Fractionalization via ${\mathbb{Z}}_2$ Gauge Fields at a Cold Atom Quantum Hall Transition

We study a single species of fermionic atoms in an “effective” magnetic field at total filling factor ${\nu }_f=1$, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ${\nu }_f=1$ fermionic integer quantum Hall state to ${\nu }_b=1\mathrm{/}4$ bosonic fractional quantum Hall state as a function of detuning. The transition is in the $(2+1)$-D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a ${\mathbb{Z}}_2$ gauge field, and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.