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 $p_x+i{p}_y$-wave superfluid. 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.

Figure 1

(a) A schematic temperature-detuning phase diagram near a $p$-wave FR, for intermediate splitting of $m=0$, $\pm 1$ FR (see below). It shows a second-order $p_x$ to $p_x+i{p}_y$ SF transition at ${\omega }_{0c}$ as well as a topological phase transition at ${\omega }_0(\mu =0)$ between two different $p_x+i{p}_y$ phases. (b), (c) show alternative phase diagrams for smaller and larger values of FR splitting, respectively.