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arXiv:2504.01394 · Physical Review A

Double unstable avoided crossings and complex-domain-pattern formation in spin-orbit-coupled spin-1 condensates

Sanu Kumar Gangwar, Rajamanickam Ravisankar, Henrique Fabrelli, Paulsamy Muruganandam, Pankaj Kumar Mishra

Published Jun 5, 2025• 2 citations
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Abstract

We analyze the impact of spin-orbit and Rabi couplings on the dynamical stability of spin-orbit-coupled spin-1 Bose-Einstein condensates for ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Determining the collective excitation spectrum through Bogoliubov--de Gennes theory, we characterize the dynamical stability regime via modulational instability. For AFM interactions, the eigenspectrum reveals the presence of both stable and unstable avoided crossings (UACs), 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 densitylike to spinlike behavior, as the collective excitation shows the transition from the stable to the unstable mode for both the FM and AFM interactions. In the multiband 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.

DOI
10.1103/physreva.111.063303

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