We theoretically predict the formation of two-photon bound states in a two-dimensional waveguide network hosting a lattice of two-level atoms. The properties of these bound pairs and the exclusive domains of the parameter space where they emerge due to the interplay between the on-site photon blockade and peculiar shape of polariton dispersion resulting from the long-range radiative couplings between the qubits are investigated in detail. In addition, we analyze the effect of the finite-size system on localization characteristics of these excitations.
The main results of the paper were obtained with the support of Russian Science Foundation (Project No. 20-12-00224). The entanglement entropy has been calculated with the support of Russian Foundation of Basic research grant 20-02-00084. I. A. S. acknowledges support from Icelandic Research Fund (project ”Hybrid polaritonics”). I. V. I. acknowledges the support of “Basis” Foundation (Project No. 21-1-2-61-1).
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