Three-body Casimir effects and nonmonotonic forces

Casimir interactions are not pairwise additive. This property leads to collective effects that we study for a pair of objects near a conducting wall. We employ a scattering approach to compute the interaction in terms of fluctuating multipoles. The wall can lead to a nonmonotonic force between the objects. For two atoms with anisotropic electric and magnetic dipole polarizabilities, we demonstrate that this nonmonotonic effect results from a competition between two- and three-body interactions. By including higher-order multipoles we obtain the force between two macroscopic metallic spheres for a wide range of sphere separations and distances to the wall.

Figure 1

Geometry of the two-sphere or atom and sidewall system. Shown are also the mirror images (gray) and two- and three-body contributions (solid and dashed curly lines, respectively).

Figure 2

Typical orientations of electric $\left(e\right)$ and magnetic $\left(m\right)$ dipoles and image dipoles for $H/L\to 0$ and $H/L\to \infty$.

Figure 3

(Color online) Numerical results for the potential energy (dashed curves) and force (solid curves) between two spheres as function of $R/L$ for different sidewall separations $H/R$. Both force and energy are normalized to their values in the absence of the sidewall. Inset: magnification of behavior for small $R/L$.

Figure 4

(Color online) Numerical results for the force (dots) between two spheres as function of the sidewall separation $H/R$ for different sphere separations $R/L$. Shown are also the analytical results of Eq. (11), including terms up to $j=10$ for $R/L\le 0.2$ (solid curves). Inset: magnification of the nonmonotonicity.