Contact and sum-rules in a near-uniform Fermi gas at unitarity

We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focussed beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum-rules to the measured Bragg spectra, we resolve the characteristic behaviour of the universal contact parameter, ${\cal C}$, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum-rule to obtain the internal energy of gases at unitarity.