Disorder-aided pulse stabilization in dissipative synthetic photonic lattices

We consider a discrete time evolution of light in dissipative and disordered photonic lattice presenting a generalization of two popular non-Hermitian models in mathematical literature: Hatano-Nelson and random clock model and suggest a possible experimental implementation using coupled fiber loops. We show that if the model is treated as non-unitary Floquet operator rather than the effective Hamiltonian the combination of controlled photon loss and static phase disorder leads to pulse stabilization in the ring topology. We have also studied the topological invariant associated with the system and found additional evidence for the absence of Anderson transition.