Compressibility of a Repulsive Fermi Gas of $^6$ Li

We studied the equilibrium properties of a two-component repulsive Fermi gas of $^6$ Li by measuring the compressibility at various interaction strengths near a Feshbach resonance at 834G. The compressibility was extracted from in-trap atomic density profiles, and agrees with first order perturbation theory. Our experiment uses phase-contrast imaging to probe atomic clouds with large optical density, requiring compensation of dispersive effects. The feasibility window for such experiments is limited by decay to a near-resonant molecular bound state, and we explore the limits of this window by measuring decay rates at various interaction strengths.