Energy scaling of the product state distribution for three-body recombination of ultracold atoms

Abstract

Three-body recombination is a chemical reaction where the collision of three atoms leads to the formation of a diatomic molecule. In the ultracold regime it is expected that the production rate of a molecule generally decreases with its binding energy ${E}_{b}$, however, its precise dependence and the physics governing it have been left unclear so far. Here we present a comprehensive experimental and theoretical study of the energy dependency for three-body recombination of ultracold Rb. For this, we determine production rates for molecules in a state-to-state resolved manner, with the binding energies ${E}_{b}$ ranging from 0.02 to 77 $\mathrm{GHz}\ifmmode\times\else\texttimes\fi{}h$. We find that the formation rate approximately scales as ${E}_{b}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ is in the vicinity of 1. The formation rate typically varies only within a factor of two for different rotational angular momenta of the molecular product, apart from a possible centrifugal barrier suppression for low binding energies. In addition to numerical three-body calculations we present a perturbative model which reveals the physical origin of the energy scaling of the formation rate. Furthermore, we show that the scaling law potentially holds universally for a broad range of interaction potentials.