  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 a system, the absorption of a single photon
can change the band structure for a subsequent photon. This occurs because the
first photon affects the atoms in the chain in an alternating fashion, thus
leading to an effective period doubling of the system and a new optical band
structure for the composite atom-nanophotonic system. We demonstrate how this
mechanism can be engineered to realize a single-photon switch, where the first
incoming photon switches the system from being highly transmissive to highly
reflective, and analyze how signatures can be observed via non-classical
correlations of the outgoing photon field.
