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 $ u_{f}=1$, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a $ u_{f} =1 $ fermionic integer quantum Hall state to $ u_{b} =1/4 $ 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.