Atomic multipole relaxation rates near surfaces

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole, and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic-field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green's function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface, we find a hierarchy of scaling laws depending on the atom-surface distance z.