  We suggest and experimentally realize a spectral photonic lattice - a signal
can hop between discrete frequency channels, driven by nonlinear interaction
with stronger pump lasers. By controlling the complex envelope and frequency
separations of multiple pumps, it is possible to introduce non- local hopping
and to break time-reversal symmetry, which opens up new possibilities for
photonic quantum simulation. As two examples, we observe a spectral quantum
walk and demonstrate the discrete Talbot effect in the spectral domain, where
we find novel instances containing asymmetry and periodicities not possible in
spatial lattices.
