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 {sup 87}Rb-F=1,m{sub f}=-1>, -F=2,m{sub f}=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 2x10{sup 6} 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.