  Imaging is central for gaining microscopic insight into physical systems, but
direct imaging of ultracold atoms in optical lattices as modern quantum
simulation platform suffers from the diffraction limit as well as high optical
density and small depth of focus. We introduce a novel approach to imaging of
quantum many-body systems using matter wave optics to magnify the density
distribution prior to optical imaging, allowing sub-lattice spacing resolution
in three-dimensional systems. Combining the site-resolved imaging with magnetic
resonance techniques for local addressing of individual lattice sites, we
demonstrate full accessibility to local information and local manipulation in
three-dimensional optical lattice systems. The method opens the path for
spatially resolved studies of new quantum many-body regimes including exotic
lattice geometries.
