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Bulletin of the American Physical Society

Measurement of Tan's contact in SU(NNN) fermions

Zejian Ren, Bo Song, Chengdong He, Elnur Hajiyev, Entong Zhao, Qianhang Cai, Jeongwon Lee, Gyu-Boong Jo

Published May 28, 2019• 0 citations
OpenAlex

Abstract

Contact interactions play a fundamental role for understanding correlated quantum systems from microscopic models. For example, the 1/k4 momentum tail, the weight of which is known as Tan's contact, reveals a set of universal relations in interacting atomic systems. Nevertheless, the experimental measurement of contact has still remained unexplored for multi-component fermions with high spins. Here, we report on the measurement of s-wave contact parameter in a cold spin-balanced gas of 173Yb atoms with SU(N) symmetry. The high-momentum tail is recorded after time-of-flight expansion, and Tan's contact is directly quantified with a tunable number of spin component N without changing the number of atoms per component. We experimentally verify the linear increase in the contact with N providing experimental confirmation of the SU(N) interaction. Furthermore, we investigate the momentum distribution of SU(N) fermions at the low momentum regime showing that multi-component fermions with large N exhibit a more bosonic behavior. Our measurement directly reveals the interaction effect in a multi-component Fermi gas with SU(N) symmetry, and paves the way for study of many-body physics with high spins.

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Ultracold fermions with SU(N >2) symmetry offer a unique opportunity to study quantum dynamics and interaction effects in the large spin systems that have no analogue in condensed matter physics. In this poster, we present a set of experiments on the measurement of contact parameters and collective excitations with a SU(N) Fermi gas of 173Yb atoms. First, we explore the short-range interaction effect via Tan’s contact parameters in a multi-component Fermi gas with SU(N >2) symmetry. The s-wave contact parameter is experimentally measured by recording the high-momentum tail of weakly interacting fermions. For a tunable number of spin component N with a fixed number of atoms per component, we verify the linear increase in the contact with N providing experimental confirmation of SU(N) interactions. Furthermore, we explore the momentum distribution of SU(N) fermions at the low momentum regime. Next, we measure collective excitations of a harmonically trapped twodimensional SU(N) Fermi gas. Various collective modes are investigated with a tunable number of spin component N showing a decrease in the ratio of quadruple and dipole mode with N. Our work will pave the way for the experimental study of interacting SU(N) Fermi gases with large spin.

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High-momentum tails as magnetic-structure probes for strongly correlated SU(κ) fermionic mixtures in one-dimensional traps

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A universal ${k}^{\ensuremath{-}4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}(\ensuremath{\kappa})$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\ensuremath{\kappa}$ components of the gas and the Young tableaux for the ${S}_{N}$ permutation symmetry group identifying the magnetic structure of the ground state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-state simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local-density approximation (LDA) on the Bethe-ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components, and interaction strength. Moreover, using a virial approach, we study the Tan's contact behavior at high temperature and in the limit of infinite interactions, and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in G. Pagano et al. [Nat. Phys. 10, 198 (2014)].

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The Tan contact is a pivotal quantity for characterizing many-body quantum systems, bridging microscopic correlations to macroscopic thermodynamic behavior. It is defined as the weight of universal [Formula: see text] momentum tails, but, so far, its direct measurement has been hindered in Bose gases due to interactions strongly altering time-of-flight imaging. Here, we report the first direct measurement of the Tan contact in a strongly correlated Lieb-Liniger gas. Leveraging the one-dimensional geometry of our system, we implement a two-stage expansion scheme, yielding interaction-immune imaging. Our results show good agreement with theoretical predictions and are consistent with a predicted universal scaling law. Our work paves the way for further characterization of the Lieb-Liniger gas across broad interaction regimes and holds promise for extension to other correlated quantum gases in confined geometries.

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Studies of the universal contact in a strongly interacting Fermi gas using Bragg spectroscopy

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We present a comprehensive experimental study of Tan's universal contact parameter in a two-component ultracold Fermi gas, using Bragg spectroscopy. The contact uniquely parameterizes a number of universal properties of Fermi gases in the strongly interacting regime. It is linked to the spin-antiparallel component of the static structure factor S ↑↓ ( k ) at high momenta, which can readily be obtained via Bragg scattering. Contact depends upon the relative interaction strength 1/( k F a ) and temperature T / T F , where k F is the Fermi wave vector, a is the s-wave scattering length and T F is the Fermi temperature. We present measurements of both of these dependencies in a cloud of 6 Li atoms and compare our findings to theoretical predictions. We also compare Bragg spectroscopic methods based on measuring the energy and momentum transferred to the cloud and examine the conditions under which the energy transfer method provides improved accuracy. Our measurements of the dynamic structure factor and contact are found to be in good agreement with theoretical predictions based on the quantum virial expansion.

