1
|
Miotti M, Martins EB, Hemmerling M, Bagnato VS. The Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method. ENTROPY (BASEL, SWITZERLAND) 2024; 26:658. [PMID: 39202128 PMCID: PMC11353380 DOI: 10.3390/e26080658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2024] [Revised: 07/26/2024] [Accepted: 07/30/2024] [Indexed: 09/03/2024]
Abstract
Quantum thermal engines have received much attention in recent years due to their potential applications. For a candidate group, harmonically trapped gases under Bose-Einstein condensation (BEC), we see little investigation on the energy transference around that transition. Therefore, we present an empirical study with rubidium-87 gas samples in a magnetic harmonic trap. We developed an empirical equation of state model to fit to our experimental dataset, expressing the pressure parameter in terms of temperature, and six technical coefficients, functions of the volume parameter and the number of atoms. By using standard thermodynamic relations, we determine the system's entropy, shown to be constant at the BEC transition, as expected. Being isentropic makes the BEC transition an energy source for non-mechanical work. Hence, we observed that the enthalpy at the BEC transition, at fixed values of the volume parameter, grows fairly linearly with the number of atoms. We fitted a linear function to that data, finding the specific enthalpy of the BEC transformation and the intrinsic enthalpic loss for BEC. We deem this study to be a step closer to practical quantum-based engines.
Collapse
Affiliation(s)
- Marcos Miotti
- São Carlos Institute of Physics, University of São Paulo, São Carlos 13566-590, Brazil (V.S.B.)
| | - Edmur Braga Martins
- São Carlos Institute of Physics, University of São Paulo, São Carlos 13566-590, Brazil (V.S.B.)
| | - Michał Hemmerling
- São Carlos Institute of Physics, University of São Paulo, São Carlos 13566-590, Brazil (V.S.B.)
| | - Vanderlei Salvador Bagnato
- São Carlos Institute of Physics, University of São Paulo, São Carlos 13566-590, Brazil (V.S.B.)
- Biomedical Engineering Department, Texas A&M University, College Station, TX 77843, USA
| |
Collapse
|
2
|
Morrell KJ, Czejdo AJ, Carter N, Drut JE. Thermodynamics of spin-1/2 fermions on coarse temporal lattices using automated algebra. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230113. [PMID: 38910401 DOI: 10.1098/rsta.2023.0113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/12/2023] [Indexed: 06/25/2024]
Abstract
Recent advances in automated algebra for dilute Fermi gases in the virial expansion, where coarse temporal lattices were found advantageous, motivate the study of more general computational schemes that could be applied to arbitrary densities, beyond the dilute limit where the virial expansion is physically reasonable. We propose here such an approach by developing what we call the Quantum Thermodynamics Computational Engine (QTCE). In QTCE, the imaginary-time direction is discretized and the interaction is accounted for via a quantum cumulant expansion, where the coefficients are expressed in terms of non-interacting expectation values. The aim of QTCE is to enable the systematic resolution of interaction effects at fixed temporal discretization, as in lattice Monte Carlo calculations, but here in an algebraic rather than numerical fashion. Using this approach, in combination with numerical integration techniques (both known and alternative ones proposed here), we explore the thermodynamics of spin-1/2 fermions across spatial dimensions, focusing on the unitary limit. We find that, remarkably, extremely coarse temporal lattices, when suitably renormalized using known results from the virial expansion, yield stable partial sums for QTCE's cumulant expansion that are qualitatively and quantitatively correct in wide regions (when compared with known experimental results). This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.
Collapse
Affiliation(s)
- K J Morrell
- Department of Physics and Astronomy, University of North Carolina , Chapel Hill, NC 27599, USA
| | - A J Czejdo
- Department of Physics and Astronomy, University of North Carolina , Chapel Hill, NC 27599, USA
| | - N Carter
- Department of Computer Science, University of North Carolina , Chapel Hill, NC 27599, USA
| | - J E Drut
- Department of Physics and Astronomy, University of North Carolina , Chapel Hill, NC 27599, USA
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
Pasqualetti G, Bettermann O, Darkwah Oppong N, Ibarra-García-Padilla E, Dasgupta S, Scalettar RT, Hazzard KRA, Bloch I, Fölling S. Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2024; 132:083401. [PMID: 38457712 DOI: 10.1103/physrevlett.132.083401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 01/09/2024] [Indexed: 03/10/2024]
Abstract
We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.
