Colliding clouds of strongly interacting fermions and out-of-phase spin modes

Motivated by recent experiments at MIT, we consider the problem of what happens when two Fermi clouds prepared in different hyperfine states collide with each other at low velocities close to a Feshbach scattering resonance. Upon coming into contact with each other, we show that the two clouds evolve preferentially into a metastable upper branch (with amplitude given by the coherent quasiparticle residue Z) where interactions are repulsive, and not the ground state lower branch. As a result, even though the underlying interaction between the fermions is attractive, for sufficiently strong interactions in the unitary region, the clouds will ``bounce" off each other. Using Boltzmann, sum rule and hydrodynamic approaches, we make predictions for the frequency of the bounce mode on the BEC side of resonance, including unitarity, where the scattering length is positive.