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The three-body parameter for Efimov states in lithium-6

Bo, Huang, Kenneth M., O'Hara, Rudolf Grimm, Jeremy M., Hutson, Dmitry S. Petrov

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

We present a state-of-the-art reanalysis of experimental results on Efimov resonances in the three-fermion system of $^6$Li. We discuss different definitions of the 3-body parameter (3BP) for Efimov states, and adopt a definition that excludes effects due to deviations from universal scaling for low-lying states. We develop a finite-temperature model for the case of three distinguishable fermions and apply it to the excited-state Efimov resonance to obtain the most accurate determination to date of the 3BP in an atomic three-body system. Our analysis of ground-state Efimov resonances in the same system yields values for the three-body parameter that are consistent with the excited-state result. Recent work has suggested that the reduced 3BP for atomic systems is a near-universal quantity, almost independent of the particular atom involved. However, the value of the 3BP obtained for $^6$Li is significantly ($\sim 20$%) different from that previously obtained from the excited-state resonance in Cs. The difference between these values poses a challenge for theory.

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We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic 6Li^{6}\mathrm{Li}6Li and bosonic 133Cs^{133}\mathrm{Cs}133Cs atoms close to a Feshbach resonance at 843 G, extending results reported previously [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120 nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\ensuremath{\eta}$ is found to be significantly larger than those for single-species systems.
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 consider a system of three 4{}^{4}4He atoms, which is so far the simplest realistic three-body system exhibiting the Efimov effect, in order to analyze deviations from the universal Efimov three-body spectrum. We first calculate the bound states using a realistic two-body potential, and then analyze how they can be reproduced by simple effective models beyond Efimov's universal theory. We find that the nonuniversal variations of the ground and first excited states can be well reproduced by models parametrized with only three quantities: the scattering length and effective range of the original potential, and a small three-body force. Furthermore, the three-body parameter, which fixes the origin of the infinite set of three-body levels, is found to be consistent with recent experimental observations in other atomic species.
We analyse the recent experiments investigating the low-energy physics of three lithium 6 atoms in three different internal states with resonant two-body scattering lengths. All observed features are qualitatively consistent with the expected Efimov effect, i.e. the effective universal three-body attraction that arises for large values of the scattering lengths. However, we find that a quantitative description at negative energy requires non-universal two- and three-body corrections due to presently unknown behaviour at short distance. An attempt to implement these corrections is made through energy-dependent parameters that are fitted to the experimental data.
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.