Collapse
Affiliation(s)
- G Pasqualetti
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - O Bettermann
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - N Darkwah Oppong
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - E Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
| | - S Dasgupta
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - K R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
| | - I Bloch
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - S Fölling
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| |
Collapse
|
5
|
Cong X, Mohammadi PA, Zheng M, Watanabe K, Taniguchi T, Rhodes D, Zhang XX. Interplay of valley polarized dark trion and dark exciton-polaron in monolayer WSe 2. Nat Commun 2023; 14:5657. [PMID: 37704654 PMCID: PMC10500002 DOI: 10.1038/s41467-023-41475-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2023] [Accepted: 09/06/2023] [Indexed: 09/15/2023] Open
Abstract
The interactions between charges and excitons involve complex many-body interactions at high densities. The exciton-polaron model has been adopted to understand the Fermi sea screening of charged excitons in monolayer transition metal dichalcogenides. The results provide good agreement with absorption measurements, which are dominated by dilute bright exciton responses. Here we investigate the Fermi sea dressing of spin-forbidden dark excitons in monolayer WSe2. With a Zeeman field, the valley-polarized dark excitons show distinct p-doping dependence in photoluminescence when the carriers reach a critical density. This density can be interpreted as the onset of strongly modified Fermi sea interactions and shifts with increasing exciton density. Through valley-selective excitation and dynamics measurements, we also infer an intervalley coupling between the dark trions and exciton-polarons mediated by the many-body interactions. Our results reveal the evolution of Fermi sea screening with increasing exciton density and the impacts of polaron-polaron interactions, which lay the foundation for understanding electronic correlations and many-body interactions in 2D systems.
Collapse
Affiliation(s)
- Xin Cong
- Department of Physics, University of Florida, Gainesville, FL, USA
| | | | - Mingyang Zheng
- Department of Physics, University of Florida, Gainesville, FL, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan
| | - Daniel Rhodes
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Xiao-Xiao Zhang
- Department of Physics, University of Florida, Gainesville, FL, USA.
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Abstract
Interactions between quasiparticles are of fundamental importance and ultimately determine the macroscopic properties of quantum matter. A famous example is the phenomenon of superconductivity, which arises from attractive electron-electron interactions that are mediated by phonons or even other more exotic fluctuations in the material. Here we introduce mobile exciton impurities into a two-dimensional electron gas and investigate the interactions between the resulting Fermi polaron quasiparticles. We employ multi-dimensional coherent spectroscopy on monolayer WS2, which provides an ideal platform for determining the nature of polaron-polaron interactions due to the underlying trion fine structure and the valley specific optical selection rules. At low electron doping densities, we find that the dominant interactions are between polaron states that are dressed by the same Fermi sea. In the absence of bound polaron pairs (bipolarons), we show using a minimal microscopic model that these interactions originate from a phase-space filling effect, where excitons compete for the same electrons. We furthermore reveal the existence of a bipolaron bound state with remarkably large binding energy, involving excitons in different valleys cooperatively bound to the same electron. Our work lays the foundation for probing and understanding strong electron correlation effects in two-dimensional layered structures such as moiré superlattices. Here, the authors investigate the interactions between Fermi polarons in monolayer WS2 by multi-dimensional coherent spectroscopy, and find that, at low electron doping densities, the dominant interactions are between polaron states that are dressed by the same Fermi sea. They also observe a bipolaron bound state with large binding energy, involving excitons in different valleys cooperatively bound to the same electron.
Collapse
|
8
|
Abstract
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
Collapse
|
9
|
Luo HQ, Xu YY, Chen XK, Zhang H, Deng XB, Mao DK, Zhou MK, Duan XC, Hu ZK. Characterizing atom clouds using a charge-coupled device for atom-interferometry-based G measurements. OPTICS EXPRESS 2022; 30:10723-10731. [PMID: 35473032 DOI: 10.1364/oe.454660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
Precise information of positions and sizes of atom clouds is required for atom-interferometry-based G measurements. In this work, characterizing atom clouds using a charge-coupled device (CCD) is presented. The parameters of atom clouds are extracted from fluorescence images captured by the CCD. For characterization, in-situ calibration of the magnification of the imaging system is implemented using the free-fall distance of atom clouds as the dimension reference. Moreover, influence of the probe beam on measuring the positions of atom clouds is investigated, and a differential measurement by reversing the direction of the probe beam is proposed to suppress the influence. Finally, precision at sub-mm level for characterizing atom clouds is achieved.
Collapse
|
10
|
Biss H, Sobirey L, Luick N, Bohlen M, Kinnunen JJ, Bruun GM, Lompe T, Moritz H. Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas. PHYSICAL REVIEW LETTERS 2022; 128:100401. [PMID: 35333076 DOI: 10.1103/physrevlett.128.100401] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
Collapse
Affiliation(s)
- Hauke Biss
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Lennart Sobirey
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Niclas Luick
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Bohlen
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jami J Kinnunen
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
| | - Georg M Bruun
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Thomas Lompe
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Henning Moritz
- Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
11
|
Li X, Luo X, Wang S, Xie K, Liu XP, Hu H, Chen YA, Yao XC, Pan JW. Second sound attenuation near quantum criticality. Science 2022; 375:528-533. [PMID: 35113717 DOI: 10.1126/science.abi4480] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Second sound attenuation, a distinctive dissipative hydrodynamic phenomenon in a superfluid, is crucial for understanding superfluidity and elucidating critical phenomena. Here, we report the observation of second sound attenuation in a homogeneous Fermi gas of lithium-6 atoms at unitarity by performing Bragg spectroscopy with high energy resolution in the long-wavelength limit. We successfully obtained the temperature dependence of second sound diffusivity [Formula: see text] and thermal conductivity κ. Furthermore, we observed a sudden rise-a precursor of critical divergence-in both [Formula: see text] and κ at a temperature of about 0.95 superfluid transition temperature [Formula: see text]. This suggests that the unitary Fermi gas has a much larger critical region than does liquid helium. Our results pave the way for determining the universal critical scaling functions near quantum criticality.
