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 study the Efimov states in highly mass-imbalanced three-body systems composed of two identical heavy atoms and one light atom, focusing on the Er-Er-Li and Dy-Dy-Li cold-atom mixtures with strong dipole-dipole interactions between the heavy atoms. By solving the Born-Oppenheimer equation for varying s -wave scattering lengths between the heavy and light atoms, we demonstrate for both bosonic and fermionic systems that the Efimov spectra and hence the three-body parameters are universal even with the dipole interaction comparable in strength to the van der Waals interaction. While the bosonic systems exhibit Efimov states only in the M z = 0 channel, the fermionic systems show a characteristic doublet of the Efimov states in the M z = 0 and M z = ± 1 channels due to the interplay of finite angular momentum and the anisotropy of the dipole interaction. Both numerical results and analytical formulas obtained with the first-order perturbation show that the ratio of the three-body parameters between these two fermionic channels exhibits universality, particularly well in the limit of large mass imbalance. Leveraging this universality, we provide quantitative predictions for the values and ratios of the three-body parameters for experimentally relevant Er-Li and Dy-Li isotopes.
This thesis investigates universal and non-universal aspects of few-body physics in a mass-imbalanced mixture of ultracold bosonic
133Cs and fermionic
6Li atoms. For this purpose an experimental apparatus for the creation of quantum degenerate gases has been constructed. Using radio-frequency association of weakly-bound LiCs molecules and additional atom-loss spectroscopy we determine the two-body interaction properties between Li and Cs atoms at low collision energies. The analysis with a coupled-channels calculation yields precise singlet and triplet electronic ground state molecular potential curves, from which scattering lengths and positions of Fano-Feshbach resonances are extracted. These results represent almost a tenfold improvement over the previous determination, and are used to study few-body recombination processes and, for the first time, their dependence on the interaction strength between the heavy atoms close to two broad scattering resonances at various temperatures. Measurements of three-body loss rates reveal two series of three and two consecutive LiCs
2 Efimov resonances that demonstrate the universal scaling factor 4.9 between the first and second excited state resonances. The ground state resonance deviates from the discrete scaling law. By the use of hyperspherical formalism with either pairwise zero-range or Lennard-Jones model potentials we identify the van der Waals interaction between Cs atoms as a significant source of these modifications.
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.
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.
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.
For a system of three identical bosons interacting via short-range forces, when two of the atoms are about to form a two-body
s-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
s-wave two-body scattering length is $a\ensuremath{\approx}\ensuremath{-}9.73{r}_{\mathrm{vdW}}$,
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
d-wave dimer, resulting in strong
d-wave interactions. In his paper [Phys. Rev. A 62, 050702(R) (2000)], Bo Gao predicted that for broad resonances the
d-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
d-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, where
a2 is the two-body
d-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.