Skyrmions with Arbitrary Topological Charges in Spinor Bose–Einstein Condensates

Topological Skyrmion defects with arbitrary topological charges are shown to appear in spinor F = 1 Bose-Einstein condensates, under the presence of external gauge or magnetic fields with cylindrical symmetry. We show that, depending on the magnetic field boundary conditions, the spin texture, at the planes perpendicular to the cylindrical axis, can be forced to show Skyrmions with topological charge zero, half-integer, or any desired arbitrary value between -1/2 and 1/2. Our findings are obtained by numerically solving the corresponding fully coupled Gross-Pitaevskii equations without any symmetry assumptions and by analyzing the Skyrmion topological charge. We study, both, polar Na-23 and ferromagnetic Rb-87 condensates.