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arXiv:2509.03344 · Physical Review A

Emergence of spin-mixed superstripe phases in spin-orbit-coupled spin-1 condensates

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

Published Jan 14, 2026• 1 citation
arXivHTMLPDF

Abstract

We numerically investigate the ground state phases and quench dynamics of spin-orbit coupled spin-1 Bose-Einstein condensates with ferromagnetic and antiferromagnetic interactions. For finite Rabi coupling, the system exhibits zero-momentum, elongated zero-momentum, and stripe phases, while in the limit $Ω\rightarrow 0$, the superstripe wave phases emerge. Varying the attractive density-density ($c_0$) and spin-exchange ($c_2$) interactions induces the transition from stripe and superstripe phases to the elongated zero-momentum phase, characterized by miscibility and polarization. The condensate remains miscible in the zero-momentum phase and partially miscible for the elongated, stripe, and superstripe phases. Quenching in Rabi coupling stabilizes the condensate, while spin-orbit coupling quenching leads to fluctuations or the formation of complex patterns, with the stripe phase exhibiting the vanishing of the zeroth spin component over time. Our results may offer valuable insights into engineering exotic quantum phases in ultracold atomic gases.

DOI
10.1103/3564-qkv7

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Abstract We study the miscibility properties and ground state phases of two-component spin–orbit (SO) coupled Bose–Einstein condensates (BECs) in a harmonic trap with strong axial confinement. By numerically solving the coupled Gross–Pitaevskii equations in the two-dimensional setting, we analyze the SO-coupled BECs for two possible permutations of the intra- and interspecies interactions, namely (i) weak intra- and weak interspecies interactions (W–W) and (ii) weak intra- and strong interspecies interactions (W–S). Considering the density overlap integral as a miscibility order parameter, we investigate the miscible–immiscible transition by varying the coupling parameters. We obtain various ground state phases, including plane wave, half quantum vortex, elongated plane wave, and different stripe wave patterns for W–W interactions. For finite Rabi coupling, an increase in SO coupling strength leads to the transition from the fully miscible to the partially miscible state. We also characterize different ground states in the coupling parameter space using the root mean square sizes of the condensate. The spin density vector for the ground state phases exhibits density, quadrupole and dipole like spin polarizations. For the W–S interaction, in addition to that observed in the W–W case, we witness semi vortex, mixed mode, and shell-like immiscible phases. We notice a wide variety of spin polarizations, such as density, dipole, quadrupole, symbiotic, necklace, and stripe-like patterns for the W–S case. A detailed investigation in the coupling parameter space indicates immiscible to miscible state phase transition upon varying the Rabi coupling for a fixed Rashba SO coupling. The critical Rabi coupling for the immiscible–miscible phase transition decreases upon increasing the SO coupling strength.