1
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Link M, Gao K, Kell A, Breyer M, Eberz D, Rauf B, Köhl M. Machine Learning the Phase Diagram of a Strongly Interacting Fermi Gas. PHYSICAL REVIEW LETTERS 2023; 130:203401. [PMID: 37267577 DOI: 10.1103/physrevlett.130.203401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Accepted: 03/31/2023] [Indexed: 06/04/2023]
Abstract
We determine the phase diagram of strongly correlated fermions in the crossover from Bose-Einstein condensates of molecules (BEC) to Cooper pairs of fermions (BCS) utilizing an artificial neural network. By applying advanced image recognition techniques to the momentum distribution of the fermions, a quantity which has been widely considered as featureless for providing information about the condensed state, we measure the critical temperature and show that it exhibits a maximum on the bosonic side of the crossover. Additionally, we backanalyze the trained neural network and demonstrate that it interprets physically relevant quantities.
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Affiliation(s)
- M Link
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - K Gao
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - A Kell
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - M Breyer
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - D Eberz
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - B Rauf
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - M Köhl
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
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2
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Ross JA, Deuar P, Shin DK, Thomas KF, Henson BM, Hodgman SS, Truscott AG. On the survival of the quantum depletion of a condensate after release from a magnetic trap. Sci Rep 2022; 12:13178. [PMID: 35915112 PMCID: PMC9343431 DOI: 10.1038/s41598-022-16477-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 07/11/2022] [Indexed: 11/26/2022] Open
Abstract
We present observations of the high momentum tail in expanding Bose-Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.
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Affiliation(s)
- J A Ross
- Research School of Physics, Australian National University, Canberra, 0200, Australia
| | - P Deuar
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-688, Warsaw, Poland
| | - D K Shin
- Research School of Physics, Australian National University, Canberra, 0200, Australia
| | - K F Thomas
- Research School of Physics, Australian National University, Canberra, 0200, Australia
| | - B M Henson
- Research School of Physics, Australian National University, Canberra, 0200, Australia
| | - S S Hodgman
- Research School of Physics, Australian National University, Canberra, 0200, Australia
| | - A G Truscott
- Research School of Physics, Australian National University, Canberra, 0200, Australia.
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3
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Rakhimov A, Abdurakhmonov T, Tanatar B. Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:465401. [PMID: 34407517 DOI: 10.1088/1361-648x/ac1ec6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 08/18/2021] [Indexed: 06/13/2023]
Abstract
The temperature dependence of Tan's contact parameterCand its derivatives for spin gapped quantum magnets are investigated. We use the paradigm of Bose-Einstein condensation (BEC) to describe the low temperature properties of quasiparticles in the system known as triplons. Since the number of particles and the condensate fraction are not fixed we use theμVTensemble to calculate the thermodynamic quantities. The interactions are treated at the Hartree-Fock-Bogoliubov approximation level. We obtained the temperature dependence ofCand its derivative with respect to temperature and applied magnetic field both above and belowTcof the phase transition from the normal phase to BEC. We have shown thatCis regular, while its derivatives are discontinuous atTcin accordance with Ehrenfest's classification of phase transitions. Moreover, we have found a sign change in ∂C/∂Tclose to the critical temperature. As to the quantum critical point,Cand its derivatives are regular as a function of the control parameterr, which induces the quantum phase transition. At very low temperatures, one may evaluateCsimply from the expressionC=m2μ2/a¯4, where the only parameter effective mass of quasiparticles should be estimated. We propose a method for measuring of Tan's contact for spin gapped dimerized magnets.
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Affiliation(s)
| | | | - B Tanatar
- Department of Physics, Bilkent University, Bilkent, 06800 Ankara, Turkey
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4
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Sun M, Zhang P, Zhai H. High Temperature Virial Expansion to Universal Quench Dynamics. PHYSICAL REVIEW LETTERS 2020; 125:110404. [PMID: 32975972 DOI: 10.1103/physrevlett.125.110404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2020] [Accepted: 08/21/2020] [Indexed: 06/11/2023]
Abstract
High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this Letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from noninteracting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for the low-momentum part with k<k^{*}, and increases for high-momentum part with k>k^{*}, where k^{*} is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of k^{*}λ that agrees perfectly with the experiment, with λ being the thermal de Broglie wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.
