The damped Jaynes-Cummings model

The dynamics of the much studied Jaynes-Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.