Quantum optics of localized light in a photonic band gap

We describe the quantum electrodynamics of photons interacting with hydrogenic atoms and molecules in a class of strongly scattering dielectric materials. These dielectrics consist of an ordered or nearly ordered array of spherical scatterers with real positive refractive index and exhibit a complete photonic band gap or pseudogap for all directions of electromagnetic propagation. For hydrogenic atoms with a transition frequency in the forbidden optical gap, we demonstrate both the existence and stability of a photon-atom bound state. For a band gap to center frequency ratio Δω/${\mathrm{\omega }}_0$∼5%, the photon localization length ${\xi }_{\mathrm{loc}}$≥10L, where L is the lattice constant of dielectric array. This strong self-dressing of the atom by its own localized radiation field leads to anomalous Lamb shifts and a splitting of the excited atomic level into a doublet when the transition frequency lies near a photonic band edge. We estimate the magnitude of this splitting to be ${10}^{\mathrm{-}6}$ at the vacuum transition energies.