A modified quasi-classical analysis to capture the effects of strong interaction in open QED lattices

We investigate the role of optical nonlinearity in light propagation through two different one-dimensional open QED lattices, namely a chain of qubits with direct coupling between the nearest neighbors and a chain of connected resonators to each of which a qubit is side-coupled. Using the more accurate truncated Heisenberg-Langevin equations method we show a reduction of light transmission with increasing intensity in these lattices due to effective photon-photon interactions and related photon blockade mediated by nonlinearity in qubits. In contrast to the direct-coupled qubits, we find a revival in the light transmission in the side-coupled qubits at relatively higher intensities due to saturation of qubits by photons. We find that in absence of bulk dissipation the standard quasi-classical analysis fails to capture the reduction in light transmission due to effective photon-photon interaction. We then devise a systemic method to modify the quasi-classical analysis to give much better results.