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arXiv:1611.09454 · Physical Review A

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

Pengfei Zhang, Zhenhua Yu

Published Mar 9, 2017• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.95.033611

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•Oct 25, 2011•1 citation
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\ensuremathθ{C}_{\ensuremath{\theta}}C\ensuremathθ​, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact C\ensuremathθ{C}_{\ensuremath{\theta}}C\ensuremathθ​ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how C\ensuremathθ{C}_{\ensuremath{\theta}}C\ensuremathθ​ 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\ensuremathθ{C}_{\ensuremath{\theta}}C\ensuremathθ​ via these observables in the many-body system.
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.
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 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 $\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$ 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.
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.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.
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.