Casimir force between a dielectric sphere and a wall: A model for amplification of vacuum fluctuations

The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall and a sphere with a dielectric function given by the Drude model is examined in detail. It is found that the force can be expressed as the sum of a monotonically decaying function of position and of an oscillatory piece. At large separations, the oscillatory piece is the dominant contribution and is much larger than the Casimir-Polder interaction that arises in the limit that the sphere is a perfect conductor. It is argued that this enhancement of the force can be interpreted in terms of the frequency spectrum of vacuum fluctuations. In the limit of a perfectly conducting sphere, there are cancellations between different parts of the spectrum that no longer occur as completely in the case of a sphere with frequency-dependent polarizability. Estimates of the magnitude of the oscillatory component of the force suggest that it may be large enough to be observable.