Perturbative evolution of far off - resonance driven two - level systems : Coherent population trapping , localization , and harmonic generation

The time evolution of driven two-level systems in the far off-resonance regime is studied analytically. We obtain a general first-order perturbative expression for the time-dependent density operator which is applicable regardless of the coupling strength value. In the strong field regime, our perturbative expansion remains valid even when the far off-resonance condition is not fulfilled. We find that, in the absence of dissipation, driven two-level systems exhibit coherent population trapping in a certain region of parameter space, a property which, in the particular case of a symmetric double-well potential, implies the well-known localization of the system in one of the two wells. Finally, we show how the high-order harmonic generation that this kind of systems display can be obtained as a straightforward application of our formulation.