Stable Solitons in Three Dimensional Free Space: Self-Trapped Bose-Einstein Condensates with Spin-Orbit Coupling

By means of variational methods and systematic numerical analysis, we demonstrate the existence of stable solitons in three-dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and spin-orbit coupling, which can be engineered by available experimental techniques. Depending on the relative strength of the intra- and inter-component attraction, the stable solitons feature a semi-vortex or mixed-mode structure. In spite of the fact that the local cubic self-attraction gives rise to the supercritical collapse in 3D, the solitons are stable against random perturbations, motion, and collisions.