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Wang L, Yan X, Min J, Sun D, Xie X, Peng SG, Zhan M, Jiang K. Scale Invariance of a Spherical Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2024; 132:243403. [PMID: 38949354 DOI: 10.1103/physrevlett.132.243403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 04/06/2024] [Accepted: 05/21/2024] [Indexed: 07/02/2024]
Abstract
A unitary Fermi gas in an isotropic harmonic trap is predicted to show scale and conformal symmetry that have important consequences in its thermodynamic and dynamical properties. By experimentally realizing a unitary Fermi gas in an isotropic harmonic trap, we demonstrate its universal expansion dynamics along each direction and at different temperatures. We show that as a consequence of SO(2,1) symmetry, the measured release energy is equal to that of the trapping energy. We further observe the breathing mode with an oscillation frequency twice the trapping frequency and a small damping rate, providing the evidence of SO(2,1) symmetry. In addition, away from resonance when scale invariance is broken, we determine the effective exponent γ that relates the chemical potential and average density along the BEC-BCS crossover, which qualitatively agrees with the mean field predictions. This Letter opens the possibility of studying nonequilibrium dynamics in a conformal invariant system in the future.
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Affiliation(s)
| | - Xiangchuan Yan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | | | - Dali Sun
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | | | - Shi-Guo Peng
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Mingsheng Zhan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Kaijun Jiang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
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2
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Wang X, Li X, Arakelyan I, Thomas JE. Hydrodynamic Relaxation in a Strongly Interacting Fermi Gas. PHYSICAL REVIEW LETTERS 2022; 128:090402. [PMID: 35302786 DOI: 10.1103/physrevlett.128.090402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Revised: 01/13/2022] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
We measure the free decay of a spatially periodic density profile in a normal fluid strongly interacting Fermi gas, which is confined in a box potential. This spatial profile is initially created in thermal equilibrium by a perturbing potential. After the perturbation is abruptly extinguished, the dominant spatial Fourier component exhibits an exponentially decaying (thermally diffusive) mode and a decaying oscillatory (first sound) mode, enabling independent measurement of the thermal conductivity and the shear viscosity directly from the time-dependent evolution.
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Affiliation(s)
- Xin Wang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Xiang Li
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Ilya Arakelyan
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - J E Thomas
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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3
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Thermal conductivity of an ultracold Fermi gas in the BCS-BEC crossover. Sci Rep 2021; 11:1228. [PMID: 33441608 PMCID: PMC7806942 DOI: 10.1038/s41598-020-79010-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Accepted: 11/27/2020] [Indexed: 11/09/2022] Open
Abstract
Recent experiments on sound waves in a unitary Fermi gas reveal many transport properties about strongly interacting fermions. Sound propagates through the coupling of momentum and heat transport, and attenuates strongly with the presence of a phase transition. In this work, focusing on the temperature regimes near and below the superfluid critical temperature [Formula: see text] in the BCS-BEC crossover, we present a Kubo-based microscopic calculation of thermal conductivity [Formula: see text], which has not attracted much attention compared to the shear viscosity. Our approach primarily addresses the contributions of the fermionic quasiparticles to thermal transport and our results return to the kinetic descriptions at high temperatures. [Formula: see text] drops upon crossing the pseudogap temperature [Formula: see text], and its temperature dependence changes below [Formula: see text]. The drops become more pronounced on the weakly coupled BCS side, where the Pauli blocking causes the upturn of [Formula: see text] above [Formula: see text]. Our calculations fit well with the sound measurement on the damping rate.
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Patel PB, Yan Z, Mukherjee B, Fletcher RJ, Struck J, Zwierlein MW. Universal sound diffusion in a strongly interacting Fermi gas. Science 2021; 370:1222-1226. [PMID: 33273102 DOI: 10.1126/science.aaz5756] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2019] [Accepted: 10/24/2020] [Indexed: 11/02/2022]
Abstract
Transport of strongly interacting fermions is crucial for the properties of modern materials, nuclear fission, the merging of neutron stars, and the expansion of the early Universe. Here, we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting atomic Fermi gas by studying sound propagation and its attenuation through the coupled transport of momentum and heat. In the normal state, the sound diffusivity D monotonically decreases upon lowering the temperature, in contrast to the diverging behavior of weakly interacting Fermi liquids. Below the superfluid transition temperature, D attains a universal value set by the ratio of Planck's constant and the particle mass. Our findings inform theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons, and quarks.
