Condensate formation with three-component ultracold fermions

We investigate the formation of Bose-Einstein condensation and a population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions as well as in two dimensions. Within mean-field theory, we derive explicit formulas for the number densities, the gap order parameter, the condensate density, and the condensate fraction of the uniform system and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers. In addition we study this Fermi mixture trapped by a harmonic potential: We calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.