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arXiv:1903.09565 · Physical Review A

Universal three-body parameter of heavy-heavy-light systems with a negative intraspecies scattering length

Caiyun Zhao, Hui-Li Han, M.-S. Wu, Ting-Yun Shi

Published Nov 12, 2019• 6 citations
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Abstract

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 ${a}_{HH}$. 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 $|{a}_{HH}|$ leads to a simple formula, which gives the general dependence of ${a}_{\ensuremath{-}}^{(1)}$ on the mass ratio and the vdW length ${r}_{vdW}$. In a special case, when the two heavy atoms are in resonance, ${a}_{\ensuremath{-}}^{(1)}$ is approximately constant: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.

DOI
10.1103/physreva.100.052702

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The three-body parameter (3BP) a\ensuremath−(1){a}_{\ensuremath{-}}^{(1)}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){a}_{\ensuremath{-}}^{(1)}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){a}_{\ensuremath{-}}^{(1)}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){a}_{\ensuremath{-}}^{(1)}a\ensuremath−(1)​ for large ∣aHH∣|{a}_{HH}|∣aHH​∣ leads to a simple formula, which gives the general dependence of a\ensuremath−(1){a}_{\ensuremath{-}}^{(1)}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){a}_{\ensuremath{-}}^{(1)}a\ensuremath−(1)​ is approximately constant: a\ensuremath−(1)=\ensuremath−(6.3\ifmmode±\else\textpm\fi0.6)rvdW,HL{a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}a\ensuremath−(1)​=\ensuremath−(6.3\ifmmode±\else\textpm\fi0.6)rvdW,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.
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 ${a}_{\ensuremath{-}}^{(n)}$ 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 aBB{a}_{\text{BB}}aBB​ govern the Efimov spectrum and set the resulting 3BP ${a}_{\ensuremath{-}}^{(0)}$. 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 ${a}_{\ensuremath{-}}^{(0)}$ 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.
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.
Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected nonuniversal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of ^{39}K-^{87}Rb and ^{41}K-^{87}Rb and do not observe any signatures of Efimov resonances for accessible scattering lengths in either mixture. Our results show good agreement with our theoretical model for the scattering dependent three-body recombination coefficient and reestablish universality across isotopic mixtures.
We use an effective-field-theory framework to analyze the Efimov effect in heteronuclear three-body systems consisting of two species of atoms with a large interspecies scattering length. In the leading-order description of this theory, various three-body observables in heteronuclear mixtures can be universally parametrized by one three-body parameter. We present the next-to-leading corrections, which include the effects of the finite interspecies effective range and the finite intraspecies scattering length, to various three-body observables. We show that only one additional three-body parameter is required to render the theory predictive at this order. By including the effective range and intraspecies scattering length corrections, we derive a set of universal relations that connect the different Efimov features near the interspecies Feshbach resonance. Furthermore, we show that these relations can be interpreted in terms of the running of the three-body counterterms that naturally emerge from proper renormalization. Finally, we make predictions for recombination observables of a number of atomic systems that are of experimental interest.