Emission decay and lame shift in photonic crystals

Motivated by the significant controversy between the two dispersion models and Weisskopf-Wigner approximation (WWA), for the first time to our knowledge, we introduce the position-dependent photon-atom interaction into the Green function method of the evolution operator and develop a universal theoretical treatment on spontaneous emission of atoms in photonic crystals (PCs). A position-sensitive generalized Lorentzian formulism (non-Lorentzian shape) for the decay of an excited atom in PCs is derived, and an exact numerical method for calculating the local coupling strength, proportional to the photonic local density of state (LDOS), is presented. For weak interaction PCs with pseudo gaps, the generalized Lorentzian formulism may be reduced to the famous Lorentzian spectrum. In this case, we introduced a lifetime distribution function for an assembly of atoms and found that the lifetime distribution strongly depend on the spread configuration of these atoms in space, which clarifies successfully the tremendous discrepancy between different experiments. For the PCs with large full gaps, we found that the atomic position can fundamentally change the decay behavior of an excited atom: in strong interaction positions, the atomic decay is non-classical or exhibits an envelope-damped Rabi oscillation, while in weak interaction positions the WWA is valid. Recently, we also predicted giant Lamb shifts for hydrogen atoms in PCs, and revealed that in inhomogeneous electromagnetic environment, the dominant contribution to the Lamb shift comes from real photon emission, while the contribution from emission and reabsorption of virtual photon is negligible, in vast contrast with the case of free space where the virtual photon processes play a key role.