Theoretical model for ultracold molecule formation via adaptive feedback control

We theoretically investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose, a perturbative model for light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of ⁸⁵Rb ₂ molecules in a magneto-optical trap. We find that optimized pulse shapes may maximize the formation of ground state molecules in a specific vibrational state at a pump-dump delay time for which unshaped pulses lead to a minimum of the formation rate. Compared to the maximum formation rate obtained for unshaped pulses at the optimum pump-dump delay, the optimized pulses lead to a significant improvement of about 40% for the target level population. Since our model yields the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments.