We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded in a waveguide. Our analysis reveals 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, being 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 a storage and processing of quantum information.
@article{arxiv.1908.04844,
title = {Inelastic scattering of photon pairs in qubit arrays with subradiant states},
author = {Yongguan Ke and Alexander V. Poshakinskiy and Chaohong Lee and Yuri S. Kivshar and Alexander N. Poddubny},
journal= {arXiv preprint arXiv:1908.04844},
year = {2019}
}