Single-photon bound states for propagating photons interacting with many atoms

We illustrate the existence of single-excitation bound states for propagating photons interacting with $N$ two-level atoms. These bound states can be calculated from a spin Hamiltonian and their existence relies on the dissipation in the system. We find that the appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and infinite bunching in the second-order photon-photon correlation functions. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases.