Exact eigenstates and magnetic response of spin-1 and spin-2 Bose-Einstein condensates

The exact eigenspectra and eigenstates of spin-1 and spin-2 Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEG, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlations among three bosons.