Collapse
Affiliation(s)
- Xi Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiang Luo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Shuai Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ke Xie
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiang-Pei Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Hui Hu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Centre for Quantum Technology Theory, Swinburne University of Technology, Melbourne, VIC 3122, Australia
| | - Yu-Ao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xing-Can Yao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.,Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.,Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| |
Collapse
|
12
|
Toward an Automated-Algebra Framework for High Orders in the Virial Expansion of Quantum Matter. CONDENSED MATTER 2022. [DOI: 10.3390/condmat7010013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order n requires analyzing (if not solving) the quantum n-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems and explain how to generalize them to other observables such as the momentum distribution, Tan contact, and the structure factor.
Collapse
|
13
|
Hoffmann DK, Singh VP, Paintner T, Jäger M, Limmer W, Mathey L, Hecker Denschlag J. Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid. Nat Commun 2021; 12:7074. [PMID: 34873169 PMCID: PMC8648831 DOI: 10.1038/s41467-021-27149-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 10/26/2021] [Indexed: 11/28/2022] Open
Abstract
Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.
Collapse
Affiliation(s)
- Daniel K Hoffmann
- Institut für Quantenmaterie and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069, Ulm, Germany
| | - Vijay Pal Singh
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
- Institut für Laserphysik, Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761, Hamburg, Germany
| | - Thomas Paintner
- Institut für Quantenmaterie and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069, Ulm, Germany
| | - Manuel Jäger
- Institut für Quantenmaterie and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069, Ulm, Germany
| | - Wolfgang Limmer
- Institut für Quantenmaterie and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069, Ulm, Germany
| | - Ludwig Mathey
- Institut für Laserphysik, Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761, Hamburg, Germany
- The Hamburg center for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany
| | - Johannes Hecker Denschlag
- Institut für Quantenmaterie and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069, Ulm, Germany.
| |
Collapse
|
14
|
De Daniloff C, Tharrault M, Enesa C, Salomon C, Chevy F, Reimann T, Struck J. In Situ Thermometry of Fermionic Cold-Atom Quantum Wires. PHYSICAL REVIEW LETTERS 2021; 127:113602. [PMID: 34558929 DOI: 10.1103/physrevlett.127.113602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 08/02/2021] [Indexed: 06/13/2023]
Abstract
We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature T/T_{F} at nearly constant entropy per particle S/Nk_{B}. The ability to probe individual atomic wires in situ paves the way to quantitatively study equilibrium and transport properties of strongly interacting 1D Fermi gases.
Collapse
Affiliation(s)
- Clément De Daniloff
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Marin Tharrault
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Cédric Enesa
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Christophe Salomon
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Frédéric Chevy
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Thomas Reimann
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| | - Julian Struck
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 rue Lhomond, 75005 Paris, France
| |
Collapse
|
15
|
Azadi S, Drummond ND, Foulkes WMC. Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo. PHYSICAL REVIEW LETTERS 2021; 127:086401. [PMID: 34477398 DOI: 10.1103/physrevlett.127.086401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.
Collapse
Affiliation(s)
- Sam Azadi
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - W M C Foulkes
- Department of Physics and the Thomas Young Centre for Theory and Simulation of Materials, South Kensington Campus, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
16
|
Long Y, Xiong F, Parker CV. Spin Susceptibility above the Superfluid Onset in Ultracold Fermi Gases. PHYSICAL REVIEW LETTERS 2021; 126:153402. [PMID: 33929234 DOI: 10.1103/physrevlett.126.153402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Revised: 10/01/2020] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
Ultracold atomic Fermi gases can be tuned to interact strongly, which produces a display of spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned since many thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radio frequency technique with ultracold ^{6}Li gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared to the equivalent value for a noninteracting Fermi gas. At unitarity, we can use the local density approximation to extract the integrated spin susceptibility for the uniform gas as a function of temperature, which at high temperatures is generally less than theoretically predicted. At low temperatures, our data lie within the range of theoretical predictions, although we can also describe the entire curve using a very simple one-parameter mean field model with monotonically increasing spin susceptibility.
