Quantum electrodynamics with nonrelativistic sources. V. Electromagnetic field correlations and intermolecular interactions between molecules in either ground or excited states.

Abstract

Spatial correlations between electromagnetic fields arising from neutral sources with electric-dipole transition moments are calculated using nonrelativistic quantum electrodynamics in the multipolar formalism. Expressions for electric-electric, magnetic-magnetic, and electric-magnetic correlation functions at two points r and r' are given for a source molecule in either a ground or an excited state. In contrast to the electric-electric and magnetic-magnetic cases there are no electric-magnetic correlations for a ground-state molecule. For an excited molecule the downward transitions contribute additional terms which have modulating factors depending on (r-r')/\ensuremath{\lambda}/. From these correlation functions electric and magnetic energy densities are found by setting r=r'. These energy densities are then used in a response formalism to calculate intermolecular energy shifts. In the case of two ground-state molecules this leads to the Casimir-Polder potential. However, for a pair of molecules, one or both excited, there are additional terms arising from downward transitions. An important feature of these energies is that they exhibit an ${\mathit{R}}^{\mathrm{\ensuremath{-}}2}$ dependence for large intermolecular separations R. This dependence is interpreted in terms of the Poynting vector, which itself can be obtained by setting r=r' in the electric-magnetic correlation function.