Quantum Hall Fractions in Rotating Bose-Einstein Condensates

We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction ν, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for ν=2/3,3/4,4/3,5/4 in addition to the Laughlin state ν=1/2 as well as the Pfaffian state for ν=1. We give gap estimates by finite-size scaling of both charged and neutral excitations.