Collapse
Affiliation(s)
- Yun Long
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Feng Xiong
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Colin V Parker
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| |
Collapse
|
17
|
Del Pace G, Kwon WJ, Zaccanti M, Roati G, Scazza F. Tunneling Transport of Unitary Fermions across the Superfluid Transition. PHYSICAL REVIEW LETTERS 2021; 126:055301. [PMID: 33605753 DOI: 10.1103/physrevlett.126.055301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
We investigate the transport of a Fermi gas with unitarity-limited interactions across the superfluid phase transition, probing its response to a direct current (dc) drive through a tunnel junction. As the superfluid critical temperature is crossed from below, we observe the evolution from a highly nonlinear to an Ohmic conduction characteristic, associated with the critical breakdown of the Josephson dc current induced by pair condensate depletion. Moreover, we reveal a large and dominant anomalous contribution to resistive currents, which reaches its maximum at the lowest attained temperature, fostered by the tunnel coupling between the condensate and phononic Bogoliubov-Anderson excitations. Increasing the temperature, while the zeroing of supercurrents marks the transition to the normal phase, the conductance drops considerably but remains much larger than that of a normal, uncorrelated Fermi gas tunneling through the same junction. We attribute such enhanced transport to incoherent tunneling of sound modes, which remain weakly damped in the collisional hydrodynamic fluid of unpaired fermions at unitarity.
Collapse
Affiliation(s)
- G Del Pace
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
| | - W J Kwon
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
| | - M Zaccanti
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
| | - G Roati
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
| | - F Scazza
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
| |
Collapse
|
18
|
Abstract
Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with the T-matrix theory used in the physics of ultracold atoms, which we generalize to the case of a non-separable finite-range interaction. A problem of the standard Nozières–Schmitt-Rink approach and different ways to solve it are discussed. It is shown that in the strong-coupling regime, the spectral function exhibits a pseudo-gap at temperatures above the critical temperature Tc. The effect of the correlated density on the density dependence of Tc is found to be rather weak, but a possibly important effect due to the reduced quasiparticle weight is identified.
Collapse
|
19
|
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.
Collapse
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
| |
Collapse
|
20
|
Hartke T, Oreg B, Jia N, Zwierlein M. Doublon-Hole Correlations and Fluctuation Thermometry in a Fermi-Hubbard Gas. PHYSICAL REVIEW LETTERS 2020; 125:113601. [PMID: 32975995 DOI: 10.1103/physrevlett.125.113601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 07/19/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the single atom and single site-resolved detection of the total density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence imaging of doublons is achieved by splitting each lattice site into a double well, thereby separating atom pairs. Full density readout yields a direct measurement of the equation of state, including direct thermometry via the fluctuation-dissipation theorem. Site-resolved density correlations reveal the Pauli hole at low filling, and strong doublon-hole correlations near half filling. These are shown to account for the difference between local and nonlocal density fluctuations in the Mott insulator. Our technique enables the study of atom-resolved charge transport in the Fermi-Hubbard model, the site-resolved observation of molecules, and the creation of bilayer Fermi-Hubbard systems.
Collapse
Affiliation(s)
- Thomas Hartke
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Botond Oreg
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ningyuan Jia
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Martin Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
21
|
Mitchison MT, Fogarty T, Guarnieri G, Campbell S, Busch T, Goold J. In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities. PHYSICAL REVIEW LETTERS 2020; 125:080402. [PMID: 32909771 DOI: 10.1103/physrevlett.125.080402] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 07/27/2020] [Indexed: 06/11/2023]
Abstract
The precise measurement of low temperatures is a challenging, important, and fundamental task for quantum science. In particular, in situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here, we demonstrate that the temperature of a noninteracting Fermi gas can be accurately inferred from the nonequilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity.
Collapse
Affiliation(s)
- Mark T Mitchison
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Giacomo Guarnieri
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| |
Collapse
|
22
|
He L, Gao P, Yu ZQ. Normal-Superfluid Phase Separation in Spin-Half Bosons at Finite Temperature. PHYSICAL REVIEW LETTERS 2020; 125:055301. [PMID: 32794831 DOI: 10.1103/physrevlett.125.055301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2019] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
For pseudospin-half bosons with interspin attraction and intraspin repulsion, the normal phase and Bose condensed phase can coexist at finite temperature. The homogeneous system is unstable against the spinodal decomposition within a medium density interval, and, consequently, a normal-superfluid phase separation takes place. The isothermal equation of state shows a characteristic plateau in the P-V (pressure-volume) diagram, which is reminiscent of a classical gas-liquid transition, although, unlike the latter, the coexistence lines never terminate at a critical point as temperature increases. In a harmonic trap, the phase separation can be revealed by the density profile of the atomic cloud, which exhibits a sudden jump across the phase boundary.
