Theory of Radio Frequency Spectroscopy of Polarized Fermi Gases

Schneider, William; Shenoy, Vijay B.; Randeria, Mohit

Theory of Radio Frequency Spectroscopy of Polarized Fermi Gases

Authors

Schneider, William

Shenoy, Vijay B.

Randeria, Mohit

Description

We present two exact results for singular features in the radio frequency intensity $I(ω)$ for ultracold Fermi gases. First, in the absence of final state interactions, $I(ω)$ has a universal high frequency tail $ Cω^{-3/2}$ for \emph{all} many-body states, where $C$ is Tan's contact. Second, in a \emph{normal} Fermi liquid at T=0, $I(ω)$ has a jump discontinuity of $Z/(1 - m/m^{*})$, where $Z$ is the quasiparticle weight and $m^*/m$ the mass renormalization. We then describe various approximations for $I(ω)$ in polarized normal gases. We show why an approximation that is exact in the $n_\dn=0$ limit, fails qualitatively for $n_{\dn} > 0$: there is no universal tail and sum rules are violated. The simple ladder approximation is qualitatively correct for very small $n_{\dn}$, but not quantitatively.
4 page, 3 figures