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The first step in the coherent control of a photoinduced binary reaction isbond making or photoassociation. We have recently demonstrated coherent controlof bond making in multi-photon femtosecond photoassociation of hot magnesiumatoms, using linearly chirped pulses [Levin et al., arXiv:1411.1542]. Thedetected yield of photoassociated magnesium dimers was enhanced by positivelychirped pulses which is explained theoretically by a combination ofpurification and chirp-dependent Raman transitions. The yield could be furtherenhanced by pulse optimization resulting in pulses with an effective linearchirp and a sub-pulse structure, where the latter allows for exploitingvibrational coherences. Here, we systematically explore the efficiency ofphase-shaped pulses for the coherent control of bond making, employing aparametrization of the spectral phases in the form of cosine functions. We findup to an order of magnitude enhancement of the yield compared to the unshapedtransform-limited pulse. The highly performing pulses all display an overalltemporally increasing instantaneous frequency and are composed of severaloverlapping sub-pulses. The time delay between the first two sub-pulses almostperfectly fits the vibrational frequency of the generated intermediatewavepacket.These findings are in agreement with chirp-dependent Ramantransitions and exploitation of vibrational dynamics as underlying controlmechanisms.

Coherent control of bond making: The performance of rationally phase-shaped femtosecond laser pulses