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Phase Diagram of a Strongly Interacting Spin-Imbalanced Fermi Gas

We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of $^6$Li atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the BCS and unitary regimes. We disagree with the QMC results in the BEC regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states.