Spin–orbit coupling induced three-dimensional topological objects in attractive Bose–Einstein condensates

Attractive Bose–Einstein condensates of dilute alkali gases are unstable against collapse in two- and three-dimensional free space. Nevertheless, we demonstrate that the spin–orbit coupling of the two-component condensates counteracts the tendency of collapse and makes the system preferable to an extended spatial distribution in the three-dimensional case. Furthermore, stable topological objects can be formed in the condensates, which are shown to be the lowest energy states. Two configurations of the density profiles, called three-dimensional skyrmion and three-dimensional dimeron, respectively, are identified depending on the strength of the spin–orbit coupling. (paper)