Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2010.06105 · Physical Review A

Effective-field-theory analysis of boson-trimer bond lengths to next-to-leading order

Julia Ya Qin, Jared Vanasse

Published Feb 25, 2021• 2 citations
arXivHTMLPDF

Abstract

Cold helium atoms are a unique system in which a single excited three-body Efimov bound state occurs, naturally, without the need for an external magnetic field. While three-body bound-state energies of cold helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between helium atoms leads to a helium-helium (dimer) scattering length $a$ much larger than the helium-helium effective range of interaction $r$. This feature is exploited in a theory that systematically expands observables in powers of $r/a$, known as short-range effective field theory (SREFT), which has been used successfully to investigate properties of cold-atom systems. Using SREFT, we investigate the average bond length of atoms in the three-body ground state and excited Efimov bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the $^{4}\mathrm{He}$ trimer ground state is 8.35(33) $\AA{}$ (10.29(2) $\AA{}$) and the average bond length of the excited $^{4}\mathrm{He}$ trimer Efimov bound state is 103(4) $\AA{}$ (105.3(2) $\AA{}$).

DOI
10.1103/physreva.103.023333

Related papers

Three- and four-boson systems expanded around the unitarity limit: Application to $^4$He molecules

Feng Wu, Xincheng Lin, U. van Kolck +1 more

The three- and four-boson systems with a large scattering length and a short effective range in the two-body sector are studied in the framework of Short-Range Effective Field Theory (SREFT). The starting point (leading order) of the EFT is taken to be the universal unitarity limit, where the two-body sector is parameter-free and only one three-body parameter enters. In this limit, physical systems manifest discrete scale invariance. Deviations from universality arising from finite scattering-length and effective-range corrections, as well as a four-body force required by renormalization, are included perturbatively at next-to-leading order. The three-body ground state and its associated four-body ground and first-excited states are studied using the Faddeev-Yakubovsky (FY) formalism and a complementary diagrammatic approach. By employing techniques to remove contributions from deep trimers in tetramer calculations, we extend our analysis to larger cutoffs than previously accessible within the FY approach to SREFT. Our results for binding energies and radii of $^4$He three- and four-atom systems converge well to results obtained with sophisticated phenomenological potentials. These successes suggest that the physics of $^4$He atomic clusters is governed by only small deviations from discrete scale invariance.

arXiv:2606.00854•May 30, 2026•0 citations

Universality and Beyond: Effective Field Theory for Three-Body Physics in Cold Atoms and Halo Nuclei

Chen Ji

Systems, such as cold atoms and light halo nuclei, share universal features at low energies, for which details of inter-particle interactions are not essential.We study threebody physics in such systems in an effective-field-theory (EFT) framework.We will discuss universal behavior in three-body systems and higher-order effectiverange corrections beyond universality.We study effective-range effects perturbatively up to the next-to-next-to-leading order (N 2 LO) for the case of three identical bosons.We apply this analysis to recombination features in cold atomic gases and properties of Helium trimers.Effective range corrections also play an important role in the EFT study of fewnucleon systems and halo nuclei.The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha core.This bound state is generated by the resonant neutron-neutron and neutron-alpha interactions.The latter is dominated by a shallow p-wave resonance.We present a calculation of Helium-6 in an EFT approach appropriate for halo systems.

•Jan 1, 2012•1 citation

Universality in strongly interacting bosonic clusters

L. Madeira, F. Pederiva, U. van Kolck

We develop an effective field theory (EFT) for strongly interacting bosonic clusters, using $^4$He as a paradigmatic example of universality in systems with large scattering length. At leading order (LO), two- and three-body zero-range interactions are entirely determined by the dimer and trimer ground-state energies. We show that ground-state energies for up to $N=15$ particles converge to cutoff-independent limits with extrapolation coefficients of natural size. At next-to-leading order (NLO), corrections stemming from the two-body interaction range and a four-body force, calibrated to the tetramer ground-state energy, reduce cutoff sensitivity. Close agreement with results from a realistic potential is found at LO and improved at NLO, demonstrating systematic convergence with few parameters at each order. The resulting EFT is directly applicable to larger clusters and bulk helium.

arXiv:2606.27823•Jun 26, 2026•0 citations

Scaling limit of weakly bound triatomic states

T. Frederico, Lauro Tomio, A. Delfino +1 more

The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of $\mathrm{the}{ }^{87}\mathrm{Rb}$ dimer to estimate the critical value of the ground-state energy of the corresponding trimer $(>~1.5 \mathrm{mK})$, in order to allow for one Efimov state above the ground state.

