Exact Calculations for Ultracold Rotating Bose Gases

Through the use of exact diagonalization, we have investigated general properties of harmonically trapped, rotating ultracold bose gases having both attractive and repulsive interactions. We have calculated the low energy spectrum for a small number of bosons and have used the similarities between fermions in a strong magnetic field and bosons subjected to rotation in order to identify different bosonic fractional quantum states which may be used to perform topological quantum computations.