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Chinese Physics B

Phase diagram of helicoidal spin-orbit coupled Bose-Einstein condensates in a harmonic potential

Ji Li, Xiaomin Wang, Tian-Chen He

Published Jul 30, 2026• 0 citations
Publisher

Abstract

Abstract We investigate ground-state phase diagram of helicoidal spin-orbit coupled Bose-Einstein condensates in a harmonic trap when the intraspecies interaction $g$ and the interspecies interaction $g_{\uparrow\downarrow}$ are unequal. In the case of $g>g_{\uparrow\downarrow}$, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with small oscillation amplitude. In the case of $g＜g_{\uparrow\downarrow}$, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with large oscillation amplitude. Our findings show that the helicoidal spin-orbit coupling plays a crucial role in inducing multiple-peak matter waves. Adjusting the spin-orbit coupling strength and the gauge potential can control the number of wave peaks. Finally, we also discuss the ground-state properties under different Zeeman splitting parameters when the helicoidal spin-orbit coupling strength and the gauge potential are fixed.

DOI
10.1088/1674-1056/ae9268

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Abstract We investigate ground-state phase diagram of helicoidal spin-orbit coupled Bose-Einstein condensates in a harmonic trap when the intraspecies interaction ggg and the interspecies interaction g↑↓g_{\uparrow\downarrow}g↑↓​ are unequal. In the case of g>g↑↓g>g_{\uparrow\downarrow}g>g↑↓​, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with small oscillation amplitude. In the case of g＜g↑↓g＜g_{\uparrow\downarrow}g＜g↑↓​, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with large oscillation amplitude. Our findings show that the helicoidal spin-orbit coupling plays a crucial role in inducing multiple-peak matter waves. Adjusting the spin-orbit coupling strength and the gauge potential can control the number of wave peaks. Finally, we also discuss the ground-state properties under different Zeeman splitting parameters when the helicoidal spin-orbit coupling strength and the gauge potential are fixed.
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Supersolidity, characterized by superfluidity and crystallization, is an exotic state of matter. The spin-orbit- (SO-) coupled Bose-Einstein condensates (BECs) provide an ideal paradigm for exploring this quantum state. Here, we present a theoretical analysis of the ground-state phases and collective modes of supersolid SO-coupled BECs in a harmonic trap. The phase diagram of three ground-state phases (i.e., the supersolid phase, plane-wave phase, and zero-momentum phase) is obtained analytically under the condition $\ensuremath{\omega}\ensuremath{\ll}{k}_{0}$ (here, $\ensuremath{\omega}$ is harmonic trap frequency, k0{k}_{0}k0​ is SO-coupling strength), showing the spin polarization, the phase diagram, and the contrast of the supersolid stripes can be effectively manipulated by trapping potential. An efficient scheme to manipulate the supersolid phase is provided. Furthermore, with particular discussion of the supersolid phase, the collective modes in all three phases are obtained with a unified approach, and softening of both dipole and breathing modes with divergence of effective mass at phase transition point is explained analytically and well confirmed by direct numerical simulations. The impact of SO coupling on local currents during the breathing mode is discussed. The anharmonic collective modes are also revealed with the appearance of the flat band in the single-particle dispersion, especially when SO-coupling strength is comparable with trapping potential. Our theoretical method provides a clear physical picture that collective modes of SO-coupled BECs can be regarded as classical harmonic oscillators with an effective mass containing the SO coupling.
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This study explores the dynamics of Bose-Einstein condensates (BECs) with helicoidal spin-orbit coupling (SOC) and Rabi coupling, confined under a two-dimensional harmonic potential. The relationship between helicoidal SOC, non-linear interactions along with Rabi coupling and their impact on the stability and non linear trapped modes of the condensate is analyzed using a coupled Gross-Pitaevski (GP) framework. A linearized GP equation is used to investigate modulation instability (MI), demonstrating the impact of strong coupling effects and anisotropic confinement on the instability dynamics. It has been shown that the modulation instability in the condensate is predominantly governed by the competition between the attractive and repulsive mean-field interactions. Additionally, stability regimes are altered by the harmonic confinement, enhancing their susceptibility to SOC-induced asymmetry and intra- and intercomponent interactions. These results shed light on the possibility for unique quantum phases and emergent characteristics of helicoidal SOC-driven condensates.