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Bekassy V, Hofmann J. Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases. PHYSICAL REVIEW LETTERS 2022; 128:193401. [PMID: 35622033 DOI: 10.1103/physrevlett.128.193401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Revised: 03/10/2022] [Accepted: 04/05/2022] [Indexed: 06/15/2023]
Abstract
Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.
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Affiliation(s)
- Viktor Bekassy
- Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Johannes Hofmann
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
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2
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Tan's two-body contact across the superfluid transition of a planar Bose gas. Nat Commun 2021; 12:760. [PMID: 33536418 PMCID: PMC7858573 DOI: 10.1038/s41467-020-20647-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Accepted: 12/11/2020] [Indexed: 11/11/2022] Open
Abstract
Tan’s contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings. Here the authors use Ramsey interferometry to study Tan’s contact in uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They find that the two-body contact is continuous across the critical point.
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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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Drut JE, McKenney JR, Daza WS, Lin CL, Ordóñez CR. Quantum Anomaly and Thermodynamics of One-Dimensional Fermions with Three-Body Interactions. PHYSICAL REVIEW LETTERS 2018; 120:243002. [PMID: 29957009 DOI: 10.1103/physrevlett.120.243002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Indexed: 06/08/2023]
Abstract
We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.
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Affiliation(s)
- J E Drut
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA
| | - J R McKenney
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA
| | - W S Daza
- Physics Department, University of Houston, Houston, Texas 77024-5005, USA
| | - C L Lin
- Physics Department, University of Houston, Houston, Texas 77024-5005, USA
| | - C R Ordóñez
- Physics Department, University of Houston, Houston, Texas 77024-5005, USA
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Schmidt R, Knap M, Ivanov DA, You JS, Cetina M, Demler E. Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:024401. [PMID: 29303118 DOI: 10.1088/1361-6633/aa9593] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.
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Affiliation(s)
- Richard Schmidt
- Department of Physics, Harvard University, Cambridge MA 02138, United States of America. ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, United States of America. Institute of Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
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Murthy PA, Neidig M, Klemt R, Bayha L, Boettcher I, Enss T, Holten M, Zürn G, Preiss PM, Jochim S. High-temperature pairing in a strongly interacting two-dimensional Fermi gas. Science 2018; 359:452-455. [DOI: 10.1126/science.aan5950] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Accepted: 12/06/2017] [Indexed: 11/02/2022]
Affiliation(s)
| | - Mathias Neidig
- Physics Institute, Heidelberg University, Heidelberg, Germany
| | - Ralf Klemt
- Physics Institute, Heidelberg University, Heidelberg, Germany
| | - Luca Bayha
- Physics Institute, Heidelberg University, Heidelberg, Germany
| | - Igor Boettcher
- Department of Physics, Simon Fraser University, Burnaby, BC, Canada
| | - Tilman Enss
- Institute for Theoretical Physics, Heidelberg University, Heidelberg, Germany
| | - Marvin Holten
- Physics Institute, Heidelberg University, Heidelberg, Germany
| | - Gerhard Zürn
- Physics Institute, Heidelberg University, Heidelberg, Germany
| | | | - Selim Jochim
- Physics Institute, Heidelberg University, Heidelberg, Germany
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Luciuk C, Smale S, Böttcher F, Sharum H, Olsen BA, Trotzky S, Enss T, Thywissen JH. Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases. PHYSICAL REVIEW LETTERS 2017; 118:130405. [PMID: 28409948 DOI: 10.1103/physrevlett.118.130405] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2016] [Indexed: 06/07/2023]
Abstract
We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.
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Affiliation(s)
- C Luciuk
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
| | - S Smale
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
| | - F Böttcher
- 5. Physikalisches Institut and Centre for Integrated Quantum Science and Technology, Universität Stuttgart, D-70569 Stuttgart, Germany
| | - H Sharum
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
| | - B A Olsen
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
| | - S Trotzky
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
| | - T Enss
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - J H Thywissen
- Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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Anderson ER, Drut JE. Pressure, compressibility, and contact of the two-dimensional attractive fermi gas. PHYSICAL REVIEW LETTERS 2015; 115:115301. [PMID: 26406837 DOI: 10.1103/physrevlett.115.115301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Indexed: 06/05/2023]
Abstract
Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e., Tan's contact) for a wide range of temperatures (mostly above the superfluid phase, including the pseudogap regime) and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.
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Affiliation(s)
- E R Anderson
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA
| | - J E Drut
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA
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Desbuquois R, Yefsah T, Chomaz L, Weitenberg C, Corman L, Nascimbène S, Dalibard J. Determination of scale-invariant equations of state without fitting parameters: application to the two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless transition. PHYSICAL REVIEW LETTERS 2014; 113:020404. [PMID: 25062145 DOI: 10.1103/physrevlett.113.020404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2014] [Indexed: 06/03/2023]
Abstract
We present a general "fit-free" method for measuring the equation of state (EoS) of a scale-invariant gas. This method, which is inspired from the procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary three-dimensional Fermi gas, provides a general formalism which can be readily applied to any quantum gas in a known trapping potential, in the frame of the local density approximation. We implement this method on a weakly interacting two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless transition and determine its EoS with unprecedented accuracy in the critical region. Our measurements provide an important experimental benchmark for classical-field approaches which are believed to accurately describe quantum systems in the weakly interacting but nonperturbative regime.
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Affiliation(s)
- Rémi Desbuquois
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Tarik Yefsah
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Lauriane Chomaz
- Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, F-75005 Paris, France and Collège de France, 11 Place Marcelin Berthelot, 75231 Paris Cedex 05, France
| | - Christof Weitenberg
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany
| | - Laura Corman
- Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, F-75005 Paris, France
| | - Sylvain Nascimbène
- Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, F-75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, F-75005 Paris, France and Collège de France, 11 Place Marcelin Berthelot, 75231 Paris Cedex 05, France
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Bauer M, Parish MM, Enss T. Universal equation of state and pseudogap in the two-dimensional Fermi gas. PHYSICAL REVIEW LETTERS 2014; 112:135302. [PMID: 24745434 DOI: 10.1103/physrevlett.112.135302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2013] [Indexed: 06/03/2023]
Abstract
We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.
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Affiliation(s)
| | - Meera M Parish
- London Centre for Nanotechnology, Gordon Street, London WC1H 0AH, United Kingdom
| | - Tilman Enss
- Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg, Germany
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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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12
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Zhang Y, Ong W, Arakelyan I, Thomas JE. Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas. PHYSICAL REVIEW LETTERS 2012; 108:235302. [PMID: 23003968 DOI: 10.1103/physrevlett.108.235302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2012] [Indexed: 06/01/2023]
Abstract
We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.
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Affiliation(s)
- Y Zhang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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Hofmann J. Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas. PHYSICAL REVIEW LETTERS 2012; 108:185303. [PMID: 22681087 DOI: 10.1103/physrevlett.108.185303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Indexed: 06/01/2023]
Abstract
In this Letter, we show that the classical SO(2,1) symmetry of a harmonically trapped Fermi gas in two dimensions is broken by quantum effects. The anomalous correction to the symmetry algebra is given by a two-body operator that is well known as the contact. Taking into account this modification, we are able to derive the virial theorem for the system and a universal relation for the pressure of a homogeneous gas. The existence of an undamped breathing mode is associated with the classical symmetry. We provide an estimate for the anomalous frequency shift of this oscillation at zero temperature and compare the result with a recent experiment by [E. Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)]. Discrepancies are attributed to finite temperature effects.
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Affiliation(s)
- Johannes Hofmann
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Cambridge CB3 0WA, United Kingdom.
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