Vibrational populations for the optimized loop (delta lambda =6 { m nm}, {{I}}_{{{m}}}=0.55 imes 10^{13} m m W,cm^{-2}, lambda _{{m}}=579.5 { m nm}, {{T}}_{{ m max}}=30 fs) for the couple <em>v</em> = 12, 13

<p><strong>Figure 8.</strong> Vibrational populations for the optimized loop (\delta \lambda =6 {\rm \ nm}, {{I}}_{{{m}}}=0.55\times 10^{13} \rm \ \rm \ W\,cm^{-2}, \lambda _{{m}}=579.5 {\rm \ nm}, {{T}}_{{\rm max}}=30 fs) for the couple <em>v</em> = 12, 13. For panels (a) and (b) the initial state is <em>v</em> = 13 and the laser loop rotation senses are clockwise and anticlockwise, respectively. P_{13,13}^{{\rm WP}} is represented by the solid black line, P_{12,13}^{{\rm WP}} by the dashed red line. For panels (c) and (d), the initial state is <em>v</em> = 12 and the laser loop rotation senses are clockwise and anticlockwise, respectively. P_{13,12}^{{\rm WP}} is represented by the solid black line, P_{12,12}^{{\rm WP}} by the dashed red line.</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>