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We investigate the role of optical nonlinearity in light propagation throughtwo different waveguide QED lattices, namely a chain of qubits with directcoupling between the nearest neighbors and a chain of connected resonators toeach of which a qubit is side-coupled. We apply an efficient truncatedHeisenberg-Langevin equations method to show loss of coherent lighttransmission with increasing intensity in these lattices due to effectivephoton-photon interactions and related photon blockade mediated by nonlinearityin qubits. In contrast to the direct-coupled qubits, we find a revival in thecoherent light transmission in the side-coupled qubits at relatively higherintensities due to saturation of qubits by photons. We further study theselattices within the quasi-classical approximation, which fails for a broad setof parameters. We then devise a technique to modify the quasi-classicalanalysis to give much better results. Lastly, we examine light propagation inan inhomogeneous lattice of side-coupled qubits and observe non-monotonicity inlight transmission with increasing light intensity.

Interplay of coherence and interaction in light propagation through waveguide QED lattices