Continuous vortex pumping into a spinor condensate with magnetic fields

We study the mechanisms and the limits of pumping vorticity into a spinor condensate through manipulations of magnetic (B-) fields. We discover a fundamental connection between the geometrical properties of the magnetic fields and the quantized circulation of magnetically trapped atoms, a result which generalizes several recent experimental and theoretical studies. The optimal procedures are devised that are capable of continuously increasing or decreasing a condensate's vorticity by repeating certain two step B-field manipulation protocols. We carry out detailed numerical simulations that support the claim that our protocols are highly efficient, stable, and robust against small imperfections of all types. Our protocols can be implemented experimentally within current technologies.