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(down arrow)/n(up arrow) 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-up arrow-N-down arrow)/(N-up arrow+N-down arrow)=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.