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

TL;DR

This study investigates how the formation rate of molecules from three-body recombination in ultracold Rb atoms depends on the molecule's binding energy, revealing a near-inverse proportionality and potential universality across interaction potentials.

Contribution

The paper provides the first comprehensive experimental and theoretical analysis of energy dependence in three-body recombination, including a new perturbative model explaining the observed scaling.

Findings

Formation rate scales approximately as E_b^{-1}

Rate varies minimally across different rotational states

Perturbative model explains the physical origin of energy scaling

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 GHz$\times h$. We find that the formation rate approximately scales as $E_b^{-\alpha}$, where $\alpha$ 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.