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 (ξ,τ), where ξ=- (kF as) -1 and τ=TTF. The function h (ξ,τ) 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 δω ̄ (ξ,τ) and the molecular fraction fc (ξ,τ) in the closed channel can be expressed in terms of h (ξ,τ) and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.