In a straightforward manner, we utilize Floquet theory and adiabatic elimination to derive an analytic expression for a monochromatically driven two-level atom, without making the rotating wave approximation. We show that the counter-rotating terms dropped in the rotating wave approximation are responsible for three major effects. First an ac-Stark phase shift of the driven transition, second increased excited state population from far-detuned driving of the Lorentzian line, and third extra frequencies in the population dynamics that result in “wiggles.” The analytic result agrees well with numerical simultations over a wide range of parameters.

The rotating wave approximation leads to ac-Stark phase shift, increased excited state population, and extra frequencies in population dynamics, resulting in "wiggles" in the driven transition.

Analytical treatment of the continuous wave driving of a two-level atom without making the rotating wave approximation

Key Takeaway: The rotating wave approximation leads to ac-Stark phase shift, increased excited state population, and extra frequencies in population dynamics, resulting in "wiggles" in the driven transition.