Measurement of the Homogeneous Contact of a Unitary Fermi Gas

By selectively probing the center of a trapped gas, we measure the local, or homogeneous, contact of a unitary Fermi gas as a function of temperature. Tan's contact, C, is proportional to the derivative of the energy with respect to the interaction strength and is thus an essential thermodynamic quantity for a gas with short-range correlations. Theoretical predictions for the temperature dependence of C differ substantially, especially near the superfluid transition, T-c, where C is predicted to either sharply decrease, sharply increase, or change very little. For T/T-F > 0.4, our measurements of the homogeneous gas contact show a gradual decrease of C with increasing temperature, as predicted by theory. We observe a sharp decrease in C at T/TF 0.16, which may be due to the superfluid phase transition. While a sharp decrease in C below T-c is predicted by some many-body theories, we find that none of the predictions fully account for the data.