Simple, analytic solutions of the semiclassical Rabi model

We considered the semiclassical Rabi model, that is, a qubit (transition frequency ω0) interacting with a single-mode, classical field (frequency ω1). Using the method of multiple-scales we obtained simple, approximate, and analytic solutions in the resonant ω0=ω1 and blue detuned ω0<ω1 cases that hold for long times in the weak and strong coupling regimes. In the blue detuned case, the solutions hold for arbitrary qubit-field couplings. Moreover, the solutions are used to determine the motion of the Bloch vector and to give a geometric interpretation. Finally, we discuss applications of the results to physical systems and we propose a very simple experiment in atomic physics where the breakdown of the rotating-wave-approximation can be observed and where the results can be applied.