Bose-einstein condensation of trapped interacting spin-1 atoms

We investigate Bose-Einstein condensation of trapped spin-1 atoms with ferromagnetic or antiferromagnetic two-body contact interactions. We adopt the mean field theory and develop a Hartree-Fock-Popov type approximation in terms of a semiclassical two-fluid model. For antiferromagnetic interactions, our study reveals double condensations as atoms in the |m{sub F}=0> state never seem to condense under the constraints of both the conservation of total atom number N and magnetization M. For ferromagnetic interactions, however, triple condensations can occur. Our results can be conveniently understood in terms of the interplay of three factors: (anti)ferromagnetic atom-atom interactions, M conservation, and the miscibilities between and among different condensed components.