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 Fulde-Ferrell-Larkin-Ovchinnikov-like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the Bardeen-Cooper-Schrieffer side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the Bose-Einstein-condensate side of the resonance, the pairing instability is present for scattering lengths 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.