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} =1/4 $ 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.
Categories: cond-mat.str-el