Quantum Hall fractions in ultracold atomic vapors

Atomic vapors can be prepared and manipulated at very low densities and temperatures. When they are rotating, they can reach a quantum Hall regime in which there should be manifestations of the fractional quantum Hall effect. We discuss the appearance of the principal sequence of fractions nu =p/(p+- 1) for bosonic atoms. The termination point of this series is the paired Moore-Read Pfaffian state. Exotic states fill the gap between the paired state and the vortex lattice expected at high filling of the lowest Landau level. In fermionic vapors, the p-wave scattering typical of ultralow energy collisions leads to the hard-core model when restricted to the lowest Landau level.