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arXiv:2102.12639 · Physical Review A

Three-body recombination near the d -wave resonance in ultracold Rb85−Rb87 mixtures

Cai-Yun Zhao, Hui-Li Han, Ting-Yun Shi

Published Jul 29, 2021• 0 citations
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Abstract

In this study, we investigate the three-body recombination (TBR) rates on both sides of the interspecies $d$-wave Feshbach resonance in the $^{85}\mathrm{Rb}$ -$^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}$ system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Our calculations are based on the Lennard-Jones model potential for the Rb-Rb interaction. Two different mechanisms of recombination-rate enhancement for positive and negative $^{85}\mathrm{Rb}$ -$^{87}\mathrm{Rb} d$-wave scattering lengths are analyzed. On the positive-scattering-length side, recombination-rate enhancement occurs due to the existence of three-body shape resonance, while on the negative-scattering-length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction has a significant role in determining the emergence of recombination-rate enhancements. Compared to the case in which the three pairwise interactions are in $d$-wave resonance, when the $^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}$ interaction is near the $d$-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the $^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}$ interaction is away from the $d$-wave resonance, the enhancement disappears on the side with negative interspecies scattering length.

DOI
10.1103/physreva.104.013317

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In this study, we investigate the three-body recombination (TBR) rates on both sides of the interspecies ddd-wave Feshbach resonance in the 85Rb^{85}\mathrm{Rb}85Rb -87Rb\ensuremath−87Rb^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}87Rb\ensuremath−87Rb system using the RRR-matrix propagation method in the hyperspherical coordinate frame. Our calculations are based on the Lennard-Jones model potential for the Rb-Rb interaction. Two different mechanisms of recombination-rate enhancement for positive and negative 85Rb^{85}\mathrm{Rb}85Rb -87Rbd^{87}\mathrm{Rb} d87Rbd-wave scattering lengths are analyzed. On the positive-scattering-length side, recombination-rate enhancement occurs due to the existence of three-body shape resonance, while on the negative-scattering-length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction has a significant role in determining the emergence of recombination-rate enhancements. Compared to the case in which the three pairwise interactions are in ddd-wave resonance, when the 87Rb\ensuremath−87Rb^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}87Rb\ensuremath−87Rb interaction is near the ddd-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the 87Rb\ensuremath−87Rb^{87}\mathrm{Rb}\ensuremath{-}^{87}\mathrm{Rb}87Rb\ensuremath−87Rb interaction is away from the ddd-wave resonance, the enhancement disappears on the side with negative interspecies scattering length.
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Abstract The study of Efimov features and their relationships in 40K-87Rb Mixtures has generated extensive discussion, yet the discrepancy between Efimov universality predictions based on the zero-range approximation and experimental observations remains unresolved. In this study, we investigate the three-body collision properties with J = 0 symmetry for a 87Rb-87Rb-40K system on both sides of Rb-K scattering length to understand the mechanisms underlying this discrepancy. Our approach employs the R-matrix propagation method within a hyperspherical coordinate frame, utilizing the Lennard-Jones model potential to describe atom interactions. We predicts the existence of three-body shape resonances at large negative Rb-K scattering lengths, which leads to the enhancement of three-body recombination rates. On the positive Rb-K scattering length side, we find an Efimov recombination minimum beyond the range of previous measurements. These Efimov features, combined with experimental observations of the atom-dimer Efimov resonance, offer an opportunity to test the universality of Efimov features. Our study demonstrates the influence of finite-range effects and non-resonant intraspecies scattering length in 40K-87Rb mixtures, providing valuable insights into the universal relations between Efimov features in heteronuclear systems.
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For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body sss-wave dimer, the Efimov effect takes place leading to the formation of an infinite number of three-body (Efimov) states. The lowest Efimov state crosses the three-body break-up threshold when the sss-wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$, rvdW{r}_{\mathrm{vdW}}rvdW​ being the van der Waals length. This article focuses on a generalized version of this Efimov scenario, where two of the atoms are about to form a two-body ddd-wave dimer, resulting in strong ddd-wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the ddd-wave dimer is always formed when $a\ensuremath{\approx}0.956{r}_{\mathrm{vdW}}$. Here we find that a single universal three-body state associated with the ddd-wave dimer is also formed near the three-body breakup threshold at $a\ensuremath{\approx}1.09{r}_{\mathrm{vdW}}$, or alternatively a2=0.902rvdW{a}_{2}=0.902{r}_{\mathrm{vdW}}a2​=0.902rvdW​, where a2{a}_{2}a2​ is the two-body ddd-wave scattering length. The signature of such a universal three-body state is signaled experimentally by an enhancement of the three-body recombination rate. The three-body effective potential curves that are crucial for understanding the recombination dynamics are also calculated and analyzed. An improved method to calculate the couplings, effective potential curves, and recombination rate coefficients is presented.
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We study collisional heating in a cold ^{7}Li-^{87}Rb mixture near a broad Feshbach resonance at 661 G. At the high field slope of the resonance, we find an enhanced three-body recombination rate that we interpret as a heteronuclear Efimov resonance. With improved Feshbach spectroscopy of two further resonances, a model for the molecular potentials has been developed that now consistently explains all known Feshbach resonances of the various Li-Rb isotope mixtures. The model is used to determine the scattering length of the observed Efimov state. Its value of -1870a_{0} Bohr radii supports the currently discussed assumption of universality of the three-body parameter also in heteronuclear mixtures.