Topological solitons of spinor Bose-Einstein condensate with spherical-shell geometry*

A class of topological solitons, called the lumps, of three-component spinor Bose-Einstein condensate (BEC) is characterized when the BEC is placed on a spherical shell, which is made possible by recent progress in trapping ultracold atoms. The lump solitons are solutions to the nonlinear coupled equations from the minimization of the energy of the BEC. The topological properties of the lump solitons come from the homotopy between the real space, which is a two-sphere, and the order-parameter space from the vector fields formed by the three components of the spinor BEC, which is also a two-sphere. We define the winding number to count the wrapping between the two spaces and present an ansatz for generating the topological lump solitons with quantized winding numbers. The excitation energies of the lumps indicate that it is not energetically favorable for a high-winding lump to decay into multiple low-winding ones, in contrast to quantum vortices in superfluids. The lump solitons are realizable in spinor BEC and showcase the interplay between topology, nonlinear physics, and ultracold atoms.