  A two-component Bose-Einstein condensate rotating in a toroidal trap is
investigated. The topological constraint depends on the density distribution of
each component along the circumference of the torus, and therefore the
quantization condition on the circulation can be controlled by changing the
miscibility using the Feshbach resonance. We find that the system exhibits a
variety of dynamics depending on the initial angular momentum when the
miscibility is changed.
