Universal short-distance structure of the single-particle spectral function of dilute Fermi gases

Abstract

We show that the universal 1/k^4 tail in the momentum distribution of dilute Fermi gases implies that the spectral function A(k,ω) must have weight below the chemical potential for large momentum k≫k_F, with observable consequences in radio-frequency spectroscopy experiments. We find that this incoherent spectral weight is centered around ω≃-ε(k) in a range of energies of order v_Fk. This “bending back” in the dispersion, while natural for superfluids, is quite surprising for normal gases. This universal structure is present in the hard-sphere gas as well as in the Fermi-liquid ground state of the highly imbalanced, attractive gas near unitarity. We argue that, even in the BCS superfluid, this bending back at large k is dominated by interaction effects which do not reflect the pairing gap.