  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.
