自旋轨道耦合自旋1玻色-氢原子压缩盒中的双不稳定迴避交叉与复杂域图案形成

我们分析了自旋轨道耦合与Rabi耦合对自旋轨道耦合自旋1玻色-氢原子压缩盒在铁磁（FM）和抗铁磁（AFM）相互作用下的动力学稳定性的影响。通过Bogoliubov-de-Gennes理论确定集体激发谱，we characterize the dynamical stability regime via modulational instability. For AFM interactions, the eigenspectrum reveals the presence of both stable and unstable avoided crossings (UAC), with the first-excited branch undergoing a double unstable avoided crossing. In contrast, with ferromagnetic interactions, only a single UAC, which occurs between the low-lying and first-excited branches, is observed. Furthermore, the eigenvectors demonstrate the transition from density-like to spin-like behaviour, as the collective excitation shows the transition from stable to unstable mode for both the FM and AFM interactions. In the multi-band instability state, eigenvectors display spin-density mixed mode, while they show spin-flip nature in the avoided crossing regime. Our analysis suggests that spin-orbit coupling enhances the instability gain, while Rabi coupling plays the opposite role. Finally, we corroborate our analytical findings of stable and unstable regimes through numerical simulations of the dynamical evolution of the condensates by introducing the perturbations upon quenching the trap strength. The dynamical phases show the formation of complex domains with AFM interaction, which may be attributed to the double unstable avoided crossings in such a system.