  Quantum coherent control of ultrafast bond making and the subsequent
molecular dynamics is crucial for the realization of a new photochemistry,
where a shaped laser field is actively driving the chemical system in a
coherent way from the thermal initial state of the reactants to the final state
of the desired products. We demonstrate here coherent control over the relative
yields of Mg$_2$ molecules that are generated via photoassociation and
subsequently photodriven into different groups of final states. The
strong-field process involves non-resonant multiphoton femtosecond
photoassociation of a pair of thermally hot magnesium atoms into a bound
Mg$_{2}$ molecule and subsequent molecular dynamics on electronically excited
states. The branching-ratio control is achieved with linearly chirped laser
pulses, utilizing the different chirp dependence that various groups of final
molecular states display for their post-pulse population. Our study establishes
the feasibility of high degree coherent control over quantum molecular dynamics
that is initiated by femtosecond photoassociation of thermal atoms.
