We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be $3.06\pm 0.08$ at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

Ultracold Fermi gases subject to tight transverse confinement offer a highly controllable setting to study the two-dimensional (2D) BCS to Berezinskii-Kosterlitz-Thouless superfluid crossover. Achieving the 2D regime requires confining particles to their transverse ground state which presents challenges in interacting systems. Here, we establish the conditions for an interacting Fermi gas to display 2D kinematics. Transverse excitations are detected by measuring the transverse expansion rate which displays a sudden increase when the atom number exceeds a critical value $N_{2D}$ signifying a density driven departure from 2D kinematics. For weak interactions $N_{2D}$ is set by the aspect ratio of the trap. Close to a Feshbach resonance, however, the stronger interactions reduce $N_{2D}$ and excitations appear at lower density.

A prominent peak in the density response function of fermions below Tc is observed experimentally using spatially resolved Bragg spectroscopy allowing for local measurements in the trapped Fermi gas.

Understanding the formation of Cooper pairs and the resulting thermodynamic properties of low-dimensional Fermi gases is an important area of research, which may help build our understanding of other low-dimensional systems, such as high-temperature superconductors. In lower dimensions, quantum fluctuations are expected to play an increasingly important role, and the reliability of strong-coupling theories becomes questionable. Here, we present a comparison of recent thermodynamic measurements and theoretical predictions from different many-body $T$-matrix theories for a two-dimensional strongly interacting Fermi gas in the normal state. We find that the fully self-consistent $T$-matrix theory provides the best description of the experimental data over a wide range of temperatures and interatomic interactions.

This article provides an overview of recent developments and emerging topics in the study of two-component Fermi gases using Bragg spectroscopy. Bragg scattering is achieved by exposing a gas to two intersecting laser beams with a slight frequency difference and measuring the momentum transferred to the atoms. By varying the Bragg laser detuning, it is possible to measure either the density or spin response functions which characterize the basic excitations present in the gas. Specifically, one can measure properties such as the dynamic and static structure factors, Tan’s universal contact parameter and observe signatures for the onset of pair condensation locally within a gas.