  We investigate the formation of Bose-Einstein condensation and 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 and also in two dimensions. Within the mean-field theory, we
derive explicit formulas for number densities, gap order parameter, condensate
density and 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.

Quantum Gases