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Science

State-to-state chemistry for three-body recombination in an ultracold rubidium gas

Joschka Wolf, Markus Deiß, Artjom Krükow, E. Tiemann, Brandon Ruzic, Yujun Wang, José Paulo D'Incao, Paul S. Julienne, Johannes Hecker Denschlag

Published Nov 17, 2017• 86 citations
Publisher

Abstract

molecule. The measured product distribution covers about 90% of the final products, and we are able to discriminate between product states with a level splitting as small as 20 megahertz multiplied by Planck's constant. Furthermore, we formulate propensity rules for the distribution of products, and we develop a theoretical model that predicts many of our experimental observations. The scheme can readily be adapted to other species and opens a door to detailed investigations of inelastic or reactive processes.

DOI
10.1126/science.aan8721

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molecule. The measured product distribution covers about 90% of the final products, and we are able to discriminate between product states with a level splitting as small as 20 megahertz multiplied by Planck's constant. Furthermore, we formulate propensity rules for the distribution of products, and we develop a theoretical model that predicts many of our experimental observations. The scheme can readily be adapted to other species and opens a door to detailed investigations of inelastic or reactive processes.
Fully understanding a chemical reaction on the quantum level is a long-standing goal in physics and chemistry. Experimental investigation of such state-to-state chemistry requires both the preparation of the reactants and the detection of the products in a quantum state resolved way, which has been a long term challenge. Using the high level control in the ultracold domain, we prepare a few-body quantum state of reactants and demonstrate state-to-state chemistry with unprecedented resolution. We present measurements and accompanying theoretical analysis for the recombination of three spin-polarized ultracold Rb atoms forming a weakly bound Rb2_22​ dimer. Detailed insights of the reaction process are obtained that suggest propensity rules for the distribution of reaction products. The scheme can readily be adapted to other species and opens a door to detailed investigations of inelastic or reactive processes in domains never before accessible.
In this thesis, I report on experiments on the detection and the production of molecules in an ultracold atomic gas. These experiments can be divided into two main parts. The first part is about state-to-state experiments where chemical reaction products are detected in a quantum state resolved way. The second part is about Rydberg molecules. In the first part, I investigate three-body recombination of neutral Rb, which is a chemical reaction leading to the formation of Rb2 dimers. The quantum states of the three-body recombination product molecules are investigated for different initial atomic samples. This includes different atomic hyperfine states and different atomic magnetic sub states that are prepared. The molecular reaction product is state-selectively ionized and detected afterwards. The detection scheme resolves total electron spin, the vibrational, the rotational, the hyperfine and even the magnetic sub state of the product molecules. We determine the population distribution of the product molecules covering the majority of all produced molecules. The insights gained enable us to formulate various propensity rules for the three-body recombination of 87Rb. The second part is furthermore divided into two parts: the investigations of charged and uncharged Rydberg molecules. The investigations of charged Rydberg molecules are the first step towards one of our goals, the photoassociation of BaRb+ or Rb2+ Rydberg molecules. For this work, we have developed a novel method to measure Stark spectra within an ion trap. In experiments with neutral Rb2 Rydberg molecules we observe a complex spin structure of the molecular states. The substructure emerges partially due to a novel, recently predicted spin-orbit interaction of the Rydberg electron and the perturber atom, which we prove for the first time.
Three-body recombination is a prime example of the fundamental interaction between three particles. Due to the complexity of this process it has resisted a comprehensive description. Experimental investigations have mainly focussed on the observation of corresponding loss rates without revealing information on the reaction products. Here, we provide the first general experimental study on the population distribution of molecular quantum states after three-body recombination in a non-resonant regime. We have developed a highly sensitive detection scheme which combines photoionization of the molecules with subsequent ion trapping. By analyzing the ionization spectrum, we identify the population of energy levels with binding energies up to h×750 h\times 750\:h×750GHz. We find a broad population of electronic and nuclear spin states and determine a range of populated vibrational and rotational states. The method presented here can be expanded to provide a full survey of the products of the recombination process. This may be pivotal in developing an in-depth model that can qualitatively and quantitatively predict the reaction products of three-body recombination.
We extend state-to-state chemistry to a realm where besides vibrational, rotational, and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect, which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of ^{87}Rb atoms forming weakly bound Rb_{2} molecules. Here, we find the propensity rule that the total m_{F} quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other reactions and inelastic collisions and will allow for novel insights into few-body processes.
The ultracold state-to-state chemistry for three-body recombination (TBR) in realistic systems has recently been experimentally investigated with full quantum state resolution. However, many detected phenomena remain challenging to be explored and explained from the theoretical viewpoints because this generally requires computational powers beyond state of the art. Here, the product-state distributions after TBR of 3He2–alkaline-earth-metal systems, i.e., after the processes of 3He + 3He + X → 3HeX + 3He with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, in the zero-collision-energy limit are theoretically studied. Two propensity rules for the distribution of the products found in current experiments have been checked, and the mechanism underlying these product-state distributions is explored. Particularly, two main intriguing transition pathways are identified, which may be responsible for the nonlinear distribution of the products vs their respective rotational quantum number. In addition, the TBR rates of these systems are also influenced by details of the interaction potential and relevant nonadiabatic couplings.
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 Eb{E}_{b}Eb​, 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 Eb{E}_{b}Eb​ 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.