The Fate of the Efimov Effect in a Many-Body World

The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields unexpected scaling relations among a tower of universal states. These seemingly unrelated problems can now be studied in the same setup thanks to the success of ultracold atomic gas experiments. In light of the tremendous effect of a background Fermi sea on two-body properties, a natural question is whether a background can modify or even destroy the Efimov effect. Here we demonstrate how the generic problem of three interacting particles changes when one particle is embedded in a background Fermi sea, and show that Efimov scaling persists. It is found in a scaling that relates the three-body physics to the background density of fermionic particles.The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields unexpected scaling relations among a tower of universal states. These seemingly unrelated problems can now be studied in the same setup thanks to the success of ultracold atomic gas experiments. In light of the tremendous effect of a background Fermi sea on two-body properties, a natural question is whether a background can modify or even destroy the Efimov effect. Here we demonstrate how the generic problem of three interacting particles changes when one particle is embedded in a background Fermi sea, and show that Efimov scaling persists. It is found in a scaling that relates the three-body physics to the background density of fermionic particles.

arXiv:1110.5854New Journal of PhysicsFeb 21, 201425 citations

Efimov physics in the presence of a Fermi sea

Mingyuan Sun, Xiaoling Cui

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 ( $^{133}\mathrm{Cs}$ ) immersed in a bath of light fermions ( $^{6}\mathrm{Li}$ ). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions ( ${k}_{F}$ ) and the boson-fermion scattering length ${a}_{s}(<0)$ , 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 ${k}_{F}$ ). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale ( ${k}_{F}$ ) 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.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 ($^{133}\mathrm{Cs}$) immersed in a bath of light fermions ($^{6}\mathrm{Li}$). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions (${k}_{F}$) and the boson-fermion scattering length ${a}_{s}(<0)$, 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 ${k}_{F}$). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale (${k}_{F}$) 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.

arXiv:1903.09751Physical Review AJun 24, 201915 citations

Few-Body Physics in Quantum Gases

K. Helfrich

Few-body effects play an important role for the understanding of ultracold quantum gases. We make use of an effective field theory approach to investigate various aspects of universal few-body physics close to a Feshbach resonance. That is the regime where the scattering length is large compared to all other length scales of the system and thus determines the observables. It is also the regime where the Efimov effect whose main characteristic is the occurrence of a sequence of three-body bound states becomes important. At unitarity, i.e., for diverging scattering length, the ratio of binding energies of neighboring states approaches a constant. The existence of those trimers can be captured by a single three-body parameter and influences observables such as recombination rates. Starting from adequate Lagrangians, we derive atom-dimer scattering amplitudes that contain all information of interest about the three-particle systems. With this method, we first investigate the scattering of atoms and dimers at finite temperature in the presence of the Efimov effect. We calculate the dimer relaxation rate and obtain good agreement with available experimental data. Furthermore, heteronuclear mixtures exhibiting large interspecies scattering length are studied in detail. If bosons are the majority species, the Efimov effect occurs in an S-wave channel and we are able to compute three-body recombination and dimer relaxation rates. The results are compared to the outcome of two existing experiments. For mainly fermionic systems, the Efimov effect is only present in an overall P-wave and three-body recombination at threshold vanishes. However, in mixtures of atoms and dimers, scattering cross sections and dimer relaxation show the typical Efimov behavior of log-periodicity. We also consider two-dimensional Bose gases, where the Efimov effect does not occur. For those systems, we derive an equation including the first non-universal corrections and deduce three-body observables such as binding energies and atom-dimer scattering parameters.Few-body effects play an important role for the understanding of ultracold quantum gases. We make use of an effective field theory approach to investigate various aspects of universal few-body physics close to a Feshbach resonance. That is the regime where the scattering length is large compared to all other length scales of the system and thus determines the observables. It is also the regime where the Efimov effect whose main characteristic is the occurrence of a sequence of three-body bound states becomes important. At unitarity, i.e., for diverging scattering length, the ratio of binding energies of neighboring states approaches a constant. The existence of those trimers can be captured by a single three-body parameter and influences observables such as recombination rates. Starting from adequate Lagrangians, we derive atom-dimer scattering amplitudes that contain all information of interest about the three-particle systems. With this method, we first investigate the scattering of atoms and dimers at finite temperature in the presence of the Efimov effect. We calculate the dimer relaxation rate and obtain good agreement with available experimental data. Furthermore, heteronuclear mixtures exhibiting large interspecies scattering length are studied in detail. If bosons are the majority species, the Efimov effect occurs in an S-wave channel and we are able to compute three-body recombination and dimer relaxation rates. The results are compared to the outcome of two existing experiments. For mainly fermionic systems, the Efimov effect is only present in an overall P-wave and three-body recombination at threshold vanishes. However, in mixtures of atoms and dimers, scattering cross sections and dimer relaxation show the typical Efimov behavior of log-periodicity. We also consider two-dimensional Bose gases, where the Efimov effect does not occur. For those systems, we derive an equation including the first non-universal corrections and deduce three-body observables such as binding energies and atom-dimer scattering parameters.

