Theory of Radio Frequency Spectroscopy of Polarized Fermi Gases

Abstract

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 $C{\omega }^{-3/2}$ 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 $Z/(1-m/m^{\ast })$, where $Z$ is the quasiparticle weight and $m^{\ast }/m$ 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 $n_\dn=0$ 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

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