  We report on the single atom and single site-resolved detection of the total
density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence
imaging of doublons is achieved by splitting each lattice site into a double
well, thereby separating atom pairs. Full density readout yields a direct
measurement of the equation of state, including direct thermometry via the
fluctuation-dissipation theorem. Site-resolved density correlations reveal the
Pauli hole at low filling, and strong doublon-hole correlations near half
filling. These are shown to account for the difference between local and
non-local density fluctuations in the Mott insulator. Our technique enables the
study of atom-resolved charge transport in the Fermi-Hubbard model, the
site-resolved observation of molecules, and the creation of bilayer
Fermi-Hubbard systems.
