Half-quantum vortex state in a spin-orbit coupled Bose-Einstein condensate

TL;DR

This paper theoretically explores the properties, stability, and phase diagram of half-quantum vortex states in a two-component Bose-Einstein condensate with Rashba spin-orbit coupling, revealing conditions for their formation and instability.

Contribution

It introduces a detailed analysis of half-quantum vortex states in spin-orbit coupled BECs, including phase diagrams, stability criteria, and dynamical simulations, advancing understanding of topological excitations.

Findings

Half-quantum vortex states exhibit skyrmion-like spin textures.

Instability occurs when inter-species interaction exceeds a critical value.

Time-dependent simulations confirm stability conditions and dynamical behavior.

Abstract

We investigate theoretically the condensate state and collective excitations of a two-component Bose gas in two-dimensional harmonic traps subject to isotropic Rashba spin-orbit coupling. In the weakly interacting regime when the inter-species interaction is larger than the intra-species interaction ($g_{\uparrow\downarrow}>g$), we find that the condensate ground state has a half-quantum-angular-momentum vortex configuration with spatial rotational symmetry and skyrmion-type spin texture. Upon increasing the interatomic interaction beyond a threshold $g_{c}$, the ground state starts to involve higher-order angular momentum components and thus breaks the rotational symmetry. In the case of $g_{\uparrow\downarrow}<g$, the condensate becomes unstable towards the superposition of two degenerate half-quantum vortex states. Both instabilities (at $g>g_{c}$ and $g_{\uparrow\downarrow}<g$) can be determined by solving the Bogoliubov equations for collective density oscillations of the half-quantum vortex state, and by analyzing the softening of mode frequencies. We present the phase diagram as functions of the interatomic interactions and the spin-orbit coupling. In addition, we directly simulate the time-dependent Gross-Pitaevskii equation to examine the dynamical properties of the system. Finally, we investigate the stability of the half-quantum vortex state against both the trap anisotropy and anisotropy in the spin-orbit coupling term.