ar X iv : p hy si cs / 0 60 41 40 v 2 3 1 Ju l 2 00 6 Theoretical model for ultracold molecule formation via adaptive feedback control

We theoretically investigate pump-dump photoassociation of ultracold molecules with amplitudeand phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the 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 Rb2 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 pumpdump 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. Theoretical model for ultracold molecule formation via adaptive feedback control 2