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:1407.7664 · Physical Review A

Super Efimov effect for mass-imbalanced systems

Sergej Moroz, Yusuke Nishida

Published Dec 22, 2014• 23 citations
arXivHTMLPDF

Abstract

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

DOI
10.1103/physreva.90.063631

Related papers

Super Efimov Effect of Resonantly Interacting Fermions in Two Dimensions

Yusuke Nishida, Sergej Moroz, Dam Thanh Son

We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a $p$-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ and their binding energies obey a universal doubly exponential scaling ${E}_{3}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}})$ at large $n$. This ``super Efimov effect'' is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}2$ four-body resonances associated with every three-body bound state at ${E}_{4}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}\ensuremath{-}0.188})$. These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.

arXiv:1301.4473•Physical Review Letters•Jun 4, 2013•79 citations

Universality of semisuper-Efimov effect

Yusuke Horinouchi

We study the semisuper-Efimov effect, which is found for four identical bosons with a resonant three-body interaction in 2D, in various systems. Based on solutions of bound-state and renormalization-group equations, we first demonstrate an emergence of the semisuper-Efimov effect in mass-imbalanced bosons in 2D. Compared with the Efimov and the super-Efimov effects, the mass ratio-dependent scaling parameter is unexpectedly found to take on a finite value even for extremely mass-imbalanced situations, where the mass ratio is 0 or $\infty$. By a renormalization-group analysis, we also show that a weak two-body interaction sustains the semisuper-Efimov effect. Finally, we liberate the universality of the semisuper-Efimov effect from 2D by showing that bosons with linear-dispersion relation support the semisuper-Efimov effect in 1D.

arXiv:2002.07330•Feb 18, 2020•0 citations

Signature of the universal super Efimov effect: Three-body contact in two-dimensional Fermi gases

Pengfei Zhang, Zhenhua Yu

A class of universal ``three-body'' bound states has been recently predicted theoretically for identical fermions interacting at $p$-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a thermodynamic quantity, the three-body contact ${C}_{\ensuremath{\theta}}$, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact ${C}_{\ensuremath{\theta}}$ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how ${C}_{\ensuremath{\theta}}$ affects physical observables such as the radio-frequency spectrum, the momentum distribution, and the atom loss rate. The signature of the elusive super Efimov effect can be pinned down by the detection of the three-body contact ${C}_{\ensuremath{\theta}}$ via these observables in the many-body system.

arXiv:1611.09454•Physical Review A•Mar 9, 2017•19 citations

Three Identical Fermions with Resonant p-wave Interactions in Two Dimensions

Chao Gao, Zhenhua Yu

A new kind of "super-Efimov" states of binding energies scaling as $\ln|E_n|\sim-e^{3nπ/4}$ were predicted by a field theory calculation for three fermions with resonant $p$-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at $p$-wave resonances, the low energy physics of states of angular momentum $\ell=\pm1$ crucially depends on the value of an emergent dimensionless parameter $Y$ determined by the detail of the inter-particle potential. Only if $Y$ is exactly zero, the predicted "super-Efimov" states exist. If $Y>0$, the scaling of the bound states changes to $\ln|E_n|\sim-(nπ)^2/2Y$, while there are no shallow bound states if $Y<0$.

arXiv:1401.0965•Jan 6, 2014•1 citation

Universal three-body bound states in mixed dimensions beyond the Efimov paradigm

Pengfei Zhang, Zhenhua Yu

The Efimov effect was first predicted for three particles interacting at an $s$-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic $A$ atoms interacting with another single $B$ atom in mixed dimensions: The $A$ atoms are confined in a space of dimension ${d}_{A}$ and the $B$ atom in a space of dimension ${d}_{B}$, and there is an interspecies $s$-wave interaction in a ${d}_{\mathrm{int}}$-codimensional space accessible to both species. We find that when the $s$-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for ${{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}$ and ${2,3,1}$. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor $s$ being unity for the former case and $\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})$ for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.

arXiv:1704.04754•Physical Review A•Sep 21, 2017•9 citations

Single-particle momentum distributions of Efimov states in mixed-species systems

Marcelo Takeshi Yamashita, F. F. Bellotti, T. Frederico +3 more

We solve the three-body bound-state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyze the tail of the momentum distribution to obtain the three-body contact parameter. Our findings demonstrate that the functional form of the three-body contact term depends on the mass ratio, and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of lithium with either two caesium or rubidium atoms which are systems of current experimental interest.

