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arXiv:2503.16374 · Physical Review A

Observable Efimov resonances in light-light-heavy systems

Karim I. Elghazawy, Chris H. Greene

Published Oct 21, 2025• 0 citations
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Abstract

Three-body loss resonances associated with heavy-heavy-light Efimov states have been observed for over a decade in ultracold mixtures tuned near interspecies Feshbach resonances. For light-light-heavy systems, observing such resonances has been far more challenging due to the substantially large Efimov spacing. In these Efimov-unfavored systems, the intraspecies scattering length ${a}_{\text{BB}}$ has been shown to significantly affect the overall Efimov scenario, namely, the positions of the Efimov resonances ${a}_{\ensuremath{-}}^{(n)}$ and the three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(0)}$. The present article explains the origin behind this influence by highlighting two primary mechanisms via which both the magnitude and sign of ${a}_{\text{BB}}$ govern the Efimov spectrum and set the resulting 3BP ${a}_{\ensuremath{-}}^{(0)}$. By employing van der Waals interactions for ${^{23}\mathrm{Na}}_{2}^{40}\mathrm{K}$, we attribute the vital role of ${a}_{\text{BB}}$ in Efimov-unfavored systems to the large difference between the Efimov scaling parameters for two and three resonant interactions, ${s}_{0}$ and ${s}_{0}^{*}$. In particular, we account for the unusually large ${a}_{\ensuremath{-}}^{(0)}$ obtained in light-light-heavy systems with ${a}_{\text{BB}}>0$ (e.g., ${^{41}\mathrm{K}}_{2}^{87}\mathrm{Rb}$), and show that the first Efimov resonance can still occur at an experimentally accessible value when ${a}_{\text{BB}}<0$.

