Spectral function and RF spectroscopy of dilute Fermi gases

The spectral function $A(k,\omega)$ is a quantity of fundamental interest in many-body physics and its occupied part can now be directly measured in angle-resolved RF spectroscopy experiments. We describe a surprising universal feature [1] in {\it all} dilute Fermi gases: for $k \gg k_F$, there is incoherent spectral weight centered about {\it negative} $k^2/2m$ in a range of energies that scales linearly with k. The total weight of this feature is exactly $n(k) \sim C / k^4$, where $C$ is Tan's contact. This ``bending back'' in the dispersion, while natural for superfluid excitations, is quite unexpected for normal gases, such as the hard-sphere Fermi gas and the Fermi liquid ground state of the highly spin-imbalanced, attractive gas near unitarity. We also argue that in the superfluid, this feature is dominated by interaction effects which do not reflect the pairing gap; e.g., the spectral weight in this feature is not exponentially small in the BCS limit, but rather a power law in $k_F a$. This incoherent spectral feature has observable consequences for both angle-resolved and usual RF spectroscopy. We will also describe observable properties of the low-energy spectral function in both the normal and superfluid ground states. [1] W. Schneider and M. Randeria, arXiv:0910.2693