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Affiliation(s)
- Mingyuan Sun
- State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Peng Zhang
- Department of Physics, Renmin University of China, Beijing 100872, China
- Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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5
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Jensen S, Gilbreth CN, Alhassid Y. Contact in the Unitary Fermi Gas across the Superfluid Phase Transition. PHYSICAL REVIEW LETTERS 2020; 125:043402. [PMID: 32794813 DOI: 10.1103/physrevlett.125.043402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe a dramatic decrease in the contact as the superfluid critical temperature is approached from below, followed by a gradual weak decrease as the temperature increases in the normal phase. Our theoretical results are in excellent agreement with the most recent precision ultracold atomic gas experiments. We also present results for the energy as a function of temperature in the continuum limit.
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Affiliation(s)
- S Jensen
- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA
| | - C N Gilbreth
- Department of Physics, Central Washington University, Ellensburg, Washington 98926, USA
| | - Y Alhassid
- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA
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6
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Lang J, Frank B. Fast logarithmic Fourier-Laplace transform of nonintegrable functions. Phys Rev E 2019; 100:053302. [PMID: 31870008 DOI: 10.1103/physreve.100.053302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Indexed: 11/07/2022]
Abstract
We present an efficient and very flexible numerical fast Fourier-Laplace transform that extends the logarithmic Fourier transform introduced by Haines and Jones [Geophys. J. Int. 92, 171 (1988)GJINEA0956-540X10.1111/j.1365-246X.1988.tb01131.x] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form f(ν→0)∼ν^{a} and f(|ν|→∞)∼ν^{b} with arbitrary real a>b. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone |Imν|<θ|Reν| with a finite opening angle θ around the real axis and satisfies |f(ν)f(1/ν)|<ν^{c} as ν→0 with a positive constant c, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (nonintegrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.
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Affiliation(s)
- Johannes Lang
- Physik Department, Technische Universität München, D-85747 Garching, Germany and Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany
| | - Bernhard Frank
- Physik Department, Technische Universität München, D-85747 Garching, Germany and Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany
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7
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Mukherjee B, Patel PB, Yan Z, Fletcher RJ, Struck J, Zwierlein MW. Spectral Response and Contact of the Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2019; 122:203402. [PMID: 31172778 DOI: 10.1103/physrevlett.122.203402] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Indexed: 06/09/2023]
Abstract
We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.
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Affiliation(s)
- Biswaroop Mukherjee
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Parth B Patel
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zhenjie Yan
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Richard J Fletcher
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Julian Struck
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Département de Physique, Ecole Normale Supérieure / PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
| | - Martin W Zwierlein
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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8
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Carcy C, Hoinka S, Lingham MG, Dyke P, Kuhn CCN, Hu H, Vale CJ. Contact and Sum Rules in a Near-Uniform Fermi Gas at Unitarity. PHYSICAL REVIEW LETTERS 2019; 122:203401. [PMID: 31172752 DOI: 10.1103/physrevlett.122.203401] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2019] [Indexed: 06/09/2023]
Abstract
We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focused beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum rules to the measured Bragg spectra, we resolve the characteristic behavior of the universal contact parameter, C, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum rule to obtain the internal energy of gases at unitarity.
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Affiliation(s)
- C Carcy
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - S Hoinka
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - M G Lingham
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - P Dyke
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - C C N Kuhn
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - H Hu
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
| | - C J Vale
- Centre for Quantum and Optical Sciences, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Melbourne 3122, Australia
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9
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Rossi R, Ohgoe T, Kozik E, Prokof'ev N, Svistunov B, Van Houcke K, Werner F. Contact and Momentum Distribution of the Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2018; 121:130406. [PMID: 30312096 DOI: 10.1103/physrevlett.121.130406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Indexed: 06/08/2023]
Abstract
A key quantity in strongly interacting resonant Fermi gases is the contact C, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of C was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by bold diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.