Physical Review A•Jul 1, 1999•71 citations

Four-body systems at large cutoffs in effective field theory

Xincheng Lin

Four-body systems are studied using an effective-field theory with two- and three-body contact interactions. A method to systematically address deep trimers (three-body bound states that are more tightly bound than four-body bound or resonant states) in four-body calculations is developed using a diagrammatic approach. Previous calculations were limited by the existence of deep trimers, which this work overcomes. For cold $^{4}\mathrm{He}$ atoms, binding energies of 526.1(5) and 128.517(1) mK are obtained at leading order for the tetramer ground and excited states, respectively, where errors come from the truncation of three-body partial waves. Tetramer binding energies and decay widths are also computed approaching the unitary limit. In the unitary limit, there are two tetramers associated with each trimer of binding energy ${B}_{3}^{(0)}$. The binding energy and decay width for the associated tetramer ground state are ${E}_{4}^{(0)}=4.60(1){B}_{3}^{(0)}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}^{(0)}/2=0.0160(1){B}_{3}^{(0)}$, respectively, and for the associated tetramer excited state, ${E}_{4}^{(1)}=1.0022(3){B}_{3}^{(0)}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}^{(1)}/2=2.57(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{B}_{3}^{(0)}$, respectively. This calculation is a gateway to higher-order and/or more-body calculations in nuclear and atomic systems.

arXiv:2304.06172•Physical Review C•Feb 20, 2024•3 citations

Few-boson system with a single impurity: Universal bound states tied to Efimov trimers

D. Blume

Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound $N$-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass $m$ that interact with a single distinguishable impurity particle (denoted by ``X'') of mass $M$. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to $m/M$, and the two-body $s$-wave scattering length ${a}_{\text{BX}}$ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.

