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Tetramer Bound States in Heteronuclear Systems
Quantum Gases · Submitted 3 Mar 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller.
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The abstract, sentence by sentence
We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. | contribution 1.00 | 0.95 | 0.10 | asserted 0.96 |
| s1 | To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. | method 1.00 | 0.95 | 0.03 | asserted 0.98 |
| s2 | We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. | contribution 0.56 | 0.30 | 0.03 | asserted 0.92 |
| s3 | We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. | result 1.00 | 0.97 | 0.78 | asserted 1.00 |
| s4 | We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work. | contribution 0.48 | 0.60 | 0.05 | hedged possibility 0.87 |
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The paper
Original abstract
We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.
Human review
How the literature uses it
2 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 1 paper
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The short-range part has been used in many works to investigate the Efimov effect [ref] .
Efimov universality with Coulomb interaction · Interaction · 0.87
What it cites · 48 sentences without a confident label
Builds on 1 paper
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Our results confirm and extend the findings of Blume and Yan [ref] , who conducted calculations down to $M/m = 8/1$.
Generalized Efimov scenario for heavy-light mixtures · Summary and Outlook · 0.95
Uses the method or tool of 1 paper
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Using the effective field theory formalism for unequal mass particles with resonant interaction discussed in Ref. [ref] , we can calculate the coefficient $c_d$ up to one free parameter, namely the effective three-body parameter of the $HL$-$H$-$H$ system.
Three-body problem in heteronuclear mixtures with resonant interspecies interaction · Tetramer and Trimer Close to the Dimer Threshold · 0.99
Uses data or values from 3 papers
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Using the Born-Oppenheimer approximation, Wang et al. [ref] find somewhat tenuous evidence for an excited tetramer separated from the lower tetramer by a scaling factor of $14.3$ on the positive $a^*_HH$ side and $19.3$ on the negative side.
Efimov physics in heteronuclear four-body systems · The Scaling Factor · 0.82
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The scenario with the smallest scaling factor is $m/M →0$, in which case it is 1986.1 [ref] .
Universality in Few-body Systems with Large Scattering Length · The Scaling Factor · 0.81
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We also thank Doerte Blume for providing data from her figures from [ref] .
Generalized Efimov scenario for heavy-light mixtures · Summary and Outlook · 1.00
Compares with 3 papers
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In order to benchmark our method, we calculate the trimer and tetramer energies in the vicinity of the unitary limit and compare with the results for the mass ratio $M/m = 133/6$ obtained by Blume and Yan [ref] .
Generalized Efimov scenario for heavy-light mixtures · Benchmarking · 0.99
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The correlation between $c_d$ and $M/m$ does not appear to be linear, and the results from the four-body calculation could be reconciled only partly with effective three-body results in the framework of a STM-like equation derived from effective field theory [ref] .
Three-body problem in heteronuclear mixtures with resonant interspecies interaction · Summary and Outlook · 0.90
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We have compared our results to the results of [ref] and highlighted some important differences between the two approaches.
Efimov physics in heteronuclear four-body systems · Summary and Outlook · 1.00
Cites as background 8 papers
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A detailed study of the four-body states in a mixture of Cesium and Lithium atoms in the vicinity of the unitary limit and the three-atom threshold was recently performed by Blume and Yan [ref] .
Generalized Efimov scenario for heavy-light mixtures · Introduction · 0.83
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The signatures of Efimov physics in heteronuclear four-body systems were first investigated in Ref. [ref] .
Efimov physics in heteronuclear four-body systems · Introduction · 0.95
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An effective field theory for heteronuclear three-body systems consisting of an atom of mass $m_1$ and two identical bosonic atoms of mass $m_2$ was developed by Helfrich et al. [ref] .
Three-body problem in heteronuclear mixtures with resonant interspecies interaction · Effective field theory framework · 0.94
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