Collapse
Affiliation(s)
- Li He
- College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
| | - Peipei Gao
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
| | - Zeng-Qiang Yu
- Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
| |
Collapse
|
23
|
Hou Y, Drut JE. Fourth- and Fifth-Order Virial Coefficients from Weak Coupling to Unitarity. PHYSICAL REVIEW LETTERS 2020; 125:050403. [PMID: 32794845 DOI: 10.1103/physrevlett.125.050403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
In the current era of precision quantum many-body physics, one of the most scrutinized systems is the unitary limit of the nonrelativistic spin-1/2 Fermi gas, due to its simplicity and relevance for atomic, condensed matter, and nuclear physics. The thermodynamics of this strongly correlated system is determined by universal functions which, at high temperatures, are governed by universal virial coefficients b_{n} that capture the effects of the n-body system on the many-body dynamics. Currently, b_{2} and b_{3} are well understood, but the situation is less clear for b_{4}, and no predictions have been made for b_{5}. To answer these open questions, we implement a nonperturbative analytic approach based on the Trotter-Suzuki factorization of the imaginary-time evolution operator, using progressively finer temporal lattice spacings. By means of these factorizations and automated algebra codes, we obtain the interaction-induced change Δb_{n} from weak coupling to unitarity. At unitarity, we find that Δb_{3}=-0.356(4) in agreement with previous results, Δb_{4}=0.062(2), which is in agreement with all previous theoretical estimates but at odds with experimental determinations, and Δb_{5}=0.078(6), which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and trace their origin back to their polarized and unpolarized components.
Collapse
Affiliation(s)
- Y Hou
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - J E Drut
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| |
Collapse
|
24
|
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.
Collapse
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
| |
Collapse
|
25
|
Kurkjian H, Tempere J, Klimin SN. Linear response of a superfluid Fermi gas inside its pair-breaking continuum. Sci Rep 2020; 10:11591. [PMID: 32665570 PMCID: PMC7360786 DOI: 10.1038/s41598-020-65371-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 04/20/2020] [Indexed: 11/09/2022] Open
Abstract
We study the signatures of the collective modes of a superfluid Fermi gas in its linear response functions for the order-parameter and density fluctuations in the Random Phase Approximation (RPA). We show that a resonance associated to the Popov-Andrianov (or sometimes "Higgs") mode is visible inside the pair-breaking continuum at all values of the wavevector q, not only in the (order-parameter) modulus-modulus response function but also in the modulus-density and density-density responses. At nonzero temperature, the resonance survives in the presence of thermally broken pairs even until the vicinity of the critical temperature Tc, and coexists with both the Anderson-Bogoliubov modes at temperatures comparable to the gap Δ and with the low-velocity phononic mode predicted by RPA near Tc. The existence of a Popov-Andrianov-"Higgs" resonance is thus a robust, generic feature of the high-energy phenomenology of pair-condensed Fermi gases, and should be accessible to state-of-the-art cold atom experiments.
Collapse
Affiliation(s)
- H Kurkjian
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610, Antwerp, Belgium.
| | - J Tempere
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610, Antwerp, Belgium
| | - S N Klimin
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610, Antwerp, Belgium
| |
Collapse
|
26
|
Roux K, Konishi H, Helson V, Brantut JP. Strongly correlated Fermions strongly coupled to light. Nat Commun 2020; 11:2974. [PMID: 32532985 PMCID: PMC7293285 DOI: 10.1038/s41467-020-16767-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 05/20/2020] [Indexed: 11/17/2022] Open
Abstract
Strong quantum correlations in matter are responsible for some of the most extraordinary properties of materials, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interactions, have thus far been strongly coupled with photons. Here we report on the strong coupling of a quantum-degenerate unitary Fermi gas with light in a high finesse cavity. We map out the spectrum of the coupled system and observe well resolved dressed states, resulting from the strong coupling of cavity photons with each spin component of the gas. We investigate spin-balanced and spin-polarized gases and find quantitative agreement with ab initio calculation describing light-matter interaction. Our system offers complete and simultaneous control of atom-atom and atom-photon interactions in the quantum degenerate regime, opening a wide range of perspectives for quantum simulation.
Collapse
Affiliation(s)
- Kevin Roux
- Institute of Physics, EPFL, 1015, Lausanne, Switzerland
| | | | - Victor Helson
- Institute of Physics, EPFL, 1015, Lausanne, Switzerland
| | | |
Collapse
|
27
|
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.
Collapse
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
| |
Collapse
|
28
|
Jensen S, Gilbreth CN, Alhassid Y. Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas. PHYSICAL REVIEW LETTERS 2020; 124:090604. [PMID: 32202890 DOI: 10.1103/physrevlett.124.090604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2018] [Revised: 06/17/2019] [Accepted: 01/17/2020] [Indexed: 06/10/2023]
Abstract
In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature T_{c} and a temperature T^{*}>T_{c}. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor ν≃0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate T_{c} at the corresponding filling factor. We find that the energy-staggering pairing gap vanishes above T_{c}, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.
