Theory of Radio Frequency Spectroscopy of Polarized Fermi Gases

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