Zero Temperature Thermodynamics of Asymmetric Fermi Gases at Unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one non-trivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the T=0 equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.