自旋-1自旋-轨道耦合玻色-爱因斯坦凝聚体集体激发中不稳定免交叉的出现
Emergence of unstable avoided crossing in the collective excitations of spin-1 spin-orbit coupled Bose-Einstein condensates
AI总结：
本文通过Bogoliubov-de-Gennes理论和Gross-Pitaevskii动力学模拟，系统研究了自旋-1自旋-轨道耦合玻色-爱因斯坦凝聚体的集体激发谱，在$k_L-Ω$平面中划分出三类区域，并揭示了不稳定免交叉、自旋偶极模式及超条纹相等丰富物理现象。
摘要：
我们给出了准一维自旋-轨道（SO）耦合自旋-1玻色-爱因斯坦凝聚体集体激发谱的解析和数值结果。利用Bogoliubov-de-Gennes理论得到的集体激发谱揭示了SO和Rabi（$k_L-Ω$）耦合平面中存在多种相。基于激发谱的本征值，我们将$k_L-Ω$平面划分为三个不同区域。在区域I中，观察到具有类声子激发的稳定模式。在区域IIa中，注意到带隙模式下的单带和多带不稳定性；而在区域IIb中，实现了低激发态与第一激发态之间伴随无能隙模式的多带不稳定性，这也为低激发态与第一激发态模式之间存在不稳定免交叉提供了证据。低激发态与第一激发态之间的能隙随Rabi耦合增强而增大，随SO耦合增强而减小。利用本征矢量分析，我们确认了区域II中类自旋模式里存在自旋偶极模式。我们通过使用平均场Gross-Pitaevskii模型对受到阱淬火扰动的基态进行实时动力学演化，进一步证实了集体激发的性质。该分析表明存在动力学不稳定性，导致凝聚体第$0$个分量消失。在区域III中，主要涵盖$Ω\sim 0$和有限$k_L$的情况，我们在第一激发态和低激发态中都观察到类声子激发。该区域的本征矢量揭示了自旋分量交替出现的同相和反相行为。数值分析表明，在该区域的小Rabi耦合下存在超条纹相，其中本征矢量表明存在更复杂的类自旋-密度混合模式。
英文摘要：
We present the analytical and numerical results on the collective excitation spectrum of quasi-one-dimensional spin-orbit (SO) coupled spin-1 Bose-Einstein condensates. The collective excitation spectrum, using Bogoliubov-de-Gennes theory, reveals the existence of a diverse range of phases in the SO and Rabi ($k_L-Ω$) coupling plane. Based on eigenvalue of the excitation spectrum, we categorize the $k_L-Ω$ plane into three distinct regions. In region I, a stable mode with phonon-like excitations is observed. In region IIa, single and multi-band instabilities are noted with a gapped mode, while multi-band instability accompanied by a gapless mode between low-lying and first excited states is realized in region IIb, which also provides evidence of unstable avoided crossing between low-lying and first excited modes The gap between low-lying and first-excited states increases upon increasing the Rabi coupling while decreases upon increase of SO coupling. Using eigenvector analysis, we confirm the presence of the spin-dipole mode in the spin-like modes in Region II. We corroborate the nature of the collective excitation through real-time dynamical evolution of the ground state perturbed with the quench of the trap using the mean-field Gross-Pitaevskii model. This analysis suggests the presence of dynamical instability leading to the disappearance of the $0$-th component of the condensate. In Region III, mainly encompassing $Ω\sim 0$ and finite $k_L$, we observe phonon-like excitations in both the first excited and the low-lying state. The eigenvectors in this region reveal alternative in- and out-of-phase behaviours of the spin components. Numerical analysis reveals the presence of a super stripe phase for small Rabi coupling in this region, wherein the eigenvector indicates the presence of more complicated spin-like-density mixed modes.
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