  Strong coupling between a two-level system (TLS) and bosonic modes produces
dramatic quantum optics effects. We consider a one-dimensional continuum of
bosons coupled to a single localized TLS, a system which may be realized in a
variety of plasmonic, photonic, or electronic contexts. We present the exact
many-body scattering eigenstate obtained by imposing open boundary conditions.
Multi-photon bound states appear in the scattering of two or more photons due
to the coupling between the photons and the TLS. Such bound states are shown to
have a large effect on scattering of both Fock and coherent state wavepackets,
especially in the intermediate coupling strength regime. We compare the
statistics of the transmitted light with a coherent state having the same mean
photon number: as the interaction strength increases, the one-photon
probability is suppressed rapidly, and the two- and three-photon probabilities
are greatly enhanced due to the many-body bound states. This results in
non-Poissonian light.
