Temperature Dependence of the Universal Contact Parameter in a Unitary Fermi Gas

The contact $\mathcal{I}$, 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 interaction 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.

Figure 1

Bragg spectra and dynamic structure factor of a unitary Fermi gas. Measured change in (a) the first moment (center of mass displacement) $\Delta X(\omega )$ and (b) the second moment (increase in mean square size) $\Delta {\sigma }_x^2(\omega )$ as a function of the Bragg frequency $\omega$ at temperatures $T/T_F=0.09$, 0.27, 0.55, and 0.97. (c) Dynamic structure factor $S(k,\omega )$ obtained from a weighted average of the first and second moments. Points are the experimental data and the solid lines are double Gaussian fits normalized according to the $f$-sum rule.

Figure 2

Temperature dependence of the contact over the range $T/T_F=0.1–1.0$. Data points are the measured values of $\mathcal{I}$ obtained from the static structure factors. Solid, dash-dotted, and dash-double dotted lines are predictions based on three different strong-coupling theories as described in the text [14, 19, 20]. The long-dashed and short-dashed lines are second and third order quantum virial expansion calculations, respectively [20].