  The attractive Fermi-Hubbard model is the simplest theoretical model for
studying pairing and superconductivity of fermions on a lattice. Although its
s-wave pairing symmetry excludes it as a microscopic model for high-temperature
superconductivity, it exhibits much of the relevant phenomenology, including a
short-coherence length at intermediate coupling and a pseudogap regime with
anomalous properties. Here we study an experimental realization of this model
using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Our
site-resolved measurements on the normal state reveal checkerboard
charge-density-wave correlations close to half-filling. A "hidden" SU(2)
pseudo-spin symmetry of the Hubbard model at half-filling guarantees superfluid
correlations in our system, the first evidence for such correlations in a
single-band Hubbard system of ultracold fermions. Compared to the paired atom
fraction, we find the charge-density-wave correlations to be a much more
sensitive thermometer, useful for optimizing cooling into superfluid phases in
future experiments.
