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Link M, Gao K, Kell A, Breyer M, Eberz D, Rauf B, Köhl M. Machine Learning the Phase Diagram of a Strongly Interacting Fermi Gas. PHYSICAL REVIEW LETTERS 2023; 130:203401. [PMID: 37267577 DOI: 10.1103/physrevlett.130.203401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Accepted: 03/31/2023] [Indexed: 06/04/2023]
Abstract
We determine the phase diagram of strongly correlated fermions in the crossover from Bose-Einstein condensates of molecules (BEC) to Cooper pairs of fermions (BCS) utilizing an artificial neural network. By applying advanced image recognition techniques to the momentum distribution of the fermions, a quantity which has been widely considered as featureless for providing information about the condensed state, we measure the critical temperature and show that it exhibits a maximum on the bosonic side of the crossover. Additionally, we backanalyze the trained neural network and demonstrate that it interprets physically relevant quantities.
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Affiliation(s)
- M Link
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - K Gao
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - A Kell
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - M Breyer
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - D Eberz
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - B Rauf
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - M Köhl
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
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2
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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.
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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.
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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.
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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
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4
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Aftabi A, Mozaffari M. Fluctuation induced conductivity and pseudogap state studies of Bi 1.6Pb 0.4Sr 2Ca 2Cu 3O 10+δ superconductor added with ZnO nanoparticles. Sci Rep 2021; 11:4341. [PMID: 33619318 PMCID: PMC7900248 DOI: 10.1038/s41598-021-83218-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2020] [Accepted: 02/01/2021] [Indexed: 01/31/2023] Open
Abstract
The major limitations of the Bi1.6Pb0.4Sr2Ca2Cu3O10+δ superconductor are weak flux pinning capability and weak inter-grains coupling that lead to a low critical current density and low critical magnetic field which impedes the suppleness of this material towards practical applications. The addition of nanoscales impurities can create artificial pining centers that may improve flux pinning capability and intergranular coupling. In this work, the influences of ZnO nanoparticles on the superconducting parameters and pseudogap properties of the Bi1.6Pb0.4Sr2Ca2Cu3O10+δ superconductor are investigated using fluctuation induced conductivity analyses. Results demonstrate that the ZnO nanoparticles addition improves the formation of the Bi1.6Pb0.4Sr2Ca2Cu3O10+δ phase significantly. Various superconducting parameters include coherence length along c-axis (ξc(0)), penetration depth (λpd(0)), Fermi velocity (vF), Fermi energy (EF), lower and upper critical magnetic fields (Bc1(0) and Bc2(0) respectively) and critical current density (Jc(0)), are estimated for samples with different amounts of ZnO nanoparticles. It is found that the values of the Bc1(0), Bc2(0), and Jc(0) are improved significantly in the 0.2 wt% ZnO added sample in comparison to the ZnO-free sample. The magnitude and temperature dependence of the pseudogap Δ*(T) is calculated using the local pairs model. The obtained values of Tpair, the temperature at which local pairs are transformed from strongly coupled bosons into the fluctuating Cooper pairs, increases as the added ZnO nanoparticles concentration enhances up to 0.2 wt%. Also, the estimated values for the superconducting gap at T = 0 K (Δ(0)) are decreased from about 26 meV in ZnO-free sample to about 22 meV in 0.2 wt% ZnO added sample and then increases for higher values of additive.
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Affiliation(s)
- Ali Aftabi
- grid.411189.40000 0000 9352 9878Department of Physics, Faculty of Science, University of Kurdistan, 66177-15175 Sanandaj, Iran
| | - Morteza Mozaffari
- grid.411750.60000 0001 0454 365XDepartment of Physics, Faculty of Physics, University of Isfahan, 81746-73441 Isfahan, Iran
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Beygi A, Klevansky S, Lemmer R. Continuous quantum phase transition in the fermionic mass solutions of the Nambu–Jona-Lasinio model. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.036005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Alcoba DR, Capuzzi P, Rubio-García A, Dukelsky J, Massaccesi GE, Oña OB, Torre A, Lain L. Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particleN-representability conditions. J Chem Phys 2018; 149:194105. [DOI: 10.1063/1.5056247] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Diego R. Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Pablo Capuzzi
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Alvaro Rubio-García
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
| | - Gustavo E. Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ofelia B. Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
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7
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Mueller EJ. Review of pseudogaps in strongly interacting Fermi gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:104401. [PMID: 28686169 DOI: 10.1088/1361-6633/aa7e53] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.
