证明增加非线性旋转强度会导致从环形涡旋晶格到巨型涡旋态的结构转变。发现与巨型涡旋相关的量子环流对非线性旋转强度高度敏感，且巨型涡旋出现在负化学势区域。此外，我们通过基于非线性旋转强度和限制势半径映射解空间来确定托马斯 - 费米密度分布仍然有效的参数范围。基于博戈留波夫 - 德热纳分析，我们研究了非线性旋转对集体激发谱的影响。结果揭示了对科恩定理的违反以及表明凝聚体径向变形的呼吸模式频率变化。通过全面的流体动力学分析进一步证实了我们的发现。最后，我们分析了非线性旋转下多量子化涡旋的稳定性。结果表明虽然非线性旋转可增强这些态的全局稳定性，但不一定确保其局部稳定性。
英文摘要
We numerically investigate the effects of a density-dependent gauge potential which induces nonlinear rotation on a Bose-Einstein condensate confined in a toroidal trapping geometry. By focusing on the resulting vortex lattice configurations, we demonstrate that increasing the strength of the nonlinear rotation leads to a structural transition from a ring-shaped vortex lattice to a giant vortex state. The quantum circulation associated with the giant vortex is found to be highly sensitive to the strength of the nonlinear rotation and the giant vortex appears in the regime of negative chemical potential. Additionally, we identify the parameter regime in which the Thomas-Fermi density profile remains valid by mapping the solution space based on the strength of the nonlinear rotation and the radius of the confining potential. Based on the Bogoliubov de Gennes analysis, we investigate the impact of nonlinear rotation on the collective excitation spectrum. Our results reveal a violation of the Kohn theorem, accompanied by changes in the breathing mode frequency that indicate radial deformation of the condensate. Our findings are further substantiated through a comprehensive hydrodynamic analysis. Finally, we analyze the stability of multiply quantized vortices under nonlinear rotation. Our findings indicate that while nonlinear rotation can enhance the global stability of these states, it does not necessarily ensure their local stability.
Comments16 pages, 12 figures
