Quantum phase transitions across p-wave Feshbach resonance*

We study a single-species polarized Fermi gas tuned across a narrow $p$-wave Feshbach resonance. We show the existence of a magnetic field-tuned quantum phase transition as detuning sweeps across the Fermi energy, between a $p_x$-wave BCS superfluid and a $p_x+ i p_y$ molecular superfluid in the BEC regime. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological $p_x+ i p_y$ to $p_x+ i p_y$ transition at zero chemical potential, $\mu$. In two-dimensions, for $\mu>0$ it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.