New Journal of Physics•May 24, 2011•27 citations
Contact interactions play a fundamental role for understanding correlated quantum systems from microscopic models. For example, the 1/k4 momentum tail, the weight of which is known as Tan's contact, reveals a set of universal relations in interacting atomic systems. Nevertheless, the experimental measurement of contact has still remained unexplored for multi-component fermions with high spins. Here, we report on the measurement of s-wave contact parameter in a cold spin-balanced gas of 173Yb atoms with SU(N) symmetry. The high-momentum tail is recorded after time-of-flight expansion, and Tan's contact is directly quantified with a tunable number of spin component N without changing the number of atoms per component. We experimentally verify the linear increase in the contact with N providing experimental confirmation of the SU(N) interaction. Furthermore, we investigate the momentum distribution of SU(N) fermions at the low momentum regime showing that multi-component fermions with large N exhibit a more bosonic behavior. Our measurement directly reveals the interaction effect in a multi-component Fermi gas with SU(N) symmetry, and paves the way for study of many-body physics with high spins.
Ultracold fermions with SU(N >2) symmetry offer a unique opportunity to study quantum dynamics and interaction effects in the large spin systems that have no analogue in condensed matter physics. In this poster, we present a set of experiments on the measurement of contact parameters and collective excitations with a SU(N) Fermi gas of 173Yb atoms. First, we explore the short-range interaction effect via Tan’s contact parameters in a multi-component Fermi gas with SU(N >2) symmetry. The s-wave contact parameter is experimentally measured by recording the high-momentum tail of weakly interacting fermions. For a tunable number of spin component N with a fixed number of atoms per component, we verify the linear increase in the contact with N providing experimental confirmation of SU(N) interactions. Furthermore, we explore the momentum distribution of SU(N) fermions at the low momentum regime. Next, we measure collective excitations of a harmonically trapped twodimensional SU(N) Fermi gas. Various collective modes are investigated with a tunable number of spin component N showing a decrease in the ratio of quadruple and dipole mode with N. Our work will pave the way for the experimental study of interacting SU(N) Fermi gases with large spin.
A universal ${k}^{\ensuremath{-}4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}(\ensuremath{\kappa})$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\ensuremath{\kappa}$ components of the gas and the Young tableaux for the SN{S}_{N}SN​ permutation symmetry group identifying the magnetic structure of the ground state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-state simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local-density approximation (LDA) on the Bethe-ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components, and interaction strength. Moreover, using a virial approach, we study the Tan's contact behavior at high temperature and in the limit of infinite interactions, and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in G. Pagano et al. [Nat. Phys. 10, 198 (2014)].
Many-body fermion systems are important in many branches of physics, including condensed matter, nuclear, and now cold atom physics. In many cases, the interactions between fermions can be approximated by a contact interaction. A recent theoretical advance in the study of these systems is the derivation of a number of exact universal relations that are predicted to be valid for all interaction strengths, temperatures, and spin compositions. These equations, referred to as the Tan relations, relate a microscopic quantity, namely, the amplitude of the high-momentum tail of the fermion momentum distribution, to the thermodynamics of the many-body system. In this work, we provide experimental verification of the Tan relations in a strongly interacting gas of fermionic atoms by measuring both the microscopic and macroscopic quantities in the same system.
Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics.One such example is a multicomponent Fermi gas with SUðNÞ symmetry that is expected to behave like spinless bosons in the large-N limit, where the large number of internal states weakens constraints from the Pauli exclusion principle.However, bosonization in SUðNÞ fermions has never been established in high dimensions where exact solutions are absent.Here, we report direct evidence for bosonization in a SUðNÞ fermionic ytterbium gas with tunable N in three dimensions (3D).We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a 1=N scaling in the low-fugacity regime consistent with our theoretical prediction.This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity.Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions.It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.
The Tan contact is a pivotal quantity for characterizing many-body quantum systems, bridging microscopic correlations to macroscopic thermodynamic behavior. It is defined as the weight of universal [Formula: see text] momentum tails, but, so far, its direct measurement has been hindered in Bose gases due to interactions strongly altering time-of-flight imaging. Here, we report the first direct measurement of the Tan contact in a strongly correlated Lieb-Liniger gas. Leveraging the one-dimensional geometry of our system, we implement a two-stage expansion scheme, yielding interaction-immune imaging. Our results show good agreement with theoretical predictions and are consistent with a predicted universal scaling law. Our work paves the way for further characterization of the Lieb-Liniger gas across broad interaction regimes and holds promise for extension to other correlated quantum gases in confined geometries.
We present a comprehensive experimental study of Tan's universal contact parameter in a two-component ultracold Fermi gas, using Bragg spectroscopy. The contact uniquely parameterizes a number of universal properties of Fermi gases in the strongly interacting regime. It is linked to the spin-antiparallel component of the static structure factor S ↑↓ ( k ) at high momenta, which can readily be obtained via Bragg scattering. Contact depends upon the relative interaction strength 1/( k F a ) and temperature T / T F , where k F is the Fermi wave vector, a is the s-wave scattering length and T F is the Fermi temperature. We present measurements of both of these dependencies in a cloud of 6 Li atoms and compare our findings to theoretical predictions. We also compare Bragg spectroscopic methods based on measuring the energy and momentum transferred to the cloud and examine the conditions under which the energy transfer method provides improved accuracy. Our measurements of the dynamic structure factor and contact are found to be in good agreement with theoretical predictions based on the quantum virial expansion.