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Affiliation(s)
- R Rossi
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université PSL, Sorbonne Université, Université Paris Diderot, CNRS, 75005 Paris, France
| | - T Ohgoe
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - E Kozik
- Physics Department, King's College, London WC2R 2LS, United Kingdom
| | - N Prokof'ev
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- National Research Center "Kurchatov Institute", 123182 Moscow, Russia
| | - B Svistunov
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- National Research Center "Kurchatov Institute", 123182 Moscow, Russia
- Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - K Van Houcke
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université PSL, Sorbonne Université, Université Paris Diderot, CNRS, 75005 Paris, France
| | - F Werner
- Laboratoire Kastler Brossel, Ecole Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Collège de France, 75005 Paris, France
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10
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Shkedrov C, Florshaim Y, Ness G, Gandman A, Sagi Y. High-Sensitivity rf Spectroscopy of a Strongly Interacting Fermi Gas. PHYSICAL REVIEW LETTERS 2018; 121:093402. [PMID: 30230882 DOI: 10.1103/physrevlett.121.093402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2018] [Revised: 06/25/2018] [Indexed: 06/08/2023]
Abstract
rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.
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Affiliation(s)
- Constantine Shkedrov
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Yanay Florshaim
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Gal Ness
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Andrey Gandman
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Yoav Sagi
- Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel
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11
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Mueller EJ. Review of pseudogaps in strongly interacting Fermi gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:104401. [PMID: 28686169 DOI: 10.1088/1361-6633/aa7e53] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.
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Affiliation(s)
- Erich J Mueller
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca NY 14853, United States of America
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12
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Laurent S, Pierce M, Delehaye M, Yefsah T, Chevy F, Salomon C. Connecting Few-Body Inelastic Decay to Quantum Correlations in a Many-Body System: A Weakly Coupled Impurity in a Resonant Fermi Gas. PHYSICAL REVIEW LETTERS 2017; 118:103403. [PMID: 28339272 DOI: 10.1103/physrevlett.118.103403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Indexed: 06/06/2023]
Abstract
We study three-body recombination in an ultracold Bose-Fermi mixture. We first show theoretically that, for weak interspecies coupling, the loss rate is proportional to Tan's contact. Second, using a ^{7}Li/^{6}Li mixture we probe the recombination rate in both the thermal and dual superfluid regimes. We find excellent agreement with our model in the BEC-BCS crossover. At unitarity where the fermion-fermion scattering length diverges, we show that the loss rate is proportional to n_{f}^{4/3}, where n_{f} is the fermionic density. This unusual exponent signals nontrivial two-body correlations in the system. Our results demonstrate that few-body losses can be used as a quantitative probe of quantum correlations in many-body ensembles.
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Affiliation(s)
- Sébastien Laurent
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Matthieu Pierce
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Marion Delehaye
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Tarik Yefsah
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Christophe Salomon
- Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 24 rue Lhomond, 75005 Paris, France
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13
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He M, Zhang S, Chan HM, Zhou Q. Concept of a Contact Spectrum and Its Applications in Atomic Quantum Hall States. PHYSICAL REVIEW LETTERS 2016; 116:045301. [PMID: 26871339 DOI: 10.1103/physrevlett.116.045301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2015] [Indexed: 06/05/2023]
Abstract
A unique feature of ultracold atoms is the separation of length scales, r_{0}≪k_{F}^{-1}, where k_{F} and r_{0} are the Fermi momentum characterizing the average particle distance and the range of interaction between atoms, respectively. For s-wave scattering, Shina Tan discovered that such diluteness leads to universal thermodynamic relations governed by contact. Here, we show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Contact of all partial-wave scatterings forms a contact spectrum, which establishes universal thermodynamic relations with notable differences from those in the presence of s-wave scattering alone. Such a contact spectrum is particularly useful for characterizing many-body correlations in atomic quantum Hall states (QHSs). It has an interesting connection with a special bipartite entanglement spectrum of QHSs and enables an intrinsic probe of atomic QHSs using short-range two-body correlations.