arXiv:1901.03542•Physical Review A•Jan 16, 2019•12 citations
Cold helium atoms are a unique system in which a single excited three-body Efimov bound state occurs, naturally, without the need for an external magnetic field. While three-body bound-state energies of cold helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between helium atoms leads to a helium-helium (dimer) scattering length aaa much larger than the helium-helium effective range of interaction rrr. This feature is exploited in a theory that systematically expands observables in powers of r/ar/ar/a, known as short-range effective field theory (SREFT), which has been used successfully to investigate properties of cold-atom systems. Using SREFT, we investigate the average bond length of atoms in the three-body ground state and excited Efimov bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the 4He^{4}\mathrm{He}4He trimer ground state is 8.35(33) A˚\AA{}A˚ (10.29(2) A˚\AA{}A˚) and the average bond length of the excited 4He^{4}\mathrm{He}4He trimer Efimov bound state is 103(4) A˚\AA{}A˚ (105.3(2) A˚\AA{}A˚).
Three- and four-boson systems expanded around the unitarity limit: Application to 4^44He molecules
The three- and four-boson systems with a large scattering length and a short effective range in the two-body sector are studied in the framework of Short-Range Effective Field Theory (SREFT). The starting point (leading order) of the EFT is taken to be the universal unitarity limit, where the two-body sector is parameter-free and only one three-body parameter enters. In this limit, physical systems manifest discrete scale invariance. Deviations from universality arising from finite scattering-length and effective-range corrections, as well as a four-body force required by renormalization, are included perturbatively at next-to-leading order. The three-body ground state and its associated four-body ground and first-excited states are studied using the Faddeev-Yakubovsky (FY) formalism and a complementary diagrammatic approach. By employing techniques to remove contributions from deep trimers in tetramer calculations, we extend our analysis to larger cutoffs than previously accessible within the FY approach to SREFT. Our results for binding energies and radii of 4^44He three- and four-atom systems converge well to results obtained with sophisticated phenomenological potentials. These successes suggest that the physics of 4^44He atomic clusters is governed by only small deviations from discrete scale invariance.
Systems, such as cold atoms and light halo nuclei, share universal features at low energies, for which details of inter-particle interactions are not essential.We study threebody physics in such systems in an effective-field-theory (EFT) framework.We will discuss universal behavior in three-body systems and higher-order effectiverange corrections beyond universality.We study effective-range effects perturbatively up to the next-to-next-to-leading order (N 2 LO) for the case of three identical bosons.We apply this analysis to recombination features in cold atomic gases and properties of Helium trimers.Effective range corrections also play an important role in the EFT study of fewnucleon systems and halo nuclei.The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha core.This bound state is generated by the resonant neutron-neutron and neutron-alpha interactions.The latter is dominated by a shallow p-wave resonance.We present a calculation of Helium-6 in an EFT approach appropriate for halo systems.
We develop an effective field theory (EFT) for strongly interacting bosonic clusters, using 4^44He as a paradigmatic example of universality in systems with large scattering length. At leading order (LO), two- and three-body zero-range interactions are entirely determined by the dimer and trimer ground-state energies. We show that ground-state energies for up to N=15N=15N=15 particles converge to cutoff-independent limits with extrapolation coefficients of natural size. At next-to-leading order (NLO), corrections stemming from the two-body interaction range and a four-body force, calibrated to the tetramer ground-state energy, reduce cutoff sensitivity. Close agreement with results from a realistic potential is found at LO and improved at NLO, demonstrating systematic convergence with few parameters at each order. The resulting EFT is directly applicable to larger clusters and bulk helium.
The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of the87Rb\mathrm{the}{ }^{87}\mathrm{Rb}the87Rb dimer to estimate the critical value of the ground-state energy of the corresponding trimer (> 1.5mK)(>~1.5 \mathrm{mK})(> 1.5mK), in order to allow for one Efimov state above the ground state.
Four-body systems are studied using an effective-field theory with two- and three-body contact interactions. A method to systematically address deep trimers (three-body bound states that are more tightly bound than four-body bound or resonant states) in four-body calculations is developed using a diagrammatic approach. Previous calculations were limited by the existence of deep trimers, which this work overcomes. For cold 4He^{4}\mathrm{He}4He atoms, binding energies of 526.1(5) and 128.517(1) mK are obtained at leading order for the tetramer ground and excited states, respectively, where errors come from the truncation of three-body partial waves. Tetramer binding energies and decay widths are also computed approaching the unitary limit. In the unitary limit, there are two tetramers associated with each trimer of binding energy B3(0){B}_{3}^{(0)}B3(0)​. The binding energy and decay width for the associated tetramer ground state are E4(0)=4.60(1)B3(0){E}_{4}^{(0)}=4.60(1){B}_{3}^{(0)}E4(0)​=4.60(1)B3(0)​ and ${\mathrm{\ensuremath{\Gamma}}}_{4}^{(0)}/2=0.0160(1){B}_{3}^{(0)}$, respectively, and for the associated tetramer excited state, E4(1)=1.0022(3)B3(0){E}_{4}^{(1)}=1.0022(3){B}_{3}^{(0)}E4(1)​=1.0022(3)B3(0)​ and ${\mathrm{\ensuremath{\Gamma}}}_{4}^{(1)}/2=2.57(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{B}_{3}^{(0)}$, respectively. This calculation is a gateway to higher-order and/or more-body calculations in nuclear and atomic systems.
Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound NNN-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass mmm that interact with a single distinguishable impurity particle (denoted by ``X'') of mass MMM. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to m/Mm/Mm/M, and the two-body sss-wave scattering length aBX{a}_{\text{BX}}aBX​ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.