Collapse
Affiliation(s)
- S Jensen
- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA
| | - C N Gilbreth
- Institute for Nuclear Theory, Box 351550, University of Washington, Seattle, Washington 98195, USA
| | - Y Alhassid
- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
29
|
Oscillatory-like expansion of a Fermionic superfluid. Sci Bull (Beijing) 2020; 65:7-11. [PMID: 36659071 DOI: 10.1016/j.scib.2019.10.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Revised: 09/25/2019] [Accepted: 10/14/2019] [Indexed: 01/21/2023]
Abstract
We study the expansion behaviors of a Fermionic superfluid in a cigar-shaped optical dipole trap for the whole BEC-BCS crossover and various temperatures. At low temperature (0.06(1)TF), the atom cloud undergoes an anisotropic hydrodynamic expansion over 30 ms, which behaves like oscillation in the horizontal plane. By analyzing the expansion dynamics according to the superfluid hydrodynamic equation, the effective polytropic index γ¯ of Equation-of-State (EoS) of Fermionic superfluid is extracted. The γ¯ values show a non-monotonic behavior over the BEC-BCS crossover, and have a good agreement with the theoretical results in the unitarity and BEC side. The normalized quasi-frequencies of the oscillatory expansion are measured, which drop significantly from the BEC side to the BCS side and reach a minimum value of 1.73 around 1/kFa=-0.25. Our work improves the understanding of the dynamic properties of strongly interacting Fermi gas.
Collapse
|
30
|
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.
Collapse
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
| |
Collapse
|
31
|
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.
Collapse
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
| |
Collapse
|
32
|
Yan Z, Patel PB, Mukherjee B, Fletcher RJ, Struck J, Zwierlein MW. Boiling a Unitary Fermi Liquid. PHYSICAL REVIEW LETTERS 2019; 122:093401. [PMID: 30932518 DOI: 10.1103/physrevlett.122.093401] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2018] [Indexed: 06/09/2023]
Abstract
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T^{2} dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝T^{-1/2}. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.
Collapse
Affiliation(s)
- Zhenjie Yan
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Parth B Patel
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Biswaroop Mukherjee
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Richard J Fletcher
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Julian Struck
- MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, 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, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
33
|
Hu H, Mulkerin BC, Toniolo U, He L, Liu XJ. Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions. PHYSICAL REVIEW LETTERS 2019; 122:070401. [PMID: 30848610 DOI: 10.1103/physrevlett.122.070401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Indexed: 06/09/2023]
Abstract
A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.
Collapse
Affiliation(s)
- Hui Hu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - Brendan C Mulkerin
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - Umberto Toniolo
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| | - Lianyi He
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Xia-Ji Liu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
| |
Collapse
|
34
|
Rammelmüller L, Loheac AC, Drut JE, Braun J. Finite-Temperature Equation of State of Polarized Fermions at Unitarity. PHYSICAL REVIEW LETTERS 2018; 121:173001. [PMID: 30411942 DOI: 10.1103/physrevlett.121.173001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Indexed: 06/08/2023]
Abstract
We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order virial expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization.
Collapse
Affiliation(s)
- Lukas Rammelmüller
- Institut für Kernphysik (Theoriezentrum), Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, D-64291 Darmstadt, Germany
| | - Andrew C Loheac
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Joaquín E Drut
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Jens Braun
- Institut für Kernphysik (Theoriezentrum), Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- FAIR, Facility for Antiproton and Ion Research in Europe GmbH, Planckstraße 1, D-64291 Darmstadt, Germany
- ExtreMe Matter Institute EMMI, GSI, Planckstraße 1, D-64291 Darmstadt, Germany
| |
Collapse
|
35
|
Rossi R, Ohgoe T, Van Houcke K, Werner F. Resummation of Diagrammatic Series with Zero Convergence Radius for Strongly Correlated Fermions. PHYSICAL REVIEW LETTERS 2018; 121:130405. [PMID: 30312043 DOI: 10.1103/physrevlett.121.130405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Revised: 07/26/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate that a summing up series of Feynman diagrams can yield unbiased accurate results for strongly correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of nonrelativistic fermions in three-dimensional continuous space. Diagrams are built from partially dressed or fully dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.
Collapse
Affiliation(s)
- R Rossi
- Laboratoire de Physique Statistique, Ecole Normale Supérieure-Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, 75005 Paris, France
| | - T Ohgoe
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - K Van Houcke
- Laboratoire de Physique Statistique, Ecole Normale Supérieure-Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, 75005 Paris, France
| | - F Werner
- Laboratoire Kastler Brossel, Ecole Normale Supérieure-Université PSL, CNRS, Sorbonne Université, Collège de France, 75005 Paris, France
| |
Collapse
|
36
|
Abstract
We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a nonequilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we extract the transport coefficients of the QPC and deduce a Lorenz number violating the Wiedemann-Franz law by one order of magnitude, a characteristic persisting even for a wide contact. In contrast, the Seebeck coefficient takes a value close to that expected for a noninteracting Fermi gas and shows a smooth decrease as the atom density close to the QPC is increased beyond the superfluid transition. Our work represents a fermionic analog of the fountain effect observed with superfluid helium and poses challenges for microscopic modeling of the finite temperature dynamics of the unitary Fermi gas.