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Affiliation(s)
- Mingyuan He
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Shaoliang Zhang
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Hon Ming Chan
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Qi Zhou
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
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14
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Yoshida SM, Ueda M. Universal High-Momentum Asymptote and Thermodynamic Relations in a Spinless Fermi Gas with a Resonant p-Wave Interaction. PHYSICAL REVIEW LETTERS 2015; 115:135303. [PMID: 26451563 DOI: 10.1103/physrevlett.115.135303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2015] [Indexed: 06/05/2023]
Abstract
We investigate universal relations in a spinless Fermi gas near a p-wave Feshbach resonance, and show that the momentum distribution n_{k} has an asymptote proportional to k^{-2} with the proportionality constant-the p-wave contact-scaling with the number of closed-channel molecules. We prove the adiabatic sweep theorem for a p-wave resonance which reveals the thermodynamic implication of the p-wave contact. In contrast to the unitary Fermi gas in which Tan's contact is universal, the p-wave contact depends on the short-range details of the interaction.
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Affiliation(s)
- Shuhei M Yoshida
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
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15
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Sagi Y, Drake TE, Paudel R, Chapurin R, Jin DS. Breakdown of the fermi liquid description for strongly interacting fermions. PHYSICAL REVIEW LETTERS 2015; 114:075301. [PMID: 25763961 DOI: 10.1103/physrevlett.114.075301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2014] [Indexed: 06/04/2023]
Abstract
The nature of the normal state of an ultracold Fermi gas in the BCS-BEC crossover regime is an intriguing and controversial topic. While the many-body ground state remains a condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules as a function of the interaction strength. How this occurs is still largely unknown. We explore this question with measurements of the distribution of single-particle energies and momenta in a nearly homogeneous gas above T(c). The data fit well to a function that includes a narrow, positively dispersing peak that corresponds to quasiparticles and an "incoherent background" that can accommodate broad, asymmetric line shapes. We find that the quasiparticle's spectral weight vanishes abruptly as the strength of interactions is modified, which signals the breakdown of a Fermi liquid description. Such a sharp feature is surprising in a crossover.
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Affiliation(s)
- Yoav Sagi
- JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Tara E Drake
- JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Rabin Paudel
- JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Roman Chapurin
- JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - Deborah S Jin
- JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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16
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Critical behaviours of contact near phase transitions. Nat Commun 2014; 5:5140. [PMID: 25346226 PMCID: PMC4220487 DOI: 10.1038/ncomms6140] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2014] [Accepted: 09/04/2014] [Indexed: 12/02/2022] Open
Abstract
A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviours, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition, and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviours in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition. Contact parameterises two-body correlations at short distances in dilute systems like ultracold atomic gases. Using a fundamental thermodynamic relation, Chen et al. study the contact near a continuous classical or quantum phase transition and find that it displays a number of critical behaviours.
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Bardon AB, Beattie S, Luciuk C, Cairncross W, Fine D, Cheng NS, Edge GJA, Taylor E, Zhang S, Trotzky S, Thywissen JH. Transverse Demagnetization Dynamics of a Unitary Fermi Gas. Science 2014; 344:722-4. [DOI: 10.1126/science.1247425] [Citation(s) in RCA: 73] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- A. B. Bardon
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - S. Beattie
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - C. Luciuk
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - W. Cairncross
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - D. Fine
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - N. S. Cheng
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - G. J. A. Edge
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - E. Taylor
- Department of Physics and Astronomy, McMaster University, L8S 4M1 Canada
| | - S. Zhang
- Department of Physics, Center of Theoretical and Computational Physics, University of Hong Kong, China
| | - S. Trotzky
- Department of Physics, University of Toronto, M5S 1A7 Canada
| | - J. H. Thywissen
- Department of Physics, University of Toronto, M5S 1A7 Canada
- Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8 Canada
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18
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Lingham MG, Fenech K, Hoinka S, Vale CJ. Local observation of pair condensation in a Fermi gas at unitarity. PHYSICAL REVIEW LETTERS 2014; 112:100404. [PMID: 24679273 DOI: 10.1103/physrevlett.112.100404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2013] [Indexed: 06/03/2023]
Abstract
We present measurements of the local (homogeneous) density-density response function of a Fermi gas at unitarity using spatially resolved Bragg spectroscopy. By analyzing the Bragg response across one axis of the cloud, we extract the response function for a uniform gas which shows a clear signature of the Bose-Einstein condensation of pairs of fermions when the local temperature drops below the superfluid transition temperature. The method we use for local measurement generalizes a scheme for obtaining the local pressure in a harmonically trapped cloud from the line density and can be adapted to provide any homogeneous parameter satisfying the local density approximation.
