**Figure 6.** Same as in figure 5, but with different initial states. (a) The initial state is *v* = 6. Dotted blue line for P_{6,6}^{{\rm WP}}, solid black line for P_{7,6}^{{\rm WP}}, dashed red line for P_{8,6}^{{\rm WP}}. (b) The initial state is *v* = 9. Dashed-dotted green line for P_{9,9}^{{\rm WP}}, dashed red line for P_{8,9}^{{\rm WP}}.

**Abstract**

Laser control schemes for selective population inversion between molecular vibrational states have recently been proposed in the context of molecular cooling strategies using the so-called exceptional points (corresponding to a couple of coalescing resonances). All these proposals rest on the predictions of a purely adiabatic Floquet theory. In this work we compare the Floquet model with an exact wavepacket propagation taking into account the accompanying non-adiabatic effects. We search for signatures of a given exceptional point in the wavepacket dynamics and we discuss the role of the non-adiabatic interaction between the resonances blurring the ideal Floquet scheme. Moreover, we derive an optimal laser field to achieve, within acceptable compromise and rationalizing the unavoidable non-adiabatic contamination, the expected population inversions. The molecular system taken as an illustrative example is H_{2}^{+}.