莫比乌斯场中的 8π 偏心巨涡旋:真实场实现、等效分析与 Krein 稳定性的边界(An Eccentric 8π Giant Vortex in a Möbius Field: Real-Field Realization and Krein Stability)

Abstract:We report an eccentric giant vortex in a real coil field. Injecting the full-wave field slices of a biconical Möbius coil directly into the Gross-Pitaevskii equation without any axisymmetrization yields a crescent-shaped density cloud, whose core carries a strictly quantized single-core giant vortex of 8π8π. The mechanism can be summarized as soft density, hard topology: density is a soft variable and deforms with the anisotropy of the potential, making the eccentricity a geometric imprint rather than a computational defect; the winding number is a topological quantity, and the phase singularity remains locked at the axis regardless of the shape. Stability is likewise determined by the spectral structure rather than the potential shape: the state is a saddle point on the energy landscape, but on the g≳350g≳350 side, the spectrum has no complex modes, and conservative real-time evolution remains bounded, which we identify as Krein-type dynamical stability. This stability has a boundary—the quadrupole complex mode appears at the weak-interaction end and is confirmed by directed seed experiments, thus dynamical stability requires an atom number N≳1.3×103N≳1.3×103. Joint quantitative reconciliation of imaginary-time evolution and BdG spectrum shows that the deepest eigenvalues agree with growth rates within 6%. For a μμm-scale zeroth-order tightly confined 2D 8787Rb system, we calibrate the required experimental parameters (approximately 103103 atoms at T≲50T≲50 nK), and give two testable predictions—the dissipative lifetime τ∝1/γpτ∝1/γp (2424 ms – 0.240.24 s) and threshold-type one-shot collapse under strong dissipation. A rigorous numerical auditing protocol and experimental feasibility analysis are provided at the end. 摘要:本文报告了莫比乌斯拓扑场中偏心巨涡旋的真实场实现与稳定性分析。通过将双锥-莫比乌斯线圈的全波场切片直接代入 Gross-Pitaevskii 方程(不作任何轴对称化),我们得到了一条偏心新月形的密度云,其核心承载着绕数严格量子化为 8π8π 的单核巨涡旋。该机制可概括为“密度软、拓扑硬”:密度是软变量,随势的各向异性变形(质心偏移 1.2 cm),偏心是几何的印记而非计算缺陷;而绕数是拓扑量,相位奇点始终锁在轴心。稳定性同样由谱结构而非势形决定:该态在能量曲面上是鞍点,但在强相互作用端(g≳350g≳350)谱无复模,保守实时演化有界,即 Krein 型动力学稳定。这条稳定性边界要求原子数 N≳1.3×103N≳1.3×103。联合虚时演化与 BdG 谱的定量对账显示,最深本征值与增长率在 6% 的误差内吻合。针对 μμm 尺度的零阶紧囚禁二维系统,本文标定了所需的 8787Rb 实验参数(约 103103 原子,温度 T≲50T≲50 nK),并给出了两个可检验预言:耗散寿命与阻尼率成反比(τ∝1/γpτ∝1/γp,24 ms–0.24 s),以及强耗散下的阈值型一次性崩塌。文末附带了严谨的数值审计协议与实验可实现性分析。