Atom-field interactions with a frequency-dependent reservoir

Owing to the frequency dependence of the vacuum density of states, the spontaneous emission decay rate varies as the cube of a frequency. The actual frequency that enters into the decay rate depends to some extent on the physical system under investigation. We show that, in the weak-field limit and the rotating-wave approximation, the decay parameters associated with Ralyleigh scattering are evaluated at the field frequency, while the transient response following the turn-on of the field has a decay rate evaluated at the atomic frequency. The optical Bloch equations are modified to include additional coupling between populations and coherences, both in bare and dressed-state pictures.