Collapse
|
37
|
Kinnunen JJ, Baarsma JE, Martikainen JP, Törmä P. The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:046401. [PMID: 29293087 DOI: 10.1088/1361-6633/aaa4ad] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.
Collapse
Affiliation(s)
- Jami J Kinnunen
- COMP Center of Excellence, Department of Applied Physics, Aalto University, Fi-00076, Aalto, Finland
| | | | | | | |
Collapse
|
38
|
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.
Collapse
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.
| |
Collapse
|
39
|
He L, Hu H, Liu XJ. Realizing Fulde-Ferrell Superfluids via a Dark-State Control of Feshbach Resonances. PHYSICAL REVIEW LETTERS 2018; 120:045302. [PMID: 29437455 DOI: 10.1103/physrevlett.120.045302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2017] [Indexed: 06/08/2023]
Abstract
We propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of ^{40}K or ^{6}Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superfluidity. We develop a field theoretical formulation for both two-body and many-body problems and predict that the Fulde-Ferrell state has remarkable properties, such as anisotropic single-particle dispersion relation, suppressed superfluid density at zero temperature, anisotropic sound velocity, and rotonic collective mode. The latter two features can be experimentally probed using Bragg spectroscopy, providing a smoking-gun proof of Fulde-Ferrell superfluidity.
Collapse
Affiliation(s)
- Lianyi He
- Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
| | - Hui Hu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
| | - Xia-Ji Liu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
| |
Collapse
|
40
|
Castin Y, Sinatra A, Kurkjian H. Landau Phonon-Roton Theory Revisited for Superfluid ^{4}He and Fermi Gases. PHYSICAL REVIEW LETTERS 2017; 119:260402. [PMID: 29328691 DOI: 10.1103/physrevlett.119.260402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2017] [Indexed: 06/07/2023]
Abstract
Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending the theory of Landau and Khalatnikov initially developed for helium [Zh. Exp. Teor. Fiz. 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.
Collapse
Affiliation(s)
- Yvan Castin
- Laboratoire Kastler Brossel, ENS-PSL, CNRS, Sorbonne Universités, Collège de France, 75005 Paris, France
| | - Alice Sinatra
- Laboratoire Kastler Brossel, ENS-PSL, CNRS, Sorbonne Universités, Collège de France, 75005 Paris, France
| | - Hadrien Kurkjian
- TQC, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerp, Belgium
| |
Collapse
|
41
|
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.
Collapse
Affiliation(s)
- Erich J Mueller
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca NY 14853, United States of America
| |
Collapse
|
42
|
Krinner S, Esslinger T, Brantut JP. Two-terminal transport measurements with cold atoms. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:343003. [PMID: 28749788 DOI: 10.1088/1361-648x/aa74a1] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.
Collapse
Affiliation(s)
- Sebastian Krinner
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | | | | |
Collapse
|
43
|
Bluhm M, Hou J, Schäfer T. Determination of the Density and Temperature Dependence of the Shear Viscosity of a Unitary Fermi Gas Based on Hydrodynamic Flow. PHYSICAL REVIEW LETTERS 2017; 119:065302. [PMID: 28949627 DOI: 10.1103/physrevlett.119.065302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2017] [Indexed: 06/07/2023]
Abstract
We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.
Collapse
Affiliation(s)
- Marcus Bluhm
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
- Institute of Theoretical Physics, University of Wrocław, 50204 Wrocław, Poland
| | - Jiaxun Hou
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Thomas Schäfer
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| |
Collapse
|
44
|
Lingua F, Capogrosso-Sansone B, Minardi F, Penna V. Thermometry of bosonic mixtures in Optical Lattices via Demixing. Sci Rep 2017; 7:5105. [PMID: 28698563 PMCID: PMC5506072 DOI: 10.1038/s41598-017-05353-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2017] [Accepted: 05/26/2017] [Indexed: 11/16/2022] Open
Abstract
Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected.
Collapse
Affiliation(s)
- F Lingua
- Department of Applied Science and Technology and u.d.r. CNISM, Politecnico di Torino, I-10129, Torino, Italy.
| | | | - F Minardi
- Istituto Nazionale di Ottica (INO-CNR), I-50019 Sesto Fiorentino, Italy.,European Laboratory for Non-Linear Spectroscopy (LENS) and Dipartimento di Fisica, Università di Firenze, I-50019, Sesto Fiorentino, Italy
| | - V Penna
- Department of Applied Science and Technology and u.d.r. CNISM, Politecnico di Torino, I-10129, Torino, Italy
| |
Collapse
|
45
|
Krauser JS, Heinze J, Götze S, Langbecker M, Fläschner N, Cook L, Hanna TM, Tiesinga E, Sengstock K, Becker C. Investigation of Feshbach resonances in ultracold 40K spin mixtures. PHYSICAL REVIEW. A 2017; 95:042701. [PMID: 29876533 PMCID: PMC5986192 DOI: 10.1103/physreva.95.042701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Magnetically tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on 37 thus far unpublished Feshbach resonances and four further probable Feshbach resonances in spin mixtures of ultracold fermionic 40K with temperatures well below 100 nK. In particular, we locate a broad resonance at B = 389.7G with a magnetic width of 26.7 G. Here 1 G = 10-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40K quantum gases.
