Universal properties of the ultracold Fermi gas

We present some general considerations on the properties of a two-component ultracold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the free energy can be written in terms of a single dimensionless function $h(\xi ,\tau )$, where $\xi =-{\left(k_F{a}_s\right)}^{-1}$ and $\tau =T∕T_F$. The function $h(\xi ,\tau )$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the average rf-spectroscopy shift $\overline{\delta \omega }(\xi ,\tau )$ and the molecular fraction $f_c(\xi ,\tau )$ in the closed channel can be expressed in terms of $h(\xi ,\tau )$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.