Giant Lamb shift in photonic crystals

We obtain a general result for the Lamb shift of excited states of multi-level atoms in inhomogeneous electromagnetic structures and find that the Lamb shift comes from real photon processes, in contrast to the conventional concept established in 1947 that, in the case of free space, the virtual photon processes play a key role. We find that photonic crystals can lead to a giant Lamb shift. We also predict that the position-dependent Lamb shift should extend from a single level to a mini-band for an assembly of atoms with random distributions in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.