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arXiv:2008.00396 · Physical Review Letters

Observation of Efimov Universality across a Nonuniversal Feshbach Resonance in K39

Xin Xie, Michael J. Van de Graaff, Roman Chapurin, Matthew D. Frye, Jeremy M. Hutson, José Paulo D'Incao, Paul S. Julienne, Jun Ye, Eric Cornell

Published Dec 7, 2020• 36 citations
arXivHTMLPDF

Abstract

We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.

DOI
10.1103/physrevlett.125.243401

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We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.
Using a combination of bound-state spectroscopy and loss spectroscopy, we pinpoint eight intrastate Feshbach resonances in 39K^{39}\mathrm{K}39K, as well as six previously unexplored interstate ones. We perform a detailed characterization of four of the intrastate resonances and two of the interstate ones. We carry out coupled-channel scattering calculations and find good agreement with experiment. The combination of experiment and theory provides a faithful map of the scattering length aaa and permits precision measurements of the signatures of Efimov physics across four intermediate-strength intrastate resonances. We measure the modulation of the a4{a}^{4}a4 scaling of the three-body loss coefficient for both a<0a<0a<0 and a>0a>0a>0, as well as the many-body loss dynamics at unitarity (where aaa diverges). The absolute positions of the observed Efimov features confirm a ubiquitous breakdown of Efimov--van der Waals universality in 39K^{39}\mathrm{K}39K, while their relative positions are in agreement with the universal Efimov ratios. The loss dynamics at unitarity are the same (within experimental uncertainties) for the three broadest Feshbach resonances, consistent with observing little variation in the widths of the corresponding Efimov features.
We measure the critical scattering length for the appearance of the first three-body bound state, or Efimov three-body parameter, at seven different Feshbach resonances in ultracold ^{39}K atoms. We study both intermediate and narrow resonances, where the three-body spectrum is expected to be determined by the nonuniversal coupling of two scattering channels. Instead, our observed ratio of the three-body parameter with the van der Waals radius is approximately the same universal ratio as for broader resonances. This unexpected observation suggests the presence of a new regime for three-body scattering at narrow resonances.
Ultracold atomic gases are an important testing ground for understanding few-body physics. In particular, these systems enable a detailed study of the Efimov effect. We use ultracold 39K^{39}\mathrm{K}39K to investigate the temperature dependence of an Efimov resonance. The shape and position of the observed resonance are analyzed by employing an empirical fit, and universal finite-temperature zero-range theory. Both procedures suggest that the resonance position shifts towards lower absolute scattering lengths when approaching the zero-temperature limit. We extrapolate this shift to obtain an estimate of the three-body parameter at zero temperature. A surprising finding of our study is that the resonance becomes less prominent at lower temperatures, which currently lacks a theoretical description and implies physical effects beyond available models. Finally, we present measurements performed near the Feshbach resonance center and discuss the prospects for observing the second Efimov resonance in 39K^{39}\mathrm{K}39K.
We have measured the binding energy of 7{}^{7}7Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683 (2009)]. We find the measured locations of the three- and four-body Efimov features to be consistent with universal theory at the 20%--30% level.
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.
We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter obsolete. The solution explains the empirical relation between the scattering length a − where the first Efimov state appears at the atom threshold and the van der Waals length l vdw for open-channel dominated resonances. There is a continuous crossover to the closed-channel dominated limit, where the scale in the energy level diagram as a function of the inverse scattering length 1 / a is set by the intrinsic length r ⋆ associated with the Feshbach coupling. Our results provide a number of predictions for the deviations from universal scaling relations between energies and scattering lengths that can be tested in future experiments.