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Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate

We consider a weakly-interacting Bose-Einstein condensate that rotates in either a harmonic, or a weakly-anharmonic trapping potential. Performing numerical calculations, we investigate the behaviour of the gas in these two cases as the angular momentum, or equivalently as the rotational frequency of the trap increases. While in the case of a purely-harmonic potential the gas makes a transition from the mean-field regime to the correlated, "Laughlin", regime, in the case of anharmonic confinement the mean-field approximation remains always valid. We compare our derived results in these two cases, using both the mean-field approximation, as well as the diagonalization of the many-body Hamiltonian considering a small atom number.