Low-Threshold Topological Pumping in Toroidal Spin-1 Bose-Einstein Condensate

Singular spin-nematic vortices are unique topological excitations in spin-orbit-coupled spin-1 Bose-Einstein condensates. However, dynamically generating them in harmonic traps requires excessive Raman coupling to overcome the high energy cost of creating a density-depleted core. We demonstrate that a toroidal trapping potential naturally resolves this geometric mismatch. By accommodating the vortex core, the toroidal geometry lowers the formation threshold by ~50% and significantly broadens the stable phase boundary. Crucially, this geometry-assisted stabilization enables deterministic topological pumping. Instead of the abrupt phase jumps observed in harmonic traps that completely bypass the singular vortex, the toroidal potential supports a clean, stepwise adiabatic evolution (|L_z = 0〉 → |1〉 → |2〉). Our results provide a robust, low-power protocol for initializing spin-nematic quantum qutrits, bridging the gap between theoretical prediction and experimental realization.