In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Using Ramsey interferometry, we studied coherent evolution of the resonantly interacting Bose gas, and we show here that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics and provide a direct measurement of the associated three-body contact.In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Using Ramsey interferometry, we studied coherent evolution of the resonantly interacting Bose gas, and we show here that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics and provide a direct measurement of the associated three-body contact.

Jan 27, 201758 citations

Dynamics of Three-Body Correlations in Quenched Unitary Bose Gases

V. E. Colussi, John Corson, José Paulo D'Incao

We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.

arXiv:1710.10580Physical Review LettersMar 9, 201841 citations

Efimov correlations in strongly interacting Bose gases

Marcus Barth, Johannes Hofmann

We compute the virial coefficients, the contact parameters, and the momentum distribution of a strongly interacting three-dimensional Bose gas by means of a virial expansion up to third order in the fugacity, which takes into account three-body correlations exactly. Our results characterize the nondegenerate regime of the interacting Bose gas, where the thermal wavelength is smaller than the interparticle spacing but the scattering length may be arbitrarily large. We observe a rapid variation of the third virial coefficient as the scattering length is tuned across the three-atom and the atom-dimer thresholds. The momentum distribution at unitarity displays a universal high-momentum tail with a log-periodic momentum dependence, which is a direct signature of Efimov physics. We provide a quantitative description of the momentum distribution at high momentum as measured by P. Makotyn et al. [Nat. Phys. 10, 116 (2014)], and our calculations indicate that the lowest trimer state might not be occupied in the experiment. Our results allow for a spectroscopy of Efimov states in the unitary limit.We compute the virial coefficients, the contact parameters, and the momentum distribution of a strongly interacting three-dimensional Bose gas by means of a virial expansion up to third order in the fugacity, which takes into account three-body correlations exactly. Our results characterize the nondegenerate regime of the interacting Bose gas, where the thermal wavelength is smaller than the interparticle spacing but the scattering length may be arbitrarily large. We observe a rapid variation of the third virial coefficient as the scattering length is tuned across the three-atom and the atom-dimer thresholds. The momentum distribution at unitarity displays a universal high-momentum tail with a log-periodic momentum dependence, which is a direct signature of Efimov physics. We provide a quantitative description of the momentum distribution at high momentum as measured by P. Makotyn et al. [Nat. Phys. 10, 116 (2014)], and our calculations indicate that the lowest trimer state might not be occupied in the experiment. Our results allow for a spectroscopy of Efimov states in the unitary limit.

arXiv:1506.06751Physical Review ADec 30, 201532 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.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:1611.09454Physical Review AMar 9, 201719 citations

Bunching, clustering, and the buildup of few-body correlations in a quenched unitary Bose gas

V. E. Colussi, B. E. van Zwol, José Paulo D'Incao +1 more

We study the growth of two- and three-body correlations in an ultracold Bose gas quenched to unitarity. This is encoded in the dynamics of the two- and three-body contacts analyzed in this work. Via a set of relations connecting many-body correlation dynamics with few-body models, signatures of the Efimov effect are mapped out as a function of evolution time at unitarity over a range of atomic densities $n$ . For the thermal resonantly interacting Bose gas, we find that atom bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales.We study the growth of two- and three-body correlations in an ultracold Bose gas quenched to unitarity. This is encoded in the dynamics of the two- and three-body contacts analyzed in this work. Via a set of relations connecting many-body correlation dynamics with few-body models, signatures of the Efimov effect are mapped out as a function of evolution time at unitarity over a range of atomic densities $n$. For the thermal resonantly interacting Bose gas, we find that atom bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales.

arXiv:1901.10355Physical Review AApr 4, 201915 citations

Three body contact in the unitary Fermi gas

Carl Heintze

The aim of this thesis was to measure the three-body contact in the unitary Fermi gas for the first time. The three-body contact is a physical observable that quantifies the three-body short-range correlations. Our probe, sensitive to three fermions with spins ↑↑↓ or ↓↓↑ at short distances, is three-body loss from the optical trap, caused by recombination into a deeply bound molecule and a free atom. In our system, the two spins signify two different hyperfine states of 6Li. We calibrate that recombination process by measuring three-body loss in the motional ground state of three fermions in an optical tweezer at unitarity. The numerically determined three-body contact C_3 (3) 3 of the three fermion system and the experimentally obtained loss rate allow us to extract Im[a_3], which quantifies the coupling to the deeply bound molecular state. Depending on the initial spin configuration ↑↑↓ or ↓↓↑, we find two different values, differing by almost a factor of two. This difference can only be explained by microscopic details of the interatomic coupling. In the many-body unitary Fermi gas, we use the coupling parameter Im[a_3] to extract the zero-temperature dimensionless three-body contact density $\zeta_3$ from three-body loss measurements. We obtain a value of $\zeta_3$ = 0.22(4) and observe that the loss rate scales with a characteristic three-body constant s = 1.77, which stems from an underlying SO(2,1) symmetry. We heat the gas and determine $\zeta_3$ in the thermal regime, observing agreement with the theoretical prediction based on the virial expansion. The extracted value of $\zeta_3$ > 0, which eludes theory, indicates three-body correlations. At the same time, the experimentally confirmed constant s proves the existence of irreducible three-body correlations that cannot be explained by two-body correlations alone.The aim of this thesis was to measure the three-body contact in the unitary Fermi gas for the first time. The three-body contact is a physical observable that quantifies the three-body short-range correlations. Our probe, sensitive to three fermions with spins ↑↑↓ or ↓↓↑ at short distances, is three-body loss from the optical trap, caused by recombination into a deeply bound molecule and a free atom. In our system, the two spins signify two different hyperfine states of 6Li. We calibrate that recombination process by measuring three-body loss in the motional ground state of three fermions in an optical tweezer at unitarity. The numerically determined three-body contact C_3 (3) 3 of the three fermion system and the experimentally obtained loss rate allow us to extract Im[a_3], which quantifies the coupling to the deeply bound molecular state. Depending on the initial spin configuration ↑↑↓ or ↓↓↑, we find two different values, differing by almost a factor of two. This difference can only be explained by microscopic details of the interatomic coupling. In the many-body unitary Fermi gas, we use the coupling parameter Im[a_3] to extract the zero-temperature dimensionless three-body contact density $\zeta_3$ from three-body loss measurements. We obtain a value of $\zeta_3$ = 0.22(4) and observe that the loss rate scales with a characteristic three-body constant s = 1.77, which stems from an underlying SO(2,1) symmetry. We heat the gas and determine $\zeta_3$ in the thermal regime, observing agreement with the theoretical prediction based on the virial expansion. The extracted value of $\zeta_3$ > 0, which eludes theory, indicates three-body correlations. At the same time, the experimentally confirmed constant s proves the existence of irreducible three-body correlations that cannot be explained by two-body correlations alone.

Jan 1, 20260 citations

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.

n

. For the thermal resonantly interacting Bose gas, we find that atom bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales.

\zeta_3

from three-body loss measurements. We obtain a value of

\zeta_3

= 0.22(4) and observe that the loss rate scales with a characteristic three-body constant s = 1.77, which stems from an underlying SO(2,1) symmetry. We heat the gas and determine

\zeta_3

in the thermal regime, observing agreement with the theoretical prediction based on the virial expansion. The extracted value of

\zeta_3

> 0, which eludes theory, indicates three-body correlations. At the same time, the experimentally confirmed constant s proves the existence of irreducible three-body correlations that cannot be explained by two-body correlations alone.