Sinusoidal-magnetic-field-induced topological excitations in a spin-orbit-coupled spinor condensate

We explore topological excitations in a spin-1 Bose-Einstein condensate subjected to an in-plane sinusoidally varying magnetic field and Rashba spin-orbit coupling (SOC). In the absence of SOC, the periodic magnetic field induces vortex-antivortex structures in the $|F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ condensates at saddle points such that the net topological charge remains zero. The introduction of Rashba SOC breaks the system's symmetry, leading to nonconservation of overall angular momentum in the spin-1 condensate. This anisotropy results in the emergence of certain skyrmion spin textures. We provide a comparative study for various in-plane magnetic-field configurations while keeping the SOC strength constant. Our numerical simulations within the mean-field framework reveal the potential to engineer diverse topological excitations controlled by the interplay between the spin-orbit coupling and in-plane magnetic field in a spinor condensate.