Collapse
Affiliation(s)
- J. S. Krauser
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - J. Heinze
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S. Götze
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - M. Langbecker
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Institut für Physik, Johannes Gutenberg Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - N. Fläschner
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - L. Cook
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - T. M. Hanna
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, Gaithersburg, Maryland 20899, USA
| | - E. Tiesinga
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, Gaithersburg, Maryland 20899, USA
| | - K. Sengstock
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - C. Becker
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
46
|
Mukherjee B, Yan Z, Patel PB, Hadzibabic Z, Yefsah T, Struck J, Zwierlein MW. Homogeneous Atomic Fermi Gases. PHYSICAL REVIEW LETTERS 2017; 118:123401. [PMID: 28388181 DOI: 10.1103/physrevlett.118.123401] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2016] [Indexed: 06/07/2023]
Abstract
We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.
Collapse
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
| | - Zhenjie Yan
- 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
| | - Zoran Hadzibabic
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Tarik Yefsah
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Laboratoire Kastler Brossel, CNRS, ENS-PSL Research University, UPMC-Sorbonne Universités and Collège de France, Paris 75005, France
| | - Julian Struck
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - 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
| |
Collapse
|
47
|
Giant superconducting fluctuations in the compensated semimetal FeSe at the BCS-BEC crossover. Nat Commun 2016; 7:12843. [PMID: 27687782 PMCID: PMC5056430 DOI: 10.1038/ncomms12843] [Citation(s) in RCA: 81] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2016] [Accepted: 08/03/2016] [Indexed: 11/24/2022] Open
Abstract
The physics of the crossover between weak-coupling Bardeen–Cooper–Schrieffer (BCS) and strong-coupling Bose–Einstein condensate (BEC) limits gives a unified framework of quantum-bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature Tc=8.5 K has been found to be deep inside the BCS–BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large non-linear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below T*∼20 K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance and transport data give evidence of pseudogap formation at ∼T*. The multiband superconductivity along with electron–hole compensation in FeSe may highlight a novel aspect of the BCS–BEC crossover physics. The crossover between the weak-coupling limit and strong-coupling limit provides important information for quantum bound states of interacting fermions. Here, Kasahara et al. report thermodynamic evidence for prevailing phase fluctuations of superconductivity, highlighting unusual normal state in the BCS-BEC crossover regime.
Collapse
|
48
|
Mitra D, Brown PT, Schauß P, Kondov SS, Bakr WS. Phase Separation and Pair Condensation in a Spin-Imbalanced 2D Fermi Gas. PHYSICAL REVIEW LETTERS 2016; 117:093601. [PMID: 27610853 DOI: 10.1103/physrevlett.117.093601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2016] [Indexed: 06/06/2023]
Abstract
We study a two-component quasi-two-dimensional Fermi gas with imbalanced spin populations. We probe the gas at different interaction strengths and polarizations by measuring the density of each spin component in the trap and the pair momentum distribution after time of flight. For a wide range of experimental parameters, we observe in-trap phase separation characterized by the appearance of a spin-balanced core surrounded by a polarized gas. Our momentum space measurements indicate pair condensation in the imbalanced gas even for large polarizations where phase separation vanishes, pointing to the presence of a polarized pair condensate. Our observation of zero momentum pair condensates in 2D spin-imbalanced gases opens the way to explorations of more exotic superfluid phases that occupy a large part of the phase diagram in lower dimensions.
Collapse
Affiliation(s)
- Debayan Mitra
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Peter T Brown
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Peter Schauß
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Stanimir S Kondov
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
49
|
Deng S, Shi ZY, Diao P, Yu Q, Zhai H, Qi R, Wu H. Observation of the Efimovian expansion in scale-invariant Fermi gases. Science 2016; 353:371-4. [DOI: 10.1126/science.aaf0666] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2015] [Accepted: 06/21/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Shujin Deng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Zhe-Yu Shi
- Institute for Advanced Study, Tsinghua University, Beijing 100084, P. R. China
| | - Pengpeng Diao
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Qianli Yu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, P. R. China
| | - Ran Qi
- Department of Physics, Renmin University of China, Beijing 100872, P. R. China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, P. R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| |
Collapse
|
50
|
Yan Y, Blume D. Path-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range Interactions. PHYSICAL REVIEW LETTERS 2016; 116:230401. [PMID: 27341213 DOI: 10.1103/physrevlett.116.230401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2016] [Indexed: 06/06/2023]
Abstract
The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b_{4} of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b_{4}, our b_{4} agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.
Collapse
Affiliation(s)
- Yangqian Yan
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA
| | - D Blume
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, USA
| |
Collapse
|