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

We theoretically investigate the condensate state and collective excitations of a two-component Bose gas in a two-dimensional harmonic trap subject to isotropic Rashba spin-orbit coupling. In the weakly interacting regime when the interspecies interaction is larger than the intraspecies interaction (g_↑↓>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 rotational symmetry. In the case of g_↑↓<g, the condensate becomes unstable toward the superposition of two degenerate half-quantum vortex states. Both instabilities (at g>g_c and g_↑↓<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 obtain the phase diagram as a function 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 trap anisotropy and anisotropy in the spin-orbit coupling.