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arXiv:2511.00325 · Physical Review Letters

Universality in Ionic Three-Body Systems Near an Ion-Atom Feshbach Resonance

Jacek Gȩbala, Michał Tomza, José Paulo D'Incao

Published Jun 1, 2026• 0 citations
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Abstract

We calculate the bound and scattering properties of a system of two neutral atoms and an ion near an ion-atom Feshbach resonance. Our results indicate that long-range ion-atom interactions lead to significant deviations from universal behavior derived from contact or van der Waals potentials. We find that ionic systems display an overall suppression of inelastic transitions leading to recombination rates and lifetimes of Efimov state orders of magnitude larger with respect to those for neutral atoms. We further characterize the dense spectra of triatomic molecular ions with extended lifetimes. Our results provide a deeper insight into the universality and structure of three-body ionic systems and establish them as a promising platform for exploring novel few- and many-body phenomena with long-range interactions.

DOI
10.1103/r7hw-27wv

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We calculate the bound and scattering properties of a system of two neutral atoms and an ion near an ion-atom Feshbach resonance. Our results indicate that long-range ion-atom interactions lead to significant deviations from universal behavior derived from contact or van der Waals potentials. We find that ionic systems display an overall suppression of inelastic transitions leading to recombination rates and lifetimes of Efimov state orders of magnitude larger with respect to those for neutral atoms. We further characterize the dense spectra of triatomic molecular ions with extended lifetimes. Our results provide a deeper insight into the universality and structure of three-body ionic systems and establish them as a promising platform for exploring novel few- and many-body phenomena with long-range interactions.
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in 39K^{39}\mathrm{K}39K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.
Recent measurements of Efimov resonances for a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of 40K and 87Rb atoms. We find an Efimov-like resonance in the rate of inelastic collisions between 40K87Rb Feshbach molecules and 87Rb atoms. However, we do not observe any Efimov-related resonances in the rates of inelastic collisions between three atoms. These observations are compared to previous measurements by the LENS group of Efimov resonances in a 41K and 87Rb mixture as well as to recent predictions.
We find that universal three-body physics extends beyond the threshold regime to non-zero energies. For ultracold atomic gases with a negative two-body s-wave scattering length near a Feshbach resonance, we show that the resonant peaks characteristic of Efimov physics persist in three-body recombination to higher collision energies. For this and other inelastic processes, we use the adiabatic hyperspherical representation to derive universal analytical expressions for their dependence on the scattering length, the collision energy and—for narrow resonances—the effective range. These expressions are supported by full numerical solutions of the Schrödinger equation and display log-periodic dependence on energy characteristic of Efimov physics. This dependence is robust and might be used to experimentally observe several Efimov features.
A nonrelativistic system of three identical particles will display a rich set of universal features known as Efimov physics if the scattering length aaa is much larger than the range lll of the underlying two-body interaction. An appropriate effective theory facilitates the derivation of both results in the $\ensuremath{\mid}a\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit and finite-l∕al∕al∕a corrections to observables of interest. Here we use such an effective-theory treatment to consider the impact of corrections linear in the two-body effective range, rs{r}_{s}rs​, on the three-boson bound-state spectrum and recombination rate for $\ensuremath{\mid}a\ensuremath{\mid}⪢\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$. We do this by first deriving results appropriate to the strict limit $\ensuremath{\mid}a\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ in coordinate space. We then extend these results to finite aaa using once-subtracted momentum-space integral equations. We take the cutoff on these equations to be large compared to $1∕\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$, and find that the first-order effects of $\ensuremath{\mid}{r}_{s}\ensuremath{\mid}$ are independent of the cutoff in this regime. We also discuss the implications of our results for experiments that probe three-body recombination in Bose-Einstein condensates near a Feshbach resonance.
This thesis investigates universal and non-universal aspects of few-body physics in a mass-imbalanced mixture of ultracold bosonic 133^{133}133Cs and fermionic 6^66Li atoms. For this purpose an experimental apparatus for the creation of quantum degenerate gases has been constructed. Using radio-frequency association of weakly-bound LiCs molecules and additional atom-loss spectroscopy we determine the two-body interaction properties between Li and Cs atoms at low collision energies. The analysis with a coupled-channels calculation yields precise singlet and triplet electronic ground state molecular potential curves, from which scattering lengths and positions of Fano-Feshbach resonances are extracted. These results represent almost a tenfold improvement over the previous determination, and are used to study few-body recombination processes and, for the first time, their dependence on the interaction strength between the heavy atoms close to two broad scattering resonances at various temperatures. Measurements of three-body loss rates reveal two series of three and two consecutive LiCs2_22​ Efimov resonances that demonstrate the universal scaling factor 4.9 between the first and second excited state resonances. The ground state resonance deviates from the discrete scaling law. By the use of hyperspherical formalism with either pairwise zero-range or Lennard-Jones model potentials we identify the van der Waals interaction between Cs atoms as a significant source of these modifications.
We perform precise studies of two- and three-body interactions near an intermediate-strength Feshbach resonance in ^{39}K at 33.5820(14) G. Precise measurement of dimer binding energies, spanning three orders of magnitude, enables the construction of a complete two-body coupled-channel model for determination of the scattering lengths with an unprecedented low uncertainty. Utilizing an accurate scattering length map, we measure the precise location of the Efimov ground state to test van der Waals universality. Precise control of the sample's temperature and density ensures that systematic effects on the Efimov trimer state are well understood. We measure the ground Efimov resonance location to be at -14.05(17) times the van der Waals length r_{vdW}, significantly deviating from the value of -9.7r_{vdW} predicted by van der Waals universality. We find that a refined multichannel three-body model, built on our measurement of two-body physics, can account for this difference and even successfully predict the Efimov inelasticity parameter η.