# Localization of the maximum transfers in the (δλ, *I*_{m}) plane for the four cases involving the couple *v* = 12, 13 for a pulse duration *T*_{max} = 30 fs

_{m}

**Figure 7.** Localization of the maximum transfers in the (δλ, *I _{m}*) plane for the four cases involving the couple

*v*= 12, 13 for a pulse duration

*T*

_{max}= 30 fs. The rotation sense of the loop is indicated for each case. The wavelength taken from Floquet theory is λ

_{m}= 579.5 nm. The red square indicates the optimal compromise adopted for δλ = 6 nm and I_m= 0.55\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}^{+}.