  We suggest that propagation of nonclassical light in lattices of optical
waveguides can provide a laboratory tool to simulate quantum decoherence
phenomena with high non-Markovian features. As examples, we study decoherence
of optical Schr\"{o}dinger cats in a lattice that mimics a dissipative quantum
harmonic oscillator coupled to a quantum bath, showing fractional decoherence
in the strong coupling regime, and Bloch oscillations of optical
Schr\"{o}dinger cats, where damped revivals of the coherence can be observed.
