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-anti-vortex structures in the $\ket{F=1, m_F=\pm1}$ condensates at saddle-points, such that the net topological charge remains zero. The introduction of Rashba SOC breaks the system's symmetry, leading to non-conservation 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 spin-orbit coupling and in-plane magnetic field in a spinor condensate.