Dynamical Casimir-Polder forces

We consider the dynamical (time-dependent) Casimir-Polder force between an atom and a perfectly conducting wall, as well as the dynamical Casimir-Polder force between two atoms in the presence of a boundary condition such as a conducting wall. The dynamical Casimir-Polder forces are obtained from iterative solutions of the Heisenberg equations for the time evolution of the electric and magnetic field operators around one atom in the presence of the conducting wall and related field energy densities, which are valid for any initial state. We consider both the case of an initially bare atomic state and of an initially partially dressed atomic state. The problem of relativistic causality in the field propagation during the atomic self-dressing is also discussed. Finally, we consider a specific model for an atomic partially dressed state and discuss the possibility of experimental observation of the dynamical atom-wall Casimir-Polder force.