Casimir-Polder potential as an interaction between induced dipoles

Abstract

The retarded van der Waals forces between neutral molecules in their ground states is obtained by a conceptually simple route. Vacuum fluctuations of the electromagnetic field induce a dipole moment in each molecule and these induced moments interact via the retarded potential that is appropriate for resonant coupling. The dispersion potential is the sum over the field modes of the product of this potential and the second-order spatial correlation function of the electromagnetic field. This gives the familiar Casimir-Polder potential an an integral over imaginary frequencies. An extension to obtain the interaction energy between one molecule in its ground state and another in an excited state is outlined.