Inelastic Scattering of Photon Pairs in Qubit Arrays with Subradiant States.

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded into a waveguide. Our analysis reveals a strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering, such as superradiant, subradiant, and twilight states, as a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to storage and processing of quantum information.