The limits of the rotating wave approximation in electromagnetic field propagation in a cavity

We consider three two-level atoms inside a one-dimensional cavity, interacting with the electromagnetic field in the rotating wave approximation (RWA). One of the three atoms is initially excited, and the other two are in their ground state. We numerically calculate the propagation of the field emitted by the excited atom and scattered by the second atom, as well as the excitation probability of the second and third atom. Our numerical results clearly show the limits of the RWA in subtle problems such as relativistic causality in the atom-field interaction.