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Competing instabilities in quench experiments with ultracold Fermi gases near a Feshbach resonance

Tunability of effective two body interactions near Feshbach resonances is a powerful experimental tool in systems of ultracold atoms. It has been used to explore a variety of intriguing phenomena in recent experiments. However not all of the many-body properties of such systems can be understood in terms of effective models with contact interaction given by the scattering length of the two particles in vacuum. For example, when a two component Fermi mixture is quenched to the BEC side of the Feshbach resonance, a positive scattering length suggests that interactions are repulsive and thus collective dynamics should be dominated by the Stoner instability toward a spin polarized ferromagnetic state. On the other hand, existence of low energy two particle bound states suggests a competing instability driven by molecule formation. Compe- tition between spontaneous magnetization and pair formation is determined by the the interplay of two-particle and many-body phenomena. In these lecture notes we summarize our recent theoretical results, which analyzed this competition from the point of view of unstable collective modes. We also comment on the relevance of this theoretical analysis to recent experiments reported in Ref. (Jo, Lee, Choi, Christensen, Kim, Thywissen, Pritchard and Ketterle, 2009).