Numerical study of the stability of skyrmions in Bose-Einstein condensates

We show that the stability of three-dimensional skyrmions in trapped Bose-Einstein condensates depends critically on scattering lengths, atom numbers, trap rotation, and trap anisotropy. In particular, for the Rb87F=1,mf=-1, F=2,mf=1 hyperfine states stability is sensitive to the scattering lengths at the 2% level, where the differences between them are crucial. In a cigar shaped trap, we find stable skyrmions with slightly more than 2×106 atoms, a number which scales with the inverse square root of the trap frequency. These can be stabilized against drift out of the trap by laser pinning.