  We experimentally investigate a scheme for studying lattice transport
phenomena, based on the controlled momentum-space dynamics of ultracold atomic
matter waves. In the effective tight-binding models that can be simulated, we
demonstrate that this technique allows for a local and time-dependent control
over all system parameters, and additionally allows for single-site resolved
detection of atomic populations. We demonstrate full control over site-to-site
off-diagonal tunneling elements (amplitude and phase) and diagonal
site-energies, through the observation of continuous-time quantum walks, Bloch
oscillations, and negative tunneling. These capabilities open up new prospects
in the experimental study of disordered and topological systems.
