Association of Efimov Trimers from a Three-Atom Continuum

Machtey, Olga; Shotan, Zav; Gross, Noam; Khaykovich, Lev

doi:10.1103/physrevlett.108.210406

Cited by 78 publications

(118 citation statements)

References 37 publications

(137 reference statements)

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“…The feature a * 2 is nominally located at the atom-dimer resonance where the energy of the second Efimov trimer merges with the atom-dimer continuum. Relatively sharp peaks in L 3 , located near the expected atom-dimer resonance, were previously reported for 39 K [41], and 7 Li [5,42]. Since a large dimer fraction is unexpected, a model was developed to explain the presence of enhanced loss even without a large population of dimers [41].…”

Section: (D)mentioning

confidence: 99%

Finite-range corrections near a Feshbach resonance and their role in the Efimov effect

2013

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We have measured the binding energy of 7 Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683]. We find the measured locations of the three-and four-body Efimov features to be consistent with universal theory at the 20%-30% level. Efimov showed more than 40 years ago that three particles interacting via resonant two-body interactions could form an infinite series of three-body bound states as the two-body s-wave scattering length a was varied [1]. In the limit of zero-range interactions, the ratios of scattering lengths corresponding to the appearance of each bound state were predicted to be a universal constant, equal to approximately 22.7. The only definitive observations of the Efimov effect have been in ultracold atoms, where the ability to tune a via a Feshbach resonance [2,3] has proven to be essential. Since the first evidence for Efimov trimers was obtained in ultracold Cs [4], experiments have revealed both three-and four-body Efimov states in several atomic species. Although the Efimov effect has now been confirmed, several open questions remain, including a full understanding of the role of nonuniversal finite-range effects. Accurate comparisons with theory require that these nonuniversal contributions be quantitatively determined and incorporated.We previously characterized the F = 1,m F = 1 Feshbach resonance in 7 Li, which is located at approximately 738 G, by extracting a from the measured size of trapped Bose-Einstein condensates (BEC) assuming a mean-field Thomas-Fermi density distribution [5,6]. These data were fit to obtain a(B), the function giving a versus magnetic field, which was used to assign values of a to Efimov features observed in the rate of inelastic three-and four-body loss of trapped atoms [5]. More recently, two groups have characterized the same Feshbach resonance by directly measuring the binding energy, E b , of the weakly bound dimers on the a > 0 side of the Feshbach resonance [7][8][9]. These measurements disagree with our previous measurements based on BEC size. The disagreement in the parameters characterizing the Feshbach parameters is sufficiently large to affect the comparison of the measured Efimov features with universal theory.In this paper, we report measurements of E b , which we fit to obtain a(B). The measurement of E b has fewer systematic uncertainties than the BEC size measurement, which is affected at large scattering length by beyond meanfield effects and by anharmonic contributions to the trapping potential. The extraction of a from E b can therefore be more accurate, and unlike the condensate size measurement, E b is r...

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Section: (D)mentioning

confidence: 99%

Finite-range corrections near a Feshbach resonance and their role in the Efimov effect

2013

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“…[55], as well as the results for 7 Li from Ref. [56], were obtained using a Feshbach resonance that is not well separated from another nearby resonance, possibly affecting the observed value for a * ,1 . Most of the results marked in Table III by " † " present the largest variations compared with the total averaged result for a * ,1 (≈ 6.63r vdW ).…”

Section: Brief Theoretical Backgroundmentioning

confidence: 99%

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

et al. 2017

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We study the universality of the three-body parameters for systems relevant for ultracold quantum gases with positive s-wave two-body scattering lengths. Our results account for finite-range effects and their universality is tested by changing the number of deeply bound diatomic states supported by our interaction model. We find that the physics controlling the values of the three-body parameters associated with the ground and excited Efimov states is constrained by a variational principle and can be strongly affected by d-wave interactions that prevent both trimer states from merging into the atom-dimer continuum. Our results enable comparisons to current experimental data and they suggest tests of universality for atomic systems with positive scattering lengths.

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“…It cannot explain the narrow loss features near atom-dimer resonances that have been observed in thermal gases of 39 K atoms [13] and 7 Li atoms [14,15]. These loss features were observed at relatively small scattering lengths, so they could be associated with nonuniversal effects.…”

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confidence: 71%

“…They all appear in systems that were believed to consist of atoms only and no dimers. Narrow enhancements of the loss rate near atom-dimer resonances have been observed in both a Bose-Einstein condensate (BEC) and a thermal gas of 39 K atoms [13] and in both a BEC and a thermal gas of 7 Li atoms [14,15]. In a BEC of 7 Li atoms, narrow enhancements of the loss rate have also been observed at positive values of a near two-dimer resonances [14], at which universal tetramers cross the dimer-dimer threshold and become unbound.…”

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confidence: 97%

Atom Loss Resonances in a Bose-Einstein Condensate

Langmack¹,

Smith²,

Braaten³

2013

Phys. Rev. Lett.

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Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near twodimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions. Nonrelativistic particles whose scattering lengths are large compared to the range of their interactions exhibit universal low-energy behavior [1]. The universal few-body phenomena can include a spectrum of looselybound molecules as well as reaction rates of the particles and molecules. In some cases, including identical bosons, the universal behavior is governed by discrete scale invariance. The universal molecules then include sequences of 3-particle clusters (Efimov trimers) [2, 3], 4-particle clusters (universal tetramers) [4][5][6], and clusters with even more particles [7] . The universal reaction rates exhibit intricate resonance and interference features [1].The technology for trapping atoms and cooling them to extremely low temperatures has made the universal low-energy region experimentally accessible. The use of Feshbach resonances to control the scattering length a experimentally makes ultracold atoms an ideal laboratory for universal physics. One particularly dramatic probe of universality is the loss rate of atoms from a trapping potential. Resonance and interference effects in few-body reaction rates can produce local maxima and minima in the loss rate as a function of a. The most dramatic signature for a universal N -atom cluster with N ≥ 3 is the resonant enhancement of the N -atom inelastic collision rate at a negative a where the cluster crosses the N -atom threshold and becomes unbound. We refer to such a scattering length as an N -atom resonance. The first observations of an Efimov trimer [8] and a universal tetramer [9] and the first evidence for a universal 5-atom cluster [10] were all obtained using a thermal gas of 133 Cs atoms by tuning a to 3-atom, 4-atom, and 5-atom resonances, respectively. An Efimov trimer has also been observed as an enhancement in the loss rate in a mixture of 133 Cs atoms and dimers [11] at a positive scattering length a * where an Efimov trimer crosses the atom-dimer threshold and becomes unbound. We refer to a * as an atom-dimer resonance. Another dramatic loss feature at positive a is an interfere...

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Association of Efimov Trimers from a Three-Atom Continuum

Cited by 78 publications

References 37 publications

Finite-range corrections near a Feshbach resonance and their role in the Efimov effect

Finite-range corrections near a Feshbach resonance and their role in the Efimov effect

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

Atom Loss Resonances in a Bose-Einstein Condensate

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