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 $\nu$, 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 $\nu =2/3,3/4,4/3,5/4$ in addition to the Laughlin state $\nu =1/2$ as well as the Pfaffian state for $\nu =1$. We give gap estimates by finite-size scaling of both charged and neutral excitations.