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Affiliation(s)
- Erich J Mueller
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca NY 14853, United States of America
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8
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Bighin G, Salasnich L. Vortices and antivortices in two-dimensional ultracold Fermi gases. Sci Rep 2017; 7:45702. [PMID: 28374762 PMCID: PMC5379560 DOI: 10.1038/srep45702] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Accepted: 03/03/2017] [Indexed: 11/09/2022] Open
Abstract
Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.
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Affiliation(s)
- G Bighin
- IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria
| | - L Salasnich
- Dipartimento di Fisica e Astronomia "Galileo Galilei" and CNISM, Università di Padova, Via Marzolo 8, 35131 Padova, Italy.,Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
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9
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Chen Q. Effect of the particle-hole channel on BCS-Bose-Einstein condensation crossover in atomic Fermi gases. Sci Rep 2016; 6:25772. [PMID: 27183875 PMCID: PMC4868972 DOI: 10.1038/srep25772] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Accepted: 04/22/2016] [Indexed: 11/09/2022] Open
Abstract
BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.
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Affiliation(s)
- Qijin Chen
- Department of Physics and Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, Hefei, Anhui 230026, China
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10
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Dong H, Zhang W, Zhou L, Ma Y. Transition and Damping of Collective Modes in a Trapped Fermi Gas between BCS and Unitary Limits near the Phase Transition. Sci Rep 2015; 5:15848. [PMID: 26522094 PMCID: PMC4629144 DOI: 10.1038/srep15848] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2015] [Accepted: 10/01/2015] [Indexed: 11/09/2022] Open
Abstract
We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion's scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.
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Affiliation(s)
- Hang Dong
- Surface Physics Laboratory and Department of Physics, Furan University, Shanghai 200433, China
| | - Wenyuan Zhang
- Surface Physics Laboratory and Department of Physics, Furan University, Shanghai 200433, China
| | - Li Zhou
- Surface Physics Laboratory and Department of Physics, Furan University, Shanghai 200433, China
| | - Yongli Ma
- Surface Physics Laboratory and Department of Physics, Furan University, Shanghai 200433, China
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11
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Bianconi A, Jarlborg T. Lifshitz transitions and zero point lattice fluctuations in sulfur hydride showing near room temperature superconductivity. ACTA ACUST UNITED AC 2015. [DOI: 10.1515/nsm-2015-0006] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
AbstractEmerets’s experiments on pressurized sulfur hydride have shown that H3S metal has the highest known superconducting critical temperature Tc = 203 K. The Emerets data show pressure induced changes of the isotope coefficient between 0.25 and 0.5, in disagreement with Eliashberg theory which predicts a nearly constant isotope coefficient.We assign the pressure dependent isotope coefficient to Lifshitz transitions induced by pressure and zero point lattice fluctuations. It is known that pressure could induce changes of the topology of the Fermi surface, called Lifshitz transitions, but were neglected in previous papers on the H3S superconductivity issue. Here we propose thatH3S is a multi-gap superconductor with a first condensate in the BCS regime (located in the large Fermi surface with high Fermi energy) which coexists with second condensates in the BCS-BEC crossover regime (located on the Fermi surface spots with small Fermi energy) near the and Mpoints.We discuss the Bianconi-Perali-Valletta (BPV) superconductivity theory to understand superconductivity in H3S since the BPV theory includes the corrections of the chemical potential due to pairing and the configuration interaction between different condensates, neglected by the Eliashberg theory. These two terms in the BPV theory give the shape resonance in superconducting gaps, similar to Feshbach resonance in ultracold fermionic gases, which is known to amplify the critical temperature. Therefore this work provides some key tools useful in the search for new room temperature superconductors.
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13
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Chen Y, Shanenko AA, Perali A, Peeters FM. Superconducting nanofilms: molecule-like pairing induced by quantum confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:185701. [PMID: 22481115 DOI: 10.1088/0953-8984/24/18/185701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Quantum confinement of the perpendicular motion of electrons in single-crystalline metallic superconducting nanofilms splits the conduction band into a series of single-electron subbands. A distinctive feature of such a nanoscale multi-band superconductor is that the energetic position of each subband can vary significantly with changing nanofilm thickness, substrate material, protective cover and other details of the fabrication process. It can occur that the bottom of one of the available subbands is situated in the vicinity of the Fermi level. We demonstrate that the character of the superconducting pairing in such a subband changes dramatically and exhibits a clear molecule-like trend, which is very similar to the well-known crossover from the Bardeen-Cooper-Schrieffer regime to Bose-Einstein condensation (BCS-BEC) observed in trapped ultracold fermions. For Pb nanofilms with thicknesses of 4 and 5 monolayers (MLs) this will lead to a spectacular scenario: up to half of all the Cooper pairs nearly collapse, shrinking in the lateral size (parallel to the nanofilm) down to a few nanometers. As a result, the superconducting condensate will be a coherent mixture of almost molecule-like fermionic pairs with ordinary, extended Cooper pairs.
