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arXiv:2009.13221 · Brazilian Journal of Physics

Fermions Meet Two Bosons—the Heteronuclear Efimov Effect Revisited

Binh Tran, Michael Rautenberg, Manuel Gerken, Eleonora Lippi, Bing Zhu, Juris Ulmanis, Moritz Drescher, Manfred Salmhofer B, Tilman Enss, Matthias Weidemüller

Published Nov 9, 2020• 5 citations
arXivHTMLPDF

Abstract

Abstract In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi mixture with large mass difference in the Born-Oppenheimer picture. As a specific example, we consider the combination of bosonic 133Cs and fermionic 6Li. In a system consisting of two heavy bosons and one light fermion, the fermion-mediated potential between the two heavy bosons gives rise to an infinite series of three-body bound states. The intraspecies scattering length determines the three-body parameter and the scaling factor between consecutive Efimov states. In a second scenario, we replace the single fermion by an entire Fermi Sea at zero temperature. The emerging interaction potential for the two bosons exhibits long-range oscillations leading to a weakening of the binding and a breakup of the infinite series of Efimov states. In this scenario, the binding energies follow a modified Efimov scaling law incorporating the Fermi momentum. The scaling factor between deeply bound states is governed by the intraspecies interaction, analogous to the Efimov states in vacuum.

DOI
10.1007/s13538-020-00811-5

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•Jan 1, 2015•2 citations
Abstract In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi mixture with large mass difference in the Born-Oppenheimer picture. As a specific example, we consider the combination of bosonic 133Cs and fermionic 6Li. In a system consisting of two heavy bosons and one light fermion, the fermion-mediated potential between the two heavy bosons gives rise to an infinite series of three-body bound states. The intraspecies scattering length determines the three-body parameter and the scaling factor between consecutive Efimov states. In a second scenario, we replace the single fermion by an entire Fermi Sea at zero temperature. The emerging interaction potential for the two bosons exhibits long-range oscillations leading to a weakening of the binding and a breakup of the infinite series of Efimov states. In this scenario, the binding energies follow a modified Efimov scaling law incorporating the Fermi momentum. The scaling factor between deeply bound states is governed by the intraspecies interaction, analogous to the Efimov states in vacuum.
Motivated by recent experiments on $^{6}\mathrm{Li}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ atomic mixtures with high mass imbalance, we study the Efimov correlation in an atomic system of two heavy bosons (133Cs^{133}\mathrm{Cs}133Cs) immersed in a bath of light fermions (6Li^{6}\mathrm{Li}6Li). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions (kF{k}_{F}kF​) and the boson-fermion scattering length as(<0){a}_{s}(<0)as​(<0), where the presence of an underlying Fermi sea plays distinct roles in the Efimov-type binding of bosons. Namely, in the regime ${k}_{F}|{a}_{s}|\ensuremath{\lesssim}1$ (${k}_{F}|{a}_{s}|\ensuremath{\gtrsim}1$), the Fermi sea induces an attractive (repulsive) effective interaction between bosons and thus favors (disfavors) the formation of a bound state, which can be seen as an Efimov trimer dressed by a fermion cloud. Interestingly, this implies nonmonotonic behavior of these bound states as increasing the fermion density (or kF{k}_{F}kF​). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale (kF{k}_{F}kF​) brought on by the Fermi sea. These results can be directly tested in Li-Cs cold-atom experiments by measuring the modified bound-state spectrum and the shifted Efimov resonance, which manifest an emergent nontrivial Efimov correlation in a fermionic many-body environment.
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.
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.
Abstract We study a three-body system, formed by two identical heavy bosons and a light particle, in the Born–Oppenheimer approximation for an arbitrary dimension D . We restrict D to the interval 2 < D < 4, and derive the heavy–heavy D -dimensional effective potential proportional to 1/ R 2 ( R is the relative distance between the heavy particles), which is responsible for the Efimov effect. We found that the Efimov states disappear once the critical strength of the heavy–heavy effective potential 1/ R 2 approaches the limit − ( D − 2 ) 2 / 4 . We obtained the scaling function for the 133 Cs– 133 Cs– 6 Li system as the limit cycle of the correlation between the energies of two consecutive Efimov states as a function of D and the heavy-light binding energy E D 2 . In addition, we found that the energy of the ( N + 1)th excited state reaches the two-body continuum independently of the dimension D when E 2 D / E 3 ( N ) = 0.89 , where E 3 ( N ) is the N th excited three-body binding energy.
The possibility of a zero-energy Efimov effect is investigated in a model consisting of three identical heavy particles and a lighter one, when the light-heavy interaction leads to a zero-energy bound state for the two-heavy---one-light subsystem. The model is solved in the Born-Oppenheimer approximation with the light-heavy interaction taken to be a separable sss-wave potential of Yamaguchi form. The heavy-heavy interaction is short range and, if attractive, is to be taken weak enough to support no two- or three-heavy-particle bound states. The relevant parameter is the potential strength $\ensuremath{\lambda}$ of the light-heavy interaction which for $\ensuremath{\lambda}={\ensuremath{\lambda}}_{c}$ supports a single zero-energy light-heavy bound state. If the first zero-energy bound state of the two-heavy---one-light subsystem occurs for $\ensuremath{\lambda}={\ensuremath{\lambda}}^{\ensuremath{'}}$ such that $|{\ensuremath{\lambda}}^{\ensuremath{'}}|<|{\ensuremath{\lambda}}_{c}|$, there are no Efimov four-body bound states. On the contrary, if the chosen heavy-heavy potential is repulsive enough to prevent the existence of three-body bound states for $|\ensuremath{\lambda}|<|{\ensuremath{\lambda}}_{c}|$, then as $\ensuremath{\lambda}\ensuremath{\rightarrow}{\ensuremath{\lambda}}_{c}$ a few four-body Efimov states may emerge but their number remains finite. These states disappear for $|\ensuremath{\lambda}|\ensuremath{\gtrsim}|{\ensuremath{\lambda}}_{c}|$ as the three-body cut overrides them.
This thesis investigates universal and non-universal aspects of few-body physics in a mass-imbalanced mixture of ultracold bosonic 133^{133}133Cs and fermionic 6^66Li 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 LiCs2_22​ 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.