Pairing with multiple flavors of fermions in ultracold atoms

We use Ginburg-Landau formalism to discuss s-wave pairing in ultracold Fermi gases with N flavors and with SU(N) symmetric interactions. We show that when the number of flavors is greater than two, the uniform superfluid state is unstable since the magnetization or flavor imbalance couples directly to the superfluid order parameter. We study the case of three flavors in detail to analyze the competition between phase separation and non-uniform FFLO-like superfluid states. Implications of our results for experiments will be discussed.