Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Research

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

Shinsuke Haze, José Paulo D'Incao, Dominik Dorer, Jing-Lun Li, Markus Deiß, E. Tiemann, Paul S. Julienne, Johannes Hecker Denschlag

Published Mar 3, 2023• 9 citations
Publisher

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.

DOI
10.1103/physrevresearch.5.013161

Related papers

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

Shinsuke Haze, José Paulo D'Incao, Dominik Dorer +5 more

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, 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 ranging from 0.02 to 77 GHz×h. We find that the formation rate approximately scales as Eb-α, where α 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.

arXiv:2211.03834•Nov 7, 2022•0 citations

Shedding Light on Three-Body Recombination in an Ultracold Atomic Gas

Arne Härter, Artjom Krükow, Markus Deiß +3 more

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 $h\times 750\:$GHz. 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.

arXiv:1301.5518•Jan 23, 2013•5 citations

Energy Scaling of Cold Atom-Atom-Ion Three-Body Recombination

Artjom Krükow, Amir Mohammadi, Arne Härter +3 more

We study three-body recombination of Ba^{+}+Rb+Rb in the mK regime where a single ^{138}Ba^{+} ion in a Paul trap is immersed into a cloud of ultracold ^{87}Rb atoms. We measure the energy dependence of the three-body rate coefficient k_{3} and compare the results to the theoretical prediction, k_{3}∝E_{col}^{-3/4}, where E_{col} is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.

arXiv:1510.04938•Physical Review Letters•May 12, 2016•89 citations

Single Ion as a Three-Body Reaction Center in an Ultracold Atomic Gas

Arne Härter, Artjom Krükow, Andreas Brunner +3 more

We report on three-body recombination of a single trapped Rb(+) ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K(3) depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1 eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic Rb(+) ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound Rb(2) molecules.

arXiv:1206.0242•Physical Review Letters•Sep 18, 2012•111 citations

State-to-state chemistry with ultracold neutral Rb atoms

Joschka Wolf

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.

•Jan 1, 2019•0 citations

Spin-Conservation Propensity Rule for Three-Body Recombination of Ultracold Rb Atoms

Shinsuke Haze, José Paulo D'Incao, Dominik Dorer +4 more

We explore the physical origin and the general validity of a propensity rule for the conservation of the hyperfine spin state in three-body recombination. This rule was recently discovered for the special case of ^{87}Rb with its nearly equal singlet and triplet scattering lengths. Here, we test the propensity rule for ^{85}Rb for which the scattering properties are very different from ^{87}Rb. The Rb_{2} molecular product distribution is mapped out in a state-to-state fashion using resonance-enhanced multiphoton ionization detection schemes which fully cover all possible molecular spin states. Interestingly, for the experimentally investigated range of binding energies from zero to ∼13 GHz×h we observe that the spin-conservation propensity rule also holds for ^{85}Rb. From these observations and a theoretical analysis we derive an understanding for the conservation of the hyperfine spin state. We identify several criteria to judge whether the propensity rule will also hold for other elements and collision channels.

arXiv:2112.13714•Physical Review Letters•Apr 1, 2022•18 citations
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 GHz\ifmmode×\else\texttimes\fih\mathrm{GHz}\ifmmode\times\else\texttimes\fi{}hGHz\ifmmode×\else\texttimes\fih. We find that the formation rate approximately scales as Eb\ensuremath−\ensuremathα{E}_{b}^{\ensuremath{-}\ensuremath{\alpha}}Eb\ensuremath−\ensuremathα​, where \ensuremathα\ensuremath{\alpha}\ensuremathα 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.
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, 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 ranging from 0.02 to 77 GHz×h. We find that the formation rate approximately scales as Eb-α, where α 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.
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 study three-body recombination of Ba^{+}+Rb+Rb in the mK regime where a single ^{138}Ba^{+} ion in a Paul trap is immersed into a cloud of ultracold ^{87}Rb atoms. We measure the energy dependence of the three-body rate coefficient k_{3} and compare the results to the theoretical prediction, k_{3}∝E_{col}^{-3/4}, where E_{col} is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.
We report on three-body recombination of a single trapped Rb(+) ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K(3) depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1 eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic Rb(+) ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound Rb(2) molecules.
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.
We explore the physical origin and the general validity of a propensity rule for the conservation of the hyperfine spin state in three-body recombination. This rule was recently discovered for the special case of ^{87}Rb with its nearly equal singlet and triplet scattering lengths. Here, we test the propensity rule for ^{85}Rb for which the scattering properties are very different from ^{87}Rb. The Rb_{2} molecular product distribution is mapped out in a state-to-state fashion using resonance-enhanced multiphoton ionization detection schemes which fully cover all possible molecular spin states. Interestingly, for the experimentally investigated range of binding energies from zero to ∼13 GHz×h we observe that the spin-conservation propensity rule also holds for ^{85}Rb. From these observations and a theoretical analysis we derive an understanding for the conservation of the hyperfine spin state. We identify several criteria to judge whether the propensity rule will also hold for other elements and collision channels.