Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties

We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface-surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.

Figure 1

Casimir force between silicon and teflon spheres and cubes immersed in ethanol, normalized by the PFA predictions (see text). For the sphere-sphere case, the solid circles represent data computed using the methods described in this paper, while the thick solid line reproduces data from Ref. [7]. For the other three cases, the solid and hollow circles represent data computed using the methods described in this paper, and the dotted lines are a guide to the eye.

Figure 2

Casimir force between puck-shaped polystyrene and doped-silicon (dopant density $\rho$) nanoparticles immersed in ethanol. The dotted curves indicate the force on slabs of the same materials and thickness but infinite cross-sectional area [7]. (Material properties are taken from Ref. [7].)

Figure 3

Rotational stability of hockey-puck shaped nanoparticles suspended in ethanol. One nanoparticle is composed of polystyrene, and the other of silicon with a dopant concentration of $1.4\times {10}^{19}$ cm${}^{-3}$ (corresponding to the middle curve in the previous plot). We fix the centers of the particles at center-center separations of $S=\{500,700\}$ nm to allow them to rotate about their centers. The minimum-energy configurations are depicted in the insets at right. (All angles are measured in degrees.)