Effect of finite-range interactions on rapidly rotating ultracold bosonic atoms

We investigate the effects of the finite-range interactions of six rotating ultracold bosonic atoms using a Gaussian-type interatomic interaction model. The model is analyzed numerically by exact diagonalization within the Lowest Landau Level (LLL) approximation and semiclassical approximation. The result of exact diagonalization shows that the ground-state angular momentum changes discretely with increasing angular velocity. For the short-range limit, the ground-state angular momentum and wavefunctions agree with those of the delta interaction evaluated by Bertsch and Papenbrock. Different from the delta interaction, the ground-state angular momenta higher than 30, i.e., N(N - 1), are observed at a high angular frequency as a result of the finite-range two-body interactions. For the intermediate-range interaction, the sequence of ground-state angular momenta increases in steps of five, which was not found in previous works on the Gaussian interaction. For the long-range limit of Gaussian interaction, we find that the ground-state angular momenta increase in steps of six. These steps of the ground-state angular momentum according to the width of the Gaussian interactions are explained by semiclassical and classical analysis based on the rovibrating molecule picture. The increments of the ground-state angular momentum of five and six are explained by the semiclassical quantization condition of the rotational and vibrational modes of fivefold and sixfold molecules, respectively. Our analysis based on the classical model also confirms that the fivefold molecule picture is more stable than the sixfold molecule picture in the intermediate range of the Gaussian interaction. These results suggest that the Gaussian interaction model can be used to emulate and characterize interactions by their width as the model can reproduce various rotational states including the ground states of rotating systems interacting with delta-type and Coulomb type interactions. (author)