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Affiliation(s)
- Yajiang Chen
- Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
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14
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Strinati GC. Pairing Fluctuations Approach to the BCS–BEC Crossover. THE BCS-BEC CROSSOVER AND THE UNITARY FERMI GAS 2012. [DOI: 10.1007/978-3-642-21978-8_4] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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15
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Scherer MM, Floerchinger S, Gies H. Functional renormalization for the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:2779-2799. [PMID: 21646278 DOI: 10.1098/rsta.2011.0072] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We review the functional renormalization group (RG) approach to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.
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Affiliation(s)
- Michael M Scherer
- Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07749 Jena, Germany
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16
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Kuhnle ED, Hoinka S, Dyke P, Hu H, Hannaford P, Vale CJ. Temperature dependence of the universal contact parameter in a unitary Fermi gas. PHYSICAL REVIEW LETTERS 2011; 106:170402. [PMID: 21635019 DOI: 10.1103/physrevlett.106.170402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2010] [Indexed: 05/30/2023]
Abstract
The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(k(F)a), where k(F) is the Fermi wave vector and a is the s-wave scattering length, and the temperature T/T(F), where T(F) is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.
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Affiliation(s)
- E D Kuhnle
- ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
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17
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Magierski P, Wlazłowski G, Bulgac A, Drut JE. Finite-temperature pairing gap of a unitary fermi gas by quantum monte carlo calculations. PHYSICAL REVIEW LETTERS 2009; 103:210403. [PMID: 20366021 DOI: 10.1103/physrevlett.103.210403] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2008] [Revised: 11/05/2009] [Indexed: 05/29/2023]
Abstract
We calculate the one-body temperature Green's (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function A(p,omega) using the methods of maximum entropy and singular value decomposition. From A(p,omega) we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass m{*}, a mean-field potential U, and a gap Delta. Below the critical temperature T{c}=0.15 epsilon{F} the results for m{*}, U, and Delta can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to T{*} approximately 0.20 epsilon{F}> T{c}.
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Affiliation(s)
- Piotr Magierski
- Faculty of Physics, Warsaw University of Technology, ulica Koszykowa 75, 00-662 Warsaw, Poland
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18
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Inada Y, Horikoshi M, Nakajima S, Kuwata-Gonokami M, Ueda M, Mukaiyama T. Critical temperature and condensate fraction of a fermion pair condensate. PHYSICAL REVIEW LETTERS 2008; 101:180406. [PMID: 18999802 DOI: 10.1103/physrevlett.101.180406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2008] [Indexed: 05/27/2023]
Abstract
We report on measurements of the critical temperature and the temperature dependence of the condensate fraction for a fermion pair condensate of 6Li atoms. Bragg spectroscopy is employed to determine the critical temperature and the condensate fraction after a fast magnetic field ramp to the molecular side of the Feshbach resonance. Our measurements reveal evidence of level off of the critical temperature and limiting behavior of condensate fraction near the unitarity limit.
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Affiliation(s)
- Yasuhisa Inada
- ERATO Macroscopic Quantum Control Project, JST, 2-11-16 Yayoi, Bunkyo-Ku, Tokyo 113-8656, Japan
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19
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Gubbels KB, Stoof HTC. Renormalization group theory for the imbalanced Fermi gas. PHYSICAL REVIEW LETTERS 2008; 100:140407. [PMID: 18518012 DOI: 10.1103/physrevlett.100.140407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2007] [Revised: 12/20/2007] [Indexed: 05/26/2023]
Abstract
We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)10.1038/nature06473].
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Affiliation(s)
- K B Gubbels
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands.
