Normal State of a Polarized Fermi Gas at Unitarity

We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n_↓/n_↑ of minority atoms. We predict a first order phase transition from normal to superfluid at x_c=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P_c=(N_↑-N_↓)/(N_↑+N_↓)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.