Light interaction with extended quantum systems in dispersive media

We derive a light–matter interaction Hamiltonian to describe a quantum system embedded in a dispersive environment and coupled with the electromagnetic field. We include in this theory the spatial extension of the system, taken into account through its wavefunction. This enables us to overcome the divergence problem of the Green tensor propagator that arises from a point-like approximation of the quantum system. Thus the formalism can be applied to generalize the expressions for the spontaneous emission rate and the Lamb shift for a quantum system defined by a spatially extended dipole. In particular, these quantities can be modified by the asymmetry of the spatial structure of the atomic system as demonstrated in two test-bed examples.