Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide

We investigate the interaction between a single photon and a chain of N equally spaced two-level atoms inside a one-dimensional waveguide. By solving the eigenvectors of the Hamiltonian in the subspace with a single excitation, we address quantum interference effects in two physical processes. First, we analyze the scattering of a single photon when atoms are all initially at their ground states. We discover a set of transmission peaks determined by N. These transmission peaks are narrow and sensitive to the relative position between atoms. Second, we examine the spontaneous emission of a photon from an excited atom in the chain in vacuum. The characteristic atomic decay rates are found to be enhanced and reduced by increasing the number of atoms. In particular, the slowest decay rate scales approximately as N-3.