  Ultracold atoms in optical lattices provide clean, tunable, and well-isolated
realizations of paradigmatic quantum lattice models. With the recent advent of
quantum-gas microscopes, they now also offer the possibility to measure the
occupations of individual lattice sites. What, however, has not yet been
achieved is to measure those elements of the single-particle density matrix,
which are off-diagonal in the occupation basis. Here, we propose a scheme to
access these basic quantities both for fermions as well as hard-core bosons and
investigate its accuracy and feasibility. The scheme relies on the engineering
of a large effective tunnel coupling between distant lattice sites and a
protocol that is based on measuring site occupations after two subsequent
quenches.
