Abstract
We analyze the BCS-BEC crossover for a Fermi gas made of neutral atoms in three hyperfine states with a SU(3) invariant attractive interaction. By solving the extended BCS equations for the total number of particles and the pairing gap, we calculate at zero temperature the pairing gap, the population imbalance, the condensate fraction and the first sound velocity of the uniform system as a function of the interaction strength in both three and two dimensions. Contrary to the three-dimensional case, in two dimensions the condensate fraction approaches the value 1 only for an extremely large interaction strength and, moreover, the sound velocity gives a clear signature of the disappearance of one of the three hyperfine components.
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