# Vibrational populations as a function of time, for an initial state *v* = 7 exposed to a laser pulse with λ = 300 nm (other laser loop parameters δλ = 0 and *T*_{max} = 30 fs being fixed)

**Figure 1.** Vibrational populations as a function of time, for an initial state *v* = 7 exposed to a laser pulse with λ = 300 nm (other laser loop parameters δλ = 0 and *T*_{max} = 30 fs being fixed). The solid black line represents the Floquet behaviour P_{7}^{F}(t) and the solid green line represents the exact (wavepacket) result P_{7}^{{\rm WP}}(t). The dashed lines are the populations in the field-free vibrational states during wavepacket dynamics. P_{7,7}^{{\rm WP}} is given by the red dashed line and P_{8,7}^{{\rm WP}} by the green dashed line. For panel (a) the maximum pulse intensity is I_{m}=0.2 \times 10^{13} \rm \ \rm \ W\,cm^{-2}. For panel (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}^{+}.