  We propose a method to probe the local density of states (LDOS) of atomic
systems that provides both spatial and energy resolution. The method combines
atomic and tunneling techniques to supply a simple, yet quantitative and
operational, definition of the LDOS for both interacting and non-interacting
systems: It is the rate at which particles can be siphoned from the system of
interest by a narrow energy band of non-interacting states contacted locally to
the many-body system of interest. Ultracold atoms in optical lattices are a
natural platform for implementing this broad concept to visualize the energy
and spatial dependence of the atom density in interacting, inhomogeneous
lattices. This includes models of strongly correlated condensed matter systems,
as well as ones with non-trivial topologies.
