Optimal laser pulse design for transferring the coherent nuclear wave packet of H+2

Within the Franck–Condon approximation, the single ionisation of H₂ leaves H⁺₂ in a coherent superposition of 19 nuclear vibrational states. We numerically design an optimal laser pulse train to transfer such a coherent nuclear wave packet to the ground vibrational state of H⁺₂. Frequency analysis of the designed optimal pulse reveals that the transfer principle is mainly an anti-Stokes transition, i.e. the H⁺₂ in 1sσ_g with excited nuclear vibrational states is first pumped to 2pσ_g state by the pulse at an appropriate time, and then dumped back to 1sσ_g with lower excited or ground vibrational states. The simulation results show that the population of the ground state after the transfer is more than 91%. To the best of our knowledge, this is the highest transition probability when the driving laser field is dozens of femtoseconds.