Casimir-Polder force density between an atom and a conducting wall

Abstract

In this paper we calculate the Casimir-Polder force density (force per unit area acting on the elements of the surface) on a metallic plate placed in front of a neutral atom. To obtain the force density we use the quantum operator associated to the electromagnetic stress tensor. We explicitly show that the integral of this force density over the plate reproduces the total force acting on the plate. This shows that, although the total force is obtained as a sum of surface element-atom contributions, many-body components proportional to the atomic polarizability are included in our result. The local force that we obtain can also be useful in evaluating Casimir torques or stresses on the wall.