Equation of State and Phases of Polarized Unitary Fermi Gas

The equation of state of the partially polarized two component Fermi gas at zero temperature in the unitary limit is computed by {\it ab initio} auxiliary field Monte Carlo method. We obtain the critical ratio of the chemical potentials ${\mu }_{\downarrow }\mathrm{/}{\mu }_{\uparrow }$ at the phase transitions. The value of ${\mu }_{\downarrow }\mathrm{/}{\mu }_{\uparrow }$ at the transition between the fully paired superfluid and the partially polarized phase is 0.11 while the critical value for the phase transition between the partially polarized phase and the fully polarized normal fluid is -0.59. We also determine the radial boundaries of the phase transitions of the Fermi gas in the harmonic trap as function of the total polarization. We find that beyond the critical polarization 0.65, the fully paired superfluid core disappears in the trapped Fermi gas.