  We explore a technique for probing energy spectra in synthetic lattices that
is analogous to scanning tunneling microscopy. Using one-dimensional synthetic
lattices of coupled atomic momentum states, we explore this spectroscopic
technique and observe qualitative agreement between the measured and simulated
energy spectra for small two- and three-site lattices as well as a uniform
many-site lattice. Finally, through simulations, we show that this technique
should allow for the exploration of the topological bands and the fractal
energy spectrum of the Hofstadter model as realized in synthetic lattices.
