Three-dimensional solitons in Rydberg-dressed Bose–Einstein condensates with spin–orbit coupling and a radially periodic potential

We propose a model of three-dimensional (3D) Rydberg-dressed spinor (two-component) Bose–Einstein condensates (BECs), with the spin–orbit coupling (SOC) and an axisymmetric radially periodic potential. It produces various species of stable 3D solitons with different vorticities in its two components. The shape and stability of the soliton are determined by the system’s control parameters: the SOC strength ($\lambda$), coefficients of the contact and Rydberg–Rydberg interactions ($\sigma$ and $U_{ij}$, respectively), and the depth ($w_0$) of the radial potential. The ground-state 3D solitons, with the lowest set of topological charges in its components, one of which is 0 and the other one is $\pm 1$ (these states are known as semivortices), keep the axial symmetry. Excited states with higher topological charges, which are unstable in previously studied SOC systems, feature broken axial symmetry, but may be dynamically stable states. In the absence of SOC, we also find stable two-component solitons with crescent- and hollow-shaped components.