Bose-Einstein condensation of spin-1/2 atoms with conserved total spin

Recently it has been predicted that if a gas of spin-1/2 bosonic atoms is cooled down while conserving its total spin, it can form a Bose-Einstein condensate in a new type of fragmented state. In that fragmented state two orbital wave functions are macroscopically occupied. We derive a set of Gross-Pitaevskii equations that describe the two occupied wave functions, taking into account the effects of interatomic interactions. We then analyze the solutions of those equations in some special cases. In particular, we find that if the fragmented state is realized in a toroidal trap, under certain conditions the system will spontaneously acquire macroscopic orbital angular momentum. Finally, we discuss the nature of the phase transition from an uncondensed gas to a fragmented-state condensate.