Spectral photonic lattices with complex long-range coupling

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.