Stable Three‐Dimensional Lattice Solitons in Spin‐Orbit‐Coupled Bose‐Einstein Condensates

ABSTRACT

We address three‐dimensional (3D) solitons maintained by spin‐orbit coupling (SOC) in the binary self‐interacting Bose‐Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC‐OL interplay results in the formation of stable full‐vortex (FV) solitons, built as sets of four density peaks residing in neighboring wells of the lattice potential, with the superimposed global vortical phase, and site‐centered semi‐vortices (SVs), in which the vorticity is present in only one component. The FV solitons, with their specific phase textures, do not exist in a uniform BEC with SOC. FV and SV states in the binary self‐attractive BEC are stable despite the possibility of the supercritical collapse in the 3D system. Such states also exist, as gap solitons, in the self‐repulsive 3D system. In terms of the chemical potential and number of particles, the stability regions of the 3D FV solitons and SVs expand with the increase of the SOC strength and OL depth. The results open the route to the creation of 3D complexes of vorticity‐carrying condensates that can be realized with existing experimental techniques.