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arXiv:2609.04106

Sub-barrier peaks in atom-atom-ion three-body recombination

Fabian Thielemann, Joachim Siemund, Tobias Schaetz, Krzysztof Jachymski

Published Sep 3, 2026• 0 citations
arXivHTMLPDF

Abstract

Hybrid atom-ion experiments have recently entered the few-partial wave regime in which magnetically tunable Feshbach resonances dominate the three-body loss dynamics. This necessitates a treatment of three-body recombination that can incorporate the role of the resonant dimer channel. Here, we develop a two-step Lindemann-type model for resonant atom-atom-ion three-body recombination that combines multichannel quantum-defect theory for the long-range polarization potential with a universal quantum-capture treatment of the inelastic atom-dimer step. We show that within our model, rate competition can lead to a peak in the three-body-recombination cross section of higher partial-wave channels at energies well below their corresponding centrifugal barrier. Investigating the resulting loss rates under numerically obtained non-thermal collision-energy distributions, we find that these effects survive the energy averaging and can be observed in state-of-the-art hybrid experimental setups. Our findings pave the way for a detailed characterization of atom-ion Feshbach resonances via the analysis of inelastic three-body-recombination processes.

DOI
10.48550/arxiv.2609.04106

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Hybrid atom-ion experiments have recently entered the few-partial wave regime in which magnetically tunable Feshbach resonances dominate the three-body loss dynamics. This necessitates a treatment of three-body recombination that can incorporate the role of the resonant dimer channel. Here, we develop a two-step Lindemann-type model for resonant atom-atom-ion three-body recombination that combines multichannel quantum-defect theory for the long-range polarization potential with a universal quantum-capture treatment of the inelastic atom-dimer step. We show that within our model, rate competition can lead to a peak in the three-body-recombination cross section of higher partial-wave channels at energies well below their corresponding centrifugal barrier. Investigating the resulting loss rates under numerically obtained non-thermal collision-energy distributions, we find that these effects survive the energy averaging and can be observed in state-of-the-art hybrid experimental setups. Our findings pave the way for a detailed characterization of atom-ion Feshbach resonances via the analysis of inelastic three-body-recombination processes.
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Hybrid atom-ion systems combine the precise control of a single radio-frequency-trapped atomic ion with the rich few- to many-body phenomena of ultracold degenerate quantum gases trapped in light fields. The associated long-range interaction enables studies of impurity physics and the implementation of a single-particle quantum gas microscope, sensitive to quantities beyond the atomic density, including energy distributions, atom-atom couplings, and many-body exchange symmetry. This perspective requires atom-ion coupling, which can be tuned through resonantly enhanced scattering. While atom-ion Feshbach resonances have recently become experimentally accessible, the role of quantum statistics in resonantly enhanced three-body recombination remains largely unexplored. This thesis investigates the role of fermionic quantum statistics in atom-atom-ion three-body recombination. The experiment employs a single 138Ba+ ion immersed in an ultracold two-component Fermi gas of 6Li. An atom-ion Feshbach resonance enables resonantly enhanced recombination for one spin component, while the other component acts as a non-resonant spectating collision partner. This allows a direct comparison between recombination processes involving identical and distinguishable fermions. Experimentally, recombination rates are extracted from bath polarization-dependent ion-loss spectroscopy. Expressing the results as relative rate constants largely detaches them from the total atomic density and results in suppression of recombination in the identical fermion channel. Additional measurements of two-body reactive collisions are combined with simulations of the Fermi gas, demonstrating that density modifications arising from Fermi-Dirac statistics or mutual atom-atom attraction are insufficient to explain the observed recombination behavior. To interpret the measurements, an extension of the conventional two-step model is developed. Using a hyperspherical treatment that includes all pairwise interactions and fermionic exchange symmetry, effective relaxation rates for the loosely-bound atom-ion complex are obtained. The calculations predict a suppression of recombination involving identical fermions relative to distinguishable collision partners. The experimental observations are consistent with this prediction and provide evidence that fermionic exchange symmetry significantly affects resonantly enhanced atom-atom-ion recombination. These results establish three-body recombination as a sensitive probe of short-range quantum correlations in degenerate gases and demonstrate that a single trapped ion can be employed as a localized sensor of many-body quantum statistics.
We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the three-body solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of "background" non-resonant interactions in the open channel of the two-channel model is also calculated and allows to determine which three-body quantities are `universal' and which on the contrary depend on the details of the model.
We investigate three-body recombination in a hybrid atom-ion system consisting of a single trapped Ba+^++ ion immersed in a two-component Fermi gas of Li atoms near an atom-ion Feshbach resonance. By tuning the spin composition at constant density and temperature, we isolate the role of quantum statistics in atom-atom-ion collisions. The measured ion loss rate exhibits a pronounced nonlinear dependence on spin polarization, revealing a reduced contribution of recombination pathways involving identical fermions already at the level of experimental observables. The observations are consistent with a two-step recombination picture and an adiabatic hyperspherical approach, where antisymmetrization restricts the available entrance channels and gives rise to interference between indistinguishable recombination pathways. Our work establishes atom-ion systems as a platform for controlling three-body collisions via quantum statistics and demonstrates that exchange-symmetry effects remain robust even under thermal averaging that obscures the underlying threshold-law behavior.
We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p\mathit{p}p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the three-body solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of ``background'' nonresonant interactions in the open channel of the two-channel model is also calculated and allows one to determine which three-body quantities are ``universal'' and which on the contrary depend on the details of the model.
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