Exact Groundstates of Rotating Bose Gases close to a Feshbach Resonance

We study the groundstates of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact groundstates at high angular momentum can be found analytically for a general and realistic model for the resonant interactions. We identify parameter regimes where the exact groundstates are exotic fractional quantum Hall states, the excitations of which obey non-abelian exchange statistics.