Oct 25, 20111 citation

Origin of the Three-Body Parameter Universality in Efimov Physics

Jia Wang, José Paulo D'Incao, Brett D. Esry +1 more

In recent years extensive theoretical and experimental studies of universal few-body physics have advanced our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms but less likely to extend to light nuclei.In recent years extensive theoretical and experimental studies of universal few-body physics have advanced our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms but less likely to extend to light nuclei.

arXiv:1201.1176Physical Review LettersJun 26, 2012181 citations

Three-body bound states of an atom in a Fermi mixture

Sanayei, Ali, Ludwig Mathey

We determine the three-body bound states of an atom in a Fermi mixture. Compared to the Efimov spectrum of three atoms in vacuum, we show that the Fermi seas deform the Efimov spectrum systematically. We demonstrate that this effect is more pronounced near unitarity, for which we give an analytical estimate. We show that in the presence of Fermi seas, the three-body bound states obey a generalized discrete scaling law. For an experimental confirmation of our prediction, we propose three signatures of three-body bound states of an ultracold Fermi mixture of Yb isotopes, and provide an estimate for the onset of the bound state and the binding energy.We determine the three-body bound states of an atom in a Fermi mixture. Compared to the Efimov spectrum of three atoms in vacuum, we show that the Fermi seas deform the Efimov spectrum systematically. We demonstrate that this effect is more pronounced near unitarity, for which we give an analytical estimate. We show that in the presence of Fermi seas, the three-body bound states obey a generalized discrete scaling law. For an experimental confirmation of our prediction, we propose three signatures of three-body bound states of an ultracold Fermi mixture of Yb isotopes, and provide an estimate for the onset of the bound state and the binding energy.

arXiv:2007.13511Jul 27, 20202 citations

Few-Magnon Universality beyond Contact Interactions in Long-Range Spin Chains

Yiran Huo, Pengfei Zhang

Quantum few-body systems exhibit a rich variety of phenomena that provide fundamental insights into universality. A paradigmatic example is the Efimov effect, in which an infinite tower of three-body bound states emerges with binding energies forming a geometric sequence. Motivated by advances in trapped-ion systems, recent theoretical work has predicted that the Efimov effect can arise in certain long-range quantum spin chains, where magnons exhibit a general dispersion $ε_k=u|k|^z$ with $z\in(0.52,0.88)$ and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential $V(x)=V_0/(1+|x|^β)$ . Our results demonstrate that few-body universality persists for any $β>1$ : In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.Quantum few-body systems exhibit a rich variety of phenomena that provide fundamental insights into universality. A paradigmatic example is the Efimov effect, in which an infinite tower of three-body bound states emerges with binding energies forming a geometric sequence. Motivated by advances in trapped-ion systems, recent theoretical work has predicted that the Efimov effect can arise in certain long-range quantum spin chains, where magnons exhibit a general dispersion $ε_k=u|k|^z$ with $z\in(0.52,0.88)$ and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential $V(x)=V_0/(1+|x|^β)$. Our results demonstrate that few-body universality persists for any $β>1$: In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.

cond-mat.quant-gasCross-listedarXiv:2610.16126Oct 13, 20260 citations

^{133}\mathrm{Cs}

) immersed in a bath of light fermions (

^{6}\mathrm{Li}

). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions (

{k}_{F}

) and the boson-fermion scattering length

{a}_{s}(<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

{k}_{F}

). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale (

{k}_{F}

) 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.

ε_k=u|k|^z

with

z\in(0.52,0.88)

and interact through a contact potential. Nevertheless, whether Efimov universality persists in the presence of experimentally relevant long-range interactions between magnons remains unexplored. In this work, we address this issue by investigating the two- and three-magnon problems with a model interaction potential

V(x)=V_0/(1+|x|^β)

. Our results demonstrate that few-body universality persists for any

β>1

: In the two-magnon sector, the low-energy expansion of the scattering matrix near a two-body resonance agrees with the universal form predicted by contact-interaction theory. The three-magnon bound-state spectrum exhibits Efimov scaling, with a scaling factor consistent with the theory. We further highlight the experimental relevance of our model, which can be readily realized in trapped-ion systems. Our results pave the way for quantum simulations of universal few-body physics beyond the traditional paradigm of nonrelativistic particles.