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arXiv:1609.02857 · Physical Review A

Efimov–van der Waals universality for ultracold atoms with positive scattering lengths

P. M. A. Mestrom, Jia Wang, Chris H. Greene, José Paulo D'Incao

Published Mar 30, 2017• 34 citations
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Abstract

The universality of the three-body parameter in ultracold atomic systems is studied with a single-channel model when the scattering length is positive, where the parameter is found to be constrained by a variational principle and can be strongly affected by $d$-wave interactions.

DOI
10.1103/physreva.95.032707

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The universality of the three-body parameter in ultracold atomic systems is studied with a single-channel model when the scattering length is positive, where the parameter is found to be constrained by a variational principle and can be strongly affected by ddd-wave interactions.
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.
We study three-body systems in a mass-imbalanced, two-component, cold-atom mixture, and we investigate the three-body parameter of their Efimov states for both bosonic and fermionic systems, with a major focus on the Er-Er-Li Efimov states. For a system interacting solely via van der Waals interactions, the van der Waals universality of the three-body parameter is analytically derived using the quantum defect theory. With the addition of a perturbative dipole interaction between the heavy atoms, the three-body parameters of the bosonic and fermionic Efimov states are found to behave differently. When the dipole interaction is as strong as the van der Waals interaction, corresponding to realistic Er-Er-Li Efimov states, we show that the van der Waals universality persists once the effects of the nonperturbative dipole interaction are into the s -wave and p -wave scattering parameters between the heavy atoms. For a dipole interaction much stronger than the van der Waals interaction, we find that the universality of the Efimov states can be alternatively characterized by a quasi-one-dimensional scattering parameter due to a strong anisotropic deformation of the Efimov wave functions. Our work thus clarifies the interplay of isotropic and anisotropic forces in the universality of the Efimov states. Based on the renormalized van der Waals universality, the three-body parameter is estimated for specific isotopes of Er-Li cold-atom mixtures. Published by the American Physical Society 2024
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.
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: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.
We address the microscopic origin of the universal three-body parameter that fixes the spectrum of three-atom systems in the Efimov regime. We identify it with the van der Waals two-body correlation, which causes the three-atom system to deform when the three atoms come within the distance of the van der Waals length, effectively preventing them from coming closer due to the kinetic-energy cost associated with three-body deformation. This deformation mechanism explains the universal ratio of the scattering length at the triatomic resonance to the van der Waals length observed in several experiments and confirmed by numerical calculations.