Theory of radio frequency spectroscopy experiments in ultracold Fermi gases and their relation to photoemission in the cuprates

In this paper we present an overview of radio frequency (RF) spectroscopy in the atomic Fermi superfluids with the ultimate goal of suggesting new directions in the cold gas research agenda from the condensed matter perspective. We review the experimental and theoretical literature on cold gases and the photoemission spectroscopy of the cuprates particularly as it pertains to areas of overlap. In addition to a comparison with the cuprates, this paper contains a systematic overview of the theory of RF spectroscopy, both momentum integrated and momentum resolved. It should be noted that the integrated and momentum resolved forms of photoemission are equally important in the high T_c cuprate literature. For the cold gases we introduce the reader to such topical issues as the effects of traps, population imbalance, final state interactions and, over the entire range of temperatures, we compare theory and experiment. We show that this broad range of phenomena can be accommodated within the BCS-Leggett description of BCS-BEC crossover. Importantly, this scheme captures some of the central observations in photoemission experiments in the cuprates.