  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.