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Affiliation(s)
- M G Lingham
- Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - K Fenech
- Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - S Hoinka
- Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - C J Vale
- Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
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19
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Sagi Y, Drake TE, Paudel R, Jin DS. Measurement of the homogeneous contact of a unitary Fermi gas. PHYSICAL REVIEW LETTERS 2012; 109:220402. [PMID: 23368108 DOI: 10.1103/physrevlett.109.220402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Revised: 09/20/2012] [Indexed: 06/01/2023]
Abstract
By selectively probing the center of a trapped gas, we measure the local, or homogeneous, contact of a unitary Fermi gas as a function of temperature. Tan's contact, C, is proportional to the derivative of the energy with respect to the interaction strength and is thus an essential thermodynamic quantity for a gas with short-range correlations. Theoretical predictions for the temperature dependence of C differ substantially, especially near the superfluid transition, T(c), where C is predicted to either sharply decrease, sharply increase, or change very little. For T/T(F)>0.4, our measurements of the homogeneous gas contact show a gradual decrease of C with increasing temperature, as predicted by theory. We observe a sharp decrease in C at T/T(F)=0.16, which may be due to the superfluid phase transition. While a sharp decrease in C below T(c) is predicted by some many-body theories, we find that none of the predictions fully account for the data.
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Affiliation(s)
- Yoav Sagi
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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20
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Fröhlich B, Feld M, Vogt E, Koschorreck M, Köhl M, Berthod C, Giamarchi T. Two-dimensional Fermi liquid with attractive interactions. PHYSICAL REVIEW LETTERS 2012; 109:130403. [PMID: 23030071 DOI: 10.1103/physrevlett.109.130403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2012] [Indexed: 06/01/2023]
Abstract
We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum-resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and find their dependence on the interaction strength. We successfully compare the measurements to a theoretical analysis, properly taking into account the finite temperature, harmonic trap, and the averaging over several two-dimensional gases with different peak densities.
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Affiliation(s)
- B Fröhlich
- Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
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21
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Hu H, Jiang L, Liu XJ, Pu H. Probing anisotropic superfluidity in atomic Fermi gases with Rashba spin-orbit coupling. PHYSICAL REVIEW LETTERS 2011; 107:195304. [PMID: 22181620 DOI: 10.1103/physrevlett.107.195304] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2011] [Revised: 07/16/2011] [Indexed: 05/31/2023]
Abstract
Motivated by the prospect of realizing a Fermi gas with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the twofold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet components emerge, leading to an anisotropic superfluid. We calculate the relevant physical quantities, such as the momentum distribution, the single-particle spectral function, and the spin structure factor, that characterize the system.
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Affiliation(s)
- Hui Hu
- ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
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22
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Drut JE, Lähde TA, Ten T. Momentum distribution and contact of the unitary Fermi gas. PHYSICAL REVIEW LETTERS 2011; 106:205302. [PMID: 21668239 DOI: 10.1103/physrevlett.106.205302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2011] [Revised: 04/11/2011] [Indexed: 05/30/2023]
Abstract
We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/ϵ(F) as well as in the ground state. At large momenta k/k(F), we find that n(k) falls off as C/k⁴, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/ϵ(F) and present a comparison with theory. At low T/ϵ(F), we find that C increases with temperature, and we tentatively identify a maximum around T/ϵ(F) ≃ 0.4. Our calculations are performed on lattices of spatial extent up to N(x) = 14 with a particle number per unit volume of ≃ 0.03-0.07.
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Affiliation(s)
- Joaquín E Drut
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545-0001, USA
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