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Density, spin, and pairing instabilities in polarized ultracold Fermi gases

We study the influence of population imbalance on the pairing, spin, and density instabilities of a two component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite momentum pairing, suggesting the possibility of observing FFLO-like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the BCS side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the BEC side of the resonance, the pairing instability is present for scattering lengths that are larger than a critical value that is only weakly dependent on population imbalance and always smaller than the scattering length at which the Stoner-like spin instability occurs.