Born expansion of the Casimir–Polder interaction of a ground-state atom with dielectric bodies

Within leading-order perturbation theory, the Casimir--Polder potential of a ground-state atom placed within an arbitrary arrangement of dispersing and absorbing linear bodies can be expressed in terms of the polarizability of the atom and the scattering Green tensor of the body-assisted electromagnetic field. Based on a Born series of the Green tensor, a systematic expansion of the Casimir--Polder potential in powers of the electric susceptibilities of the bodies is presented. The Born expansion is used to show how and under which conditions the Casimir--Polder force can be related to microscopic many-atom van der Waals forces, for which general expressions are presented. As an application, the Casimir--Polder potentials of an atom near a dielectric ring and an inhomogeneous dielectric half space are studied and explicit expressions are presented that are valid up to second order in the susceptibility.