On the relation between cavity-dressed states, Floquet states, RWA and semiclassical models

We show that Floquet states can be constructed as strong-field limits of cavity-dressed states. The interaction between laser beams propagating outside the cavity with atoms or molecules are described by Floquet states, constructed from dressed states of average photon number (n) over bar quantized in a cavity of volume V, by taking the limit V --> infinity, (n) over bar --> infinity, while keeping the photon density p = (n) over bar/V constant. Thus, Floquet theory can be seen as a fully quantum-mechanical model in the sense that it describes the photon exchanges between matter and radiation containing a large amount of photons. We discuss in this context adiabatic Floquet theory to treat a slow time dependence of the laser amplitude, to describe pulses, and of its frequency (chirping).