Contributions of vacuum and plasmon modes to the force on a small sphere near a plate

The force on a small sphere with a plasma model dielectric function and in the presence of a perfectly reflecting plane is considered. The contribution of both the vacuum modes of the quantized electromagnetic field and of plasmon modes in the sphere are discussed. In the case that the plasmon modes are in their ground state, quasi-oscillatory terms from the vacuum and plasmon parts cancel one another, leading a monotonic attractive force. If the plasmon modes are not in the ground state, the net force is quasi-oscillatory. In both cases, the sphere behaves in the same way as does an atom in either its ground state or an excited state