  Casimir-type forces, such as those between two neutral conducting plates, or
between a sphere, atom or molecule and a plate have been widely studied and are
becoming of increasing significance, for example, in nanotechnology. A key
challenge is to better understand, from a fundamental microscopic approach, why
the Casimir force is in some circumstances attractive and in others repulsive.
Here, we study the Casimir-Polder forces experienced by small quantum systems
such as atoms or molecules in an optical cavity. In order to make the problem
more tractable, we work in a 1+1 dimensional setting, we take into account only
the ground state and first excited state of the atom and we model the
electromagnetic field as a scalar field with Dirichlet or Neumann boundary
conditions. This allows us to determine the conditions for the Casimir force to
be attractive or repulsive for individual atoms, namely through the interplay
of paramagnetic and diamagnetic vacuum effects. We also study the
microscopic-macroscopic transition, finding that as the number of atoms in the
cavity is increased, the atoms start to affect the Casimir force exerted on the
cavity walls similarly to a dielectric medium.
