  We study the phase structure of a dilute two-component Fermi system with
attractive interactions as a function of the coupling and the polarization or
number difference between the two components. In weak coupling, a finite number
asymmetry results in phase separation. A mixed phase containing symmetric
superfluid matter and an asymmetric normal phase is favored. With increasing
coupling strength, we show that the stress on the superfluid phase to
accommodate a number asymmetry increases. Near the infinite-scattering length
limit, we calculate the single-particle excitation spectrum and the
ground-state energy at various polarizations. A picture of weakly-interacting
quasi-particles emerges for modest polarizations. In this regime near infinite
scattering length, and for modest polarizations, a homogeneous phase with a
finite population of excited quasi-particle states characterized by a gapless
spectrum should be favored over the phase separated state. These states may be
realized in cold atom experiments.
