The contact ${cal I}$, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the intera
ction parameter $1/(k_F a)$, where $k_F$ is the Fermi wave-vector and $a$ is the $s$-wave scattering length, and the temperature $T/T_F$, where $T_F$ is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.
We have studied the transition from two to three dimensions in a low temperature weakly interacting $^6$Li Fermi gas. Below a critical atom number, $N_{2D}$, only the lowest transverse vibrational state of a highly anisotropic oblate trapping potenti
al is occupied and the gas is two-dimensional. Above $N_{2D}$ the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.
We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tans relations. This is achieved through measurements of the static structure factor which displays a universal scaling proporti
onal to the ratio of Tans contact to the momentum $C/q$. Bragg spectroscopy of ultracold $^6$Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the $f$-sum rule, which is found to improve the accuracy of the structure factor measurement.
