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 system displays can be obtained as a straightforward application of our formulation.