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

## TL;DR

This study experimentally investigates the excitation spectra of a near-uniform unitary Fermi gas using Bragg spectroscopy, revealing the behavior of the contact parameter and internal energy across the superfluid transition.

## Contribution

It provides the first local measurements of the dynamic structure factor in a nearly uniform unitary Fermi gas and applies sum-rules to extract key thermodynamic quantities.

## Key findings

- Measured the dynamic structure factor at various temperatures.
- Resolved the behavior of the contact parameter across the superfluid transition.
- Determined the internal energy of the gas at unitarity.

## Abstract

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.