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Achieving strong interactions between individual photons enables a wide variety of exciting possibilities in quantum information science and many-body physics. Cold atoms interfaced with nanophotonic structures have emerged as a platform to realize novel forms of nonlinear interactions. In particular, when atoms are coupled to a photonic crystal waveguide (PCW), long-range atomic interactions can arise that are mediated by localized atom-photon bound states. We theoretically show that in such adoi:10.1088/1367-2630/aa83ea fatcat:pkg65qankfg3toxzqioz4kvupi