Dressed Atom Fields and Dressed States in Waveguide Quantum Electrodynamics

The fully quantized problem of a dipole atom coupled to transverse electric fields is solved for both simple harmonic and two-level atoms in a general lossless electromagnetic environment. The method employed is a direct factorization of the Hamiltonian in terms of coupled excitations of atom and fields. Time evolution of the system is considered with emphasis on the effect of an atom-photon bound state. The rectangular waveguide is used as an example to illustrate the predicted behavior.