The formation of diatomic molecules with rotational and vibrational coherence is
demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of
hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms,
colliding in their electronic ground state, are excited into coherent superpositions of
bound rovibrational levels in an electronically excited state. The rovibrational
coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV
fluorescence. A comprehensive theoretical model based on ab initio calculations
rationalizes the generation of coherence by Franck-Condon filtering of collision
energies and partial waves, quantifying it in terms of an increase in quantum purity of
the thermal ensemble. Our results open the way to coherent control of a binary reaction.