Chandrasekhar-Clogston limit and phase separation in Fermi mixtures at Unitarity

Using many-body results available from diagrammatic and {\it ab initio} Monte Carlo calculations we analyze the phase diagram $\mu=(\mu_{\uparrow}+\mu_{\downarrow})/2$ versus $h=(\mu_{\uparrow}-\mu_{\downarrow})/2$ of a unitary Fermi gas at zero temperature with population imbalance and unequal masses. We identify different regions where the gas is superfluid, partially polarized or fully polarized and determine the corresponding coexistence conditions. The asymmetry in the phase diagram, caused by the mass imbalance, and its effect on the Chandrasekhar-Clogston limit for the critical polarization are explicitly discussed. The equation of state of the superfluid and normal phases is employed, within the local density approximation, to predict novel phase separated configurations in the presence of harmonic trapping potentials.