Incompressible Liquid State of Rapidly Rotating Bosons at Filling Factor3/2

Bosons in the lowest Landau level, such as rapidly rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is $3/2$. When a moderate amount of a longer-range (e.g., dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.