Asymmetric Two-component Fermion Systems in Strong Coupling

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.