Quantum Phase Transitions across a p-Wave Feshbach Resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a p_x-wave to a p_x+ip_y-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological p_x+ip_y to p_x+ip_y transition at zero chemical potential μ. In two dimensions, for μ>0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.