arXiv:1303.5883•Physical Review A•Jun 4, 2013•23 citations
We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a ppp-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum \ensuremathℓ=\ifmmode±\else\textpm\fi1\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1\ensuremathℓ=\ifmmode±\else\textpm\fi1 whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.
We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a ppp-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ and their binding energies obey a universal doubly exponential scaling ${E}_{3}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}})$ at large nnn. This ``super Efimov effect'' is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}2$ four-body resonances associated with every three-body bound state at ${E}_{4}^{(n)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2{e}^{3\ensuremath{\pi}n/4+\ensuremath{\theta}\ensuremath{-}0.188})$. These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.
We study the semisuper-Efimov effect, which is found for four identical bosons with a resonant three-body interaction in 2D, in various systems. Based on solutions of bound-state and renormalization-group equations, we first demonstrate an emergence of the semisuper-Efimov effect in mass-imbalanced bosons in 2D. Compared with the Efimov and the super-Efimov effects, the mass ratio-dependent scaling parameter is unexpectedly found to take on a finite value even for extremely mass-imbalanced situations, where the mass ratio is 0 or ∞\infty∞. By a renormalization-group analysis, we also show that a weak two-body interaction sustains the semisuper-Efimov effect. Finally, we liberate the universality of the semisuper-Efimov effect from 2D by showing that bosons with linear-dispersion relation support the semisuper-Efimov effect in 1D.
A class of universal ``three-body'' bound states has been recently predicted theoretically for identical fermions interacting at ppp-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a thermodynamic quantity, the three-body contact ${C}_{\ensuremath{\theta}}$, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact ${C}_{\ensuremath{\theta}}$ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how ${C}_{\ensuremath{\theta}}$ affects physical observables such as the radio-frequency spectrum, the momentum distribution, and the atom loss rate. The signature of the elusive super Efimov effect can be pinned down by the detection of the three-body contact ${C}_{\ensuremath{\theta}}$ via these observables in the many-body system.
A new kind of "super-Efimov" states of binding energies scaling as ln⁡∣En∣∼−e3nπ/4\ln|E_n|\sim-e^{3nπ/4}ln∣En​∣∼−e3nπ/4 were predicted by a field theory calculation for three fermions with resonant ppp-wave interactions in two dimensions [Phys. Rev. Lett. \textbf{110}, 235301 (2013)]. However, the universality of these "super-Efimov" states has not been proved independently. In this Letter, we study the three fermion system through the hyperspherical formalism. Within the adiabatic approximation, we find that at ppp-wave resonances, the low energy physics of states of angular momentum ℓ=±1\ell=\pm1ℓ=±1 crucially depends on the value of an emergent dimensionless parameter YYY determined by the detail of the inter-particle potential. Only if YYY is exactly zero, the predicted "super-Efimov" states exist. If Y>0Y>0Y>0, the scaling of the bound states changes to ln⁡∣En∣∼−(nπ)2/2Y\ln|E_n|\sim-(nπ)^2/2Yln∣En​∣∼−(nπ)2/2Y, while there are no shallow bound states if Y<0Y<0Y<0.
The Efimov effect was first predicted for three particles interacting at an sss-wave resonance in three dimensions. A subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic AAA atoms interacting with another single BBB atom in mixed dimensions: The AAA atoms are confined in a space of dimension dA{d}_{A}dA​ and the BBB atom in a space of dimension dB{d}_{B}dB​, and there is an interspecies sss-wave interaction in a dint{d}_{\mathrm{int}}dint​-codimensional space accessible to both species. We find that when the sss-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for dA,dB,dint=2,2,0{{d}_{A},{d}_{B},{d}_{\mathrm{int}}}={2,2,0}dA​,dB​,dint​=2,2,0 and 2,3,1{2,3,1}2,3,1. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $ln|{E}_{n}{|\ensuremath{\sim}\ensuremath{-}s(n\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2}/4$, with the scaling factor sss being unity for the former case and mB(2mA+mB)/(mA+mB)\sqrt{{m}_{B}(2{m}_{A}+{m}_{B})}/({m}_{A}+{m}_{B})mB​(2mA​+mB​)​/(mA​+mB​) for the latter. We discuss the possibility of realizing our mixed-dimensional systems in a cold-atom experiment and how the effects of these universal three-body bound states may be detected.
We solve the three-body bound-state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyze the tail of the momentum distribution to obtain the three-body contact parameter. Our findings demonstrate that the functional form of the three-body contact term depends on the mass ratio, and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of lithium with either two caesium or rubidium atoms which are systems of current experimental interest.