DOI
10.1103/y4vl-fxk9

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Three-body loss resonances associated with heavy-heavy-light Efimov states have been observed for over a decade in ultracold mixtures tuned near interspecies Feshbach resonances. For light-light-heavy systems, observing such resonances has been far more challenging due to the substantially large Efimov spacing. In these Efimov-unfavored systems, the intraspecies scattering length aBB{a}_{\text{BB}}aBB​ has been shown to significantly affect the overall Efimov scenario, namely, the positions of the Efimov resonances a\ensuremath−(n){a}_{\ensuremath{-}}^{(n)}a\ensuremath−(n)​ and the three-body parameter (3BP) a\ensuremath−(0){a}_{\ensuremath{-}}^{(0)}a\ensuremath−(0)​. The present article explains the origin behind this influence by highlighting two primary mechanisms via which both the magnitude and sign of aBB{a}_{\text{BB}}aBB​ govern the Efimov spectrum and set the resulting 3BP a\ensuremath−(0){a}_{\ensuremath{-}}^{(0)}a\ensuremath−(0)​. By employing van der Waals interactions for 23Na240K{^{23}\mathrm{Na}}_{2}^{40}\mathrm{K}23Na240​K, we attribute the vital role of aBB{a}_{\text{BB}}aBB​ in Efimov-unfavored systems to the large difference between the Efimov scaling parameters for two and three resonant interactions, s0{s}_{0}s0​ and s0∗{s}_{0}^{*}s0∗​. In particular, we account for the unusually large a\ensuremath−(0){a}_{\ensuremath{-}}^{(0)}a\ensuremath−(0)​ obtained in light-light-heavy systems with aBB>0{a}_{\text{BB}}>0aBB​>0 (e.g., 41K287Rb{^{41}\mathrm{K}}_{2}^{87}\mathrm{Rb}41K287​Rb), and show that the first Efimov resonance can still occur at an experimentally accessible value when aBB<0{a}_{\text{BB}}<0aBB​<0.
We experimentally and theoretically study the effect of the intraspecies scattering length onto the heteronuclear Efimov scenario, following up on our earlier observation of Efimov resonances in an ultracold Cs-Li mixture for negative [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] and positive Cs-Cs scattering length [Ulmanis et al., Phys. Rev. Lett. 117, 153201 (2016)]. Three theoretical models of increasing complexity are employed to quantify its influence on the scaling factor and the three-body parameter: a simple Born-Oppenheimer picture, a zero-range theory, and a spinless van der Waals model. These models are compared to Efimov resonances observed in an ultracold mixture of bosonic 133Cs^{133}\mathrm{Cs}133Cs and fermionic 6Li^{6}\mathrm{Li}6Li atoms close to two Cs-Li Feshbach resonances located at 843 G and 889 G, characterized by different sign and magnitude of the Cs-Cs interaction. By changing the sign and magnitude of the intraspecies scattering length different scaling behaviors of the three-body loss rate are identified, in qualitative agreement with theoretical predictions. The three-body loss rate is strongly influenced by the intraspecies scattering length.
The three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(1)}$ is crucial for understanding Efimov physics, and a universal 3BP has been shown in experiments and theory in ultracold homonuclear gases. The 3BP of heteronuclear systems has been predicted to possess much richer properties than its homonuclear counterparts due to the larger parameter space. In this work, we investigate the universal properties of ${a}_{\ensuremath{-}}^{(1)}$ for heavy-heavy-light (HHL) systems with a negative intraspecies scattering length aHH{a}_{HH}aHH​. We find that ${a}_{\ensuremath{-}}^{(1)}$ follows a universal behavior determined by the van der Waals (vdW) interaction and the mass ratio. A linear fit of ${a}_{\ensuremath{-}}^{(1)}$ for large ∣aHH∣|{a}_{HH}|∣aHH​∣ leads to a simple formula, which gives the general dependence of ${a}_{\ensuremath{-}}^{(1)}$ on the mass ratio and the vdW length rvdW{r}_{vdW}rvdW​. In a special case, when the two heavy atoms are in resonance, ${a}_{\ensuremath{-}}^{(1)}$ is approximately constant: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.
In Efimov physics, a three-body parameter (3BP), previously regarded as nonuniversal, uniquely defines bound and scattering properties of three particles. A universal 3BP, however, has been recently shown in experiments and theory in ultracold homonuclear gases. Our present study further predicts a universal 3BP for heteronuclear atomic systems near broad Feshbach resonances and provides physical interpretations for its origin. We show that for a system composed of two light and one heavy atom, the physical origin of the universal 3BP is similar to the homonuclear case, while for systems composed by one light and two heavy atoms, the universality of the 3BP is now mostly controlled by the heavy-heavy interatomic properties. This new universality is explained by the universal properties of the van der Waals interactions in a simple Born-Oppenheimer picture. Finally, we show the numerically determined 3BPs for some combinations of alkali atoms used in ultracold experiments.
We investigate theoretically and experimentally the heteronuclear Efimov scenario for a three-body system that consists of two bosons and one distinguishable particle with positive intraspecies scattering lengths. The three-body parameter at the three-body scattering threshold and the scaling factor between consecutive Efimov resonances are found to be controlled by the scattering length between the two bosons, approximately independent of short-range physics. We observe two excited-state Efimov resonances in the three-body recombination spectra of an ultracold mixture of fermionic ^{6}Li and bosonic ^{133}Cs atoms close to a Li-Cs Feshbach resonance, where the Cs-Cs interaction is positive. Deviation of the obtained scaling factor of 4.0(3) from the universal prediction of 4.9 and the absence of the ground state Efimov resonance shed new light on the interpretation of the universality and the discrete scaling behavior of heteronuclear Efimov physics.
We observe two consecutive heteronuclear Efimov resonances in an ultracold Li-Cs mixture by measuring three-body loss coefficients as a function of magnetic field near a Feshbach resonance. The first resonance is detected at a scattering length of a_((0))=-320(10)a_((0)), corresponding to ∼7(∼3) times the Li-Cs (Cs-Cs) van der Waals range. The second resonance appears at 5.8(1.0)a_((0)), close to the unitarity-limited regime at the sample temperature of 450 nK. Indication of a third resonance is found in the atom loss spectra. The scaling of the resonance positions is close to the predicted universal scaling value of 4.9 for zero temperature. Deviations from universality might be caused by finite-range and temperature effects, as well as magnetic field-dependent Cs-Cs interactions.
We have analyzed our recently measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet 4{}^{4}4He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides evidence for a universal 3BP outside the group of alkali-metal elements. In addition, we give examples of other atomic systems without Feshbach resonances but with a large scattering length that would be interesting to analyze once precise measurements of three-body loss are available.