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 $^{87}$Rb $|F=1,m_{f}=-1>$, $|F=2,m_{f}=1>$ hyperfine states stability is sensitive to the scattering lengths at the level of their present experimental uncertainties. In a cigar shaped trap, we find stable Skyrmions with as few as $2\times10^{6}$ 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.