Few-photon quantum electrodynamics in a structured continuum

We extend recent work on the discretization of photonic continua. A two-level atom is coupled to a photonic bandgap reservoir, which we model by a large number of discrete modes. The atom is also coupled to a defect mode inside the gap, which acts as a photon source that can pump the atom. Propagating the wavefunction of the system, we obtain results pertaining to the problem of two and three photons in the reservoir, for various states of the defect field. For a wide range of parameters we find that part of the total initial excitation remains trapped to the atom and the defect mode in the long-time limit, while the atomic population may exhibit inversion. We further investigate the dynamics of an atomic Dicke system, with transition frequencies at the edge of a photonic bandgap.