## Same as in figure 1 with λ = 450 nm

**Figure 2.** Same as in figure 1 with λ = 450 nm. (a) The maximum intensity of the pulse is I_{m}=0.2 \times 10^{13} \rm \ \rm \ W\,cm^{-2}. (b) I_{m}=0.5 \times 10^{13} \rm \ \rm \ W\,cm^{-2}.

**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}^{+}.