Fluctuation-induced quantum interactions between compact objects and a planemirror

Abstract

The interaction of compact objects with an infinitely extended mirror plane due toquantum fluctuations of a scalar or electromagnetic field that scatters off the objects isstudied. The mirror plane is assumed to obey either Dirichlet or Neumann boundaryconditions or to be perfectly reflecting. Using the method of images, we generalize arecently developed approach for compact objects in unbounded space to show that theCasimir interaction between the objects and the mirror plane can be accuratelyobtained over a wide range of separations in terms of charge and current fluctuationsof the objects and their images. Our general result for the interaction dependsonly on the scattering matrices of the compact objects. It applies to scalar fieldswith arbitrary boundary conditions and to the electromagnetic field coupled todielectric objects. For the experimentally important electromagnetic Casimirinteraction between a perfectly conducting sphere and a plane mirror we presentthe first results that apply at all separations. We obtain both an asymptoticlarge-distance expansion and the two lowest-order correction terms to the proximity forceapproximation. The asymptotic Casimir–Polder potential for an atom and a mirror isgeneralized to describe the interaction between a dielectric sphere and a mirror,involving higher-order multipole polarizabilities that are important at sub-asymptoticdistances.