© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1506.05221 · Physical Review X

Emergence of Chaotic Scattering in Ultracold Er and Dy

Thomas Maier, Holger Kadau, M. Schmitt, M. Wenzel, Igor Ferrier-Barbut, Tilman Pfau, Albert Frisch, Simon Baier, K. Aikawa, Lauriane Chomaz, Manfred J. Mark, Francesca Ferlaino, Constantinos Makrides, Eite Tiesinga, Alexander N. Petrov, Svetlana Kotochigova

Published Nov 19, 2015• 127 citations

Abstract

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.

DOI: 10.1103/physrevx.5.041029

Related papers

Quantum chaos in Feshbach resonances of the ErYb system

Maciej B. Kosicki, Mateusz Borkowski, Piotr Szymon Żuchowski

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.

arXiv:1910.03077•New Journal of Physics•Jan 15, 2020•10 citations

Coexisting Regular and Chaotic Dynamics in the Dysprosium Feshbach Spectrum

Julie Veschambre, Alexandre Journeaux, Maxime Lecomte +7 more

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.

arXiv:2606.28233•Jun 26, 2026•0 citations

Reactive Collisions and Interactions of Ultracold Dipolar Atoms

Svetlana Kotochigova

Abstract : We explored Feshbach resonances in the collision between ultracold highly-magnetic dysprosium and erbium atoms. The resonance density is orders of magnitude larger than seen in any other previously studied atomic system. Moreover, we showed that these resonance can only exist because of the anisotropic nature of the atom-atom potentials. Analysis of nearest-neighbor spacings between Feshbach resonances shows a chaotic distribution that one would expect from random-matrix theory. We explained these statistics as originating from the large strength of the anisotropy. We demonstrated that the vibrational motion of BaCl+ molecules is quenched by collisions with ultracold calcium atoms at a rate comparable to the Langevin rate. This is over four orders of magnitude more efficient than traditional sympathetic cooling schemes. In addition, we calculated the electronic structure of BaCl+ and other molecular ions. Based on these results we found unusually-large rates for cold charge-transfer reactions between neutral and ionic atoms.

•Oct 29, 2014•0 citations

Loss features in ultracold $^{162}$Dy gases: two- versus three-body processes

Maxime Lecomte, Alexandre Journeaux, Renaud, Loan +2 more

Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviours with density and temperature, implying diverse microscopic properties. Here, we quantitatively investigate the low-field ($B < 6\,\text{G}$) loss features in ultracold thermal samples of $^{162}$Dy, revealing two- and three-body dominated loss processes. We investigate their temperature dependence and detect a feature compatible with a $d$-wave Fano-Feshbach resonance, which has not been observed before. We also analyse the expansion of the dipolar Bose-Einstein condensate as a function of the magnetic field and interpret the changes in size close to the resonances with a variation in the scattering length.

arXiv:2310.11418•Oct 17, 2023•0 citations

Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?

Jordi Mur-Petit, Rafael A. Molina

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in (166)Er and (168)Er observed in recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until B∼30 G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a 20%-25% fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.

arXiv:1506.08086•Physical Review E•Oct 5, 2015•46 citations

Broad universal Feshbach resonances in the chaotic spectrum of dysprosium atoms

T. Maier, Igor Ferrier-Barbut, Holger Kadau +6 more

We report on the observation of weakly bound dimers of bosonic dysprosium with a strong universal $s$-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 ${a}_{\mathrm{bg}}=91(16)\phantom{\rule{0.16em}{0ex}}{a}_{0}$. These results offer prospects of a tunability of the interactions in dysprosium, which we illustrate by observing the saturation of three-body losses.

arXiv:1506.01875•Physical Review A•Dec 14, 2015•76 citations

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.

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.

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.

Abstract : We explored Feshbach resonances in the collision between ultracold highly-magnetic dysprosium and erbium atoms. The resonance density is orders of magnitude larger than seen in any other previously studied atomic system. Moreover, we showed that these resonance can only exist because of the anisotropic nature of the atom-atom potentials. Analysis of nearest-neighbor spacings between Feshbach resonances shows a chaotic distribution that one would expect from random-matrix theory. We explained these statistics as originating from the large strength of the anisotropy. We demonstrated that the vibrational motion of BaCl+ molecules is quenched by collisions with ultracold calcium atoms at a rate comparable to the Langevin rate. This is over four orders of magnitude more efficient than traditional sympathetic cooling schemes. In addition, we calculated the electronic structure of BaCl+ and other molecular ions. Based on these results we found unusually-large rates for cold charge-transfer reactions between neutral and ionic atoms.

Loss features in ultracold

^{162}

Dy gases: two- versus three-body processes

Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviours with density and temperature, implying diverse microscopic properties. Here, we quantitatively investigate the low-field (

B < 6\,\text{G}

) loss features in ultracold thermal samples of

^{162}

Dy, revealing two- and three-body dominated loss processes. We investigate their temperature dependence and detect a feature compatible with a

d

-wave Fano-Feshbach resonance, which has not been observed before. We also analyse the expansion of the dipolar Bose-Einstein condensate as a function of the magnetic field and interpret the changes in size close to the resonances with a variation in the scattering length.

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in (166)Er and (168)Er observed in recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until B∼30 G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a 20%-25% fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.

We report on the observation of weakly bound dimers of bosonic dysprosium with a strong universal

s

-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

{a}_{\mathrm{bg}}=91(16)\phantom{\rule{0.16em}{0ex}}{a}_{0}

. These results offer prospects of a tunability of the interactions in dysprosium, which we illustrate by observing the saturation of three-body losses.