Lamb shift due to surface plasmon polariton modes

Abstract

The Lamb shift of a hydrogen atom due to the surface plasmon polariton (SPP) modes is calculated and we observe both band edge and surface enhancement. The atom sits inside a thin metal slab which is sandwiched by two semi-infinite dielectrics. The SPP dispersion relation shows a band gap if the two dielectrics have different dielectric constants. We find the magnitude of the $2{P}_{1/2}$ level shift increases rapidly when the level separation is close to the high band edge. But the low band edge enhancement can be overwhelmed by the decreasing trend of the shift. If the atom is placed close to either surface or if the slab is narrow, all the level shifts would be large because of the surface enhancement. An interesting feature is that the $2{P}_{1/2}$ level shift can be larger than the $2S$ level shift due to the nonisotropic fields.