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Affiliation(s)
- Parth B Patel
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Zhenjie Yan
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Biswaroop Mukherjee
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Richard J Fletcher
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Julian Struck
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Département de Physique, Ecole Normale Supérieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Martin W Zwierlein
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. .,MIT-Harvard Center for Ultracold Atoms, Cambridge, MA 02139, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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5
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Schaefer T. Quantum-limited sound attenuation. Science 2020; 370:1162-1163. [DOI: 10.1126/science.abb6155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Resonantly interacting atoms confined by lasers have implications for neutron stars
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Affiliation(s)
- Thomas Schaefer
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
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6
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Kuhn CCN, Hoinka S, Herrera I, Dyke P, Kinnunen JJ, Bruun GM, Vale CJ. High-Frequency Sound in a Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2020; 124:150401. [PMID: 32357063 DOI: 10.1103/physrevlett.124.150401] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2019] [Accepted: 02/25/2020] [Indexed: 06/11/2023]
Abstract
We present an experimental and theoretical study of the phonon mode in a unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation spectra at a momentum of approximately half the Fermi momentum, both above and below the superfluid critical temperature T_{c}. Below T_{c}, the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by gradients in the phase of the superfluid order parameter. The temperature dependence of the BA phonon is consistent with a theoretical model based on the quasiparticle random phase approximation in which the dominant damping mechanism is via collisions with thermally excited quasiparticles. As the temperature is increased above T_{c}, the phonon evolves into a strongly damped collisional mode, accompanied by an abrupt increase in spectral width. Our study reveals strong similarities between sound propagation in the unitary Fermi gas and bosonic liquid helium.
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Affiliation(s)
- C C N Kuhn
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Centre for Quantum and Optical Sciences, Swinburne University of Technology, Melbourne 3122, Australia
| | - S Hoinka
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Centre for Quantum and Optical Sciences, Swinburne University of Technology, Melbourne 3122, Australia
| | - I Herrera
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Centre for Quantum and Optical Sciences, Swinburne University of Technology, Melbourne 3122, Australia
| | - P Dyke
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Centre for Quantum and Optical Sciences, Swinburne University of Technology, Melbourne 3122, Australia
| | - J J Kinnunen
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - G M Bruun
- Institut for Fysik og Astronomi, Aarhus Universitet, 8000 Aarhus C, Denmark
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - C J Vale
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Centre for Quantum and Optical Sciences, Swinburne University of Technology, Melbourne 3122, Australia
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Enss T. Bulk Viscosity and Contact Correlations in Attractive Fermi Gases. PHYSICAL REVIEW LETTERS 2019; 123:205301. [PMID: 31809121 DOI: 10.1103/physrevlett.123.205301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Indexed: 06/10/2023]
Abstract
The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity ζ/η is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics, and sound attenuation.
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Affiliation(s)
- Tilman Enss
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
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Baird L, Wang X, Roof S, Thomas JE. Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2019; 123:160402. [PMID: 31702342 DOI: 10.1103/physrevlett.123.160402] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Indexed: 06/10/2023]
Abstract
We directly observe the hydrodynamic linear response of a unitary Fermi gas confined in a box potential and subject to a spatially periodic optical potential that is translated into the cloud at speeds ranging from subsonic to supersonic. We show that the time-dependent change of the density profile is sensitive to the thermal conductivity, which controls the relaxation rate of the temperature gradients and hence the responses arising from adiabatic and isothermal compression.
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Affiliation(s)
- Lorin Baird
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Xin Wang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Stetson Roof
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - J E Thomas
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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9
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Mykhaylova V, Bluhm M, Redlich K, Sasaki C. Quark-flavor dependence of the shear viscosity in a quasiparticle model. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.100.034002] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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10
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Cai W, Guo H, He Y, Chien CC. Shear Viscosity of Uniform Fermi Gases with Population Imbalance. Sci Rep 2018; 8:3981. [PMID: 29507313 PMCID: PMC5838242 DOI: 10.1038/s41598-018-22273-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2017] [Accepted: 02/19/2018] [Indexed: 11/15/2022] Open
Abstract
The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.
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Affiliation(s)
- Weimin Cai
- Department of Physics, Southeast University, Nanjing, 211189, China
| | - Hao Guo
- Department of Physics, Southeast University, Nanjing, 211189, China.
| | - Yan He
- College of Physical Science and Technology, Sichuan University, Chengdu, Sichuan, 610064, China
| | - Chih-Chun Chien
- School of Natural Sciences, University of California, Merced, CA, 95343, USA.
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