Anisotropic semivortices in dipolar spinor condensates controlled by Zeeman splitting

Abstract

Spatially anisotropic solitary vortices, i.e., bright anisotropic vortex solitons (AVSs), supported by anisotropic dipole-dipole interactions, were recently predicted in spin-orbit-coupled binary Bose--Einstein condensates (BECs), in the form of two-dimensional semivortices (complexes built of zero-vorticity and vortical components). We demonstrate that the shape of the AVSs---horizontal or vertical, with respect to the in-plane polarization of the atomic dipole moments in the underlying BEC---may be effectively controlled by the strength $\mathrm{\ensuremath{\Omega}}$ of the Zeeman splitting (ZS). A transition from the horizontal to vertical shape with the increase of $\mathrm{\ensuremath{\Omega}}$ is found numerically and explained analytically. At the transition point, the AVS assumes the shape of an elliptical ring. The mobility of horizontal AVSs is studied, too, with the conclusion that, with the increase of $\mathrm{\ensuremath{\Omega}}$, their negative effective mass changes the sign to positive via a point at which the effective mass diverges. Lastly, we report a new species of inverted AVSs, with the zero-vorticity and vortex component placed in lower- and higher-energy components, as defined by the ZS. They are excited states, with respect to the ground states provided by the usual AVSs. Quite surprisingly, inverted AVSs are stable in a large parameter region.