Casimir-Polder repulsion near edges: Wedge apex and a screen with an aperture

Abstract

Although repulsive effects have been predicted for quantum vacuum forces between bodies with nontrivial electromagnetic properties, such as between a perfect electric conductor and a perfect magnetic conductor, realistic repulsion seems difficult to achieve. Repulsion is possible if the medium between the bodies has a permittivity in value intermediate to those of the two bodies, but this may not be a useful configuration. Here, inspired by recent numerical work, we initiate analytic calculations of the Casimir-Polder interaction between an atom with anisotropic polarizability and a plate with an aperture. In particular, for a semi-infinite plate, and, more generally, for a wedge, the problem is exactly solvable, and for sufficiently large anisotropy, Casimir-Polder repulsion is indeed possible, in agreement with the previous numerical studies. In order to achieve repulsion, what is needed is a sufficiently sharp edge (not so very sharp, in fact) so that the directions of polarizability of the conductor and the atom are roughly normal to each other. The machinery for carrying out the calculation with a finite aperture is presented. As a motivation for the quantum calculation, we carry out the corresponding classical analysis for the force between a dipole and a metallic sheet with a circular aperture, when the dipole is on the symmetry axis and oriented in the same direction.

Field theoretic description of partially reflective surfaces

“…Recently Parashar, Milton, Shajesh and Schaden carried out a detailed analysis clarifying the controversies involving different models of boundary condition and studied the Casimi-Polder interaction between an atom and a δ-function plate, among other things [4]. This important issue, of atoms and charges in interaction with material boundaries, has generated a renewed interest for both practical and theoretical reasons [5][6][7][8]. In this context Eberlein and Zietal devised a remarkable method [9], closely related to the electrostatic image method [10], to deal with a wide range of physical setups.…”

Casimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids

“…Earlier, we observed that Casimir-Polder repulsion along a direction perpendicular to the symmetry axis of a semi-infinite planar conductor or a conducting wedge and an anisotropically polarizable atom could be achieved in the region close to the conductor [13]. Here we have shown that anisotropically polarizable atoms can also repel in this sense, provided they are sufficiently anisotropic, and have perpendicular principal axes.…”

“…The authors quite correctly point out that the statement in Ref. [13] that no repulsion is possible in the weak-coupling regime is erroneous. conductor, which just states that the tangential components of the electric field must vanish on the conductor.…”

“…Such have been given considerable attention lately [2,13,21]. Here we consider the interaction between a perfectly conducting ellipsoid polarized by a constant electric field and a fixed dipole.…”

“…We subsequently showed [13] that repulsive Casimir-Polder forces between anisotropic atoms and a conducting half-plane, and even between such an atom and a conducting wedge of rather large opening angle, could be achieved. Of course, we must be careful to explain what we mean by repulsion: the total force on the atom is attractive, but the component of the force perpendicular to the symmetry axis of the conductor changes sign when the atom is sufficiently close to that axis.…”