Radio frequency spectroscopy of the attractive Hubbard model in a trap

Attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. In contrast to the `continuum', on a lattice the trap induced density variation can generate a non monotonic profile of the pairing amplitude, and completely modify the spectral signatures of any possible pseudogap phase. Using a tool that fully captures the inhomogeneity and strong thermal fluctuations, we demonstrate how the crucial radio frequency signatures of pairing are `inverted' in a trapped attractive fermion lattice compared to the traditional continuum case. These features would be central in interpreting any spectroscopic hint of fermion pairing and superfluidity.