Precision test of statistical dynamics with state-to-state ultracold chemistry

Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities(1). Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, because they can be experimentally studied with unprecedented control(2), yet display dynamics that are highly complex(3). Here we report the full product state distribution for the reaction 2KRb -> K-2 + Rb-2. Ultracold preparation of the reactants allows us complete control over their initial quantum degrees of freedom, whereas state-resolved, coincident detection of both products enables the probability of scattering into each of the 57 allowed rotational state-pairs to be measured. Our results show an overall agreement with a state-counting model based on statistical theory(4-6), but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a benchmark for quantum dynamics calculations beyond the current state of the art.