Few-photon quantum electrodynamics in a structured continuum

We extend recent work on the discretization of photonic continua. A two-lev el atom is coupled to a photonic bandgap reservoir, which we model by a lar ge number of discrete modes. The atom is also coupled to a defect mode insi de the gap, which acts as a photon source that can pump the atom. Propagati ng the wavefunction of the system, we obtain results pertaining to the prob lem of two and three photons in the reservoir, for various states of the de fect field. For a wide range of parameters we find that part of the total i nitial excitation remains trapped to the atom and the defect mode in the lo ng-time limit, while the atomic population may exhibit inversion. We furthe r investigate the dynamics of an atomic Dicke system, with transition frequ encies at the edge of a photonic bandgap.