Quantum Hall fractions in ultracold fermionic vapors

We study the quantum Hall states that appear in the dilute limit of rotating ultracold fermionic gases when a single hyperfine species is present. We show that the $p$-wave scattering translates into a pure hard-core interaction in the lowest Landau level. The Laughlin wave function is then the exact ground state at filling fraction $\nu =1∕3$. We give estimates of some of the gaps of the incompressible liquids for $\nu =p∕(2p\pm 1)$. We estimate the mass of the composite fermions at $\nu =1∕2$. The width of the quantum Hall plateaus is discussed by considering the equation of state of the system.