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arXiv:2606.28233

Coexisting Regular and Chaotic Dynamics in the Dysprosium Feshbach Spectrum

Julie Veschambre, Alexandre Journeaux, Maxime Lecomte, Alice Belmon, Ethan Uzan, Inès de Verdelhan, P. C. M. Castilho, Jakub Zakrzewski, Jean Dalibard, Raphael Lopes

Published Jun 26, 2026• 0 citations
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Abstract

Strongly dipolar gases, such as dysprosium, erbium and thulium, exhibit dense Feshbach spectra whose level statistics have been associated with quantum chaos arising from couplings among many molecular channels. Here, we combine a precise calibration of the Feshbach spectrum of $^{162}$Dy with spectroscopic measurements of the differential magnetic moments of bound states associated with more than 80 resonances between 0 and 30 G. These magnetic moments provide an eigenstate-sensitive probe of the molecular states underlying the resonance spectrum. We find that the level statistics are not uniform: resonances associated with states near the center of the magnetic-moment distribution display enhanced level repulsion, whereas those near the lower edge remain close to Poisson statistics. Our results reveal hidden structure within the chaotic dysprosium Feshbach spectrum and identify molecular-state composition as a key ingredient in the emergence of quantum chaos in strongly dipolar scattering.

DOI
10.48550/arxiv.2606.28233

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Strongly dipolar gases, such as dysprosium, erbium and thulium, exhibit dense Feshbach spectra whose level statistics have been associated with quantum chaos arising from couplings among many molecular channels. Here, we combine a precise calibration of the Feshbach spectrum of 162^{162}162Dy with spectroscopic measurements of the differential magnetic moments of bound states associated with more than 80 resonances between 0 and 30 G. These magnetic moments provide an eigenstate-sensitive probe of the molecular states underlying the resonance spectrum. We find that the level statistics are not uniform: resonances associated with states near the center of the magnetic-moment distribution display enhanced level repulsion, whereas those near the lower edge remain close to Poisson statistics. Our results reveal hidden structure within the chaotic dysprosium Feshbach spectrum and identify molecular-state composition as a key ingredient in the emergence of quantum chaos in strongly dipolar scattering.
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.
We report on the observation of weakly bound dimers of bosonic dysprosium with a strong universal sss-wave halo character, associated with broad magnetic Feshbach resonances. These states surprisingly decouple from the chaotic background of narrow resonances, persisting across many such narrow resonances. In addition they show the highest reported magnetic moment $\ensuremath{\mu}\ensuremath{\simeq}20{\ensuremath{\mu}}_{\mathrm{B}}$ of any ultracold molecule. We analyze our findings using a coupled-channel theory taking into account the short range van der Waals interaction and a correction due to the strong dipole moment of dysprosium. We are able to extract the scattering length as a function of magnetic field associated with these resonances and obtain a background scattering length abg=91(16)a0{a}_{\mathrm{bg}}=91(16)\phantom{\rule{0.16em}{0ex}}{a}_{0}abg​=91(16)a0​. These results offer prospects of a tunability of the interactions in dysprosium, which we illustrate by observing the saturation of three-body losses.
Abstract We investigate ultracold magnetic-field-assisted collisions in the so far unexplored ErYb system. The nonsphericity of the Er atom leads to weakly anisotropic interactions that provide the mechanism for Feshbach resonances to emerge. The resonances are moderately sparsely distributed with a density of 0.1–0.3 G−1 and exhibit chaotic statistics characterized by a Brody parameter η ≈ 0.5–0.7. The chaotic behaviour of Feshbach resonances is accompanied by strong mixing of magnetic and rotational quantum numbers in near-threshold bound states. We predict the existence of broad resonances at fields < 300 G that may be useful for the precise control of scattering properties and magnetoassociation of ErYb molecules. The high number of bosonic Er–Yb isotopic combinations gives many opportunities for mass scaling of interactions. Uniquely, two isotopic combinations have nearly identical reduced masses (differing by less than 10−5 relative) that we expect to have strikingly similar Feshbach resonance spectra, which would make it possible to experimentally measure their sensitivity to hypothetical variations of proton-to-electron mass ratio.
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by random matrix theory. Scattering resonances observed in ultracold atomic and molecular systems exhibit similar features as a consequence of their energy level structure. We study how the overlap between Feshbach resonances affects the distribution of resonance spacings. The spectrum of strongly overlapping resonances turns out to be non-Poisson even when the assumptions of random matrix theory are not fulfilled, but the spectrum is also not completely chaotic and tends towards being semi-Poisson.
We explore the anisotropic nature of Feshbach resonances in the collision between ultracold highly magnetic submerged-shell dysprosium atoms in their energetically lowest magnetic sublevel, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where broadest (strongest) Feshbach resonances are hyperfine induced and due to rotationless bound states. Our first-principle coupled-channel calculation of the collisions between these spin-polarized bosonic dysprosium atoms reveals a strong interplay between the anisotropies in the dispersion and magnetic dipole-dipole interaction. The former anisotropy is absent in alkali-metal and chromium collisions. We show that both types of anisotropy significantly affect the Feshbach spectrum as a function of an external magnetic field. Effects of the electrostatic quadrupole-quadrupole interaction are small. Over a 20 mT magnetic field range, we predict about 10 Feshbach resonances and show that the resonance locations depend on the dysprosium isotope.
We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2)\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})Yb(1S0​)+Yb(3P2​) collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.