Three-dimensional plot of transfer peaks from <em>v</em> = 7 to <em>v</em> = 8 for different pulse durations in the λ/I plane

<p><strong>Figure 4.</strong> Three-dimensional plot of transfer peaks from <em>v</em> = 7 to <em>v</em> = 8 for different pulse durations in the λ/I plane. The colour code applies to P_{8,7}^{{\rm WP}}(T_{{\rm max}})/P_{7,7}^{{\rm WP}}(T_{{\rm max}}). The position of the EP(7,8) as calculated from the Floquet formalism, is indicated by the red solid rectangle at λ<sup>EP</sup> = 363 nm , I^{{\rm EP}}=0.58\times 10^{13} \rm \ \rm \ W\,cm^{-2}.</p> <p><strong>Abstract</strong></p> <p>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}^{+}.</p>