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20
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Wright MJ, Riedl S, Altmeyer A, Kohstall C, Guajardo ERS, Denschlag JH, Grimm R. Finite-temperature collective dynamics of a Fermi gas in the BEC-BCS crossover. PHYSICAL REVIEW LETTERS 2007; 99:150403. [PMID: 17995145 DOI: 10.1103/physrevlett.99.150403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2007] [Indexed: 05/25/2023]
Abstract
We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of the quantum gas in terms of hydrodynamic or near-collisionless behavior. We obtain a crossover phase diagram for collisional properties, showing a large region where a nonsuperfluid strongly interacting gas shows hydrodynamic behavior. In a narrow interaction regime on the BCS side of the crossover, we find a novel temperature-dependent damping peak, suggesting a relation to the superfluid phase transition.
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Affiliation(s)
- M J Wright
- Institut für Experimentalphysik und Forschungszentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
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21
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Zwierlein MW, Schunck CH, Schirotzek A, Ketterle W. Direct observation of the superfluid phase transition in ultracold Fermi gases. Nature 2006; 442:54-8. [PMID: 16823447 DOI: 10.1038/nature04936] [Citation(s) in RCA: 289] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2006] [Accepted: 05/23/2006] [Indexed: 11/09/2022]
Abstract
Phase transitions are dramatic phenomena: water freezes into ice, atomic spins spontaneously align in a magnet, and liquid helium becomes superfluid. Sometimes, such a drastic change in behaviour is accompanied by a visible change in appearance. The hallmark of Bose-Einstein condensation and superfluidity in trapped, weakly interacting Bose gases is the sudden formation of a dense central core inside a thermal cloud. However, in strongly interacting gases--such as the recently observed fermionic superfluids--there is no longer a clear separation between the superfluid and the normal parts of the cloud. The detection of fermion pair condensates has required magnetic field sweeps into the weakly interacting regime, and the quantitative description of these sweeps presents a major theoretical challenge. Here we report the direct observation of the superfluid phase transition in a strongly interacting gas of 6Li fermions, through sudden changes in the shape of the clouds--in complete analogy to the case of weakly interacting Bose gases. By preparing unequal mixtures of the two spin components involved in the pairing, we greatly enhance the contrast between the superfluid core and the normal component. Furthermore, the distribution of non-interacting excess atoms serves as a direct and reliable thermometer. Even in the normal state, strong interactions significantly deform the density profile of the majority spin component. We show that it is these interactions that drive the normal-to-superfluid transition at the critical population imbalance of 70 +/- 5 per cent (ref. 12).
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Affiliation(s)
- Martin W Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA.
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22
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Burovski E, Prokof'ev N, Svistunov B, Troyer M. Critical temperature and thermodynamics of attractive fermions at unitarity. PHYSICAL REVIEW LETTERS 2006; 96:160402. [PMID: 16712207 DOI: 10.1103/physrevlett.96.160402] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2006] [Indexed: 05/09/2023]
Abstract
The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of two-component lattice fermions with an on-site attractive interaction. We perform a systematic-error-free finite-temperature simulation of this system by diagrammatic determinant Monte Carlo method. The critical temperature in units of Fermi energy is found to be T(C)/epsilonF=0.152(7). We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.
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Affiliation(s)
- Evgeni Burovski
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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23
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Bulgac A, Drut JE, Magierski P. Spin 1/2 fermions in the unitary regime: a superfluid of a new type. PHYSICAL REVIEW LETTERS 2006; 96:090404. [PMID: 16606247 DOI: 10.1103/physrevlett.96.090404] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2005] [Revised: 11/14/2005] [Indexed: 05/08/2023]
Abstract
We study, in a fully nonperturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction are calculated and we also determine the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid.
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Affiliation(s)
- Aurel Bulgac
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
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24
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Botelho SS, Sá de Melo CAR. Vortex-antivortex lattice in ultracold fermionic gases. PHYSICAL REVIEW LETTERS 2006; 96:040404. [PMID: 16486795 DOI: 10.1103/physrevlett.96.040404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2005] [Indexed: 05/06/2023]
Abstract
We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.
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Affiliation(s)
- S S Botelho
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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25
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Romans MWJ, Stoof HTC. Dressed Feshbach molecules in the BEC-BCS crossover. PHYSICAL REVIEW LETTERS 2005; 95:260407. [PMID: 16486323 DOI: 10.1103/physrevlett.95.260407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2005] [Revised: 09/23/2005] [Indexed: 05/06/2023]
Abstract
We present the random phase approximation (RPA) theory of the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge et al. [95, 020404 (2005)10.1103/PhysRevLett.95.020404] with , who have measured the same quantity.
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Affiliation(s)
- M W J Romans
- Institute for Theoretical Physics, Utrecht University, The Netherlands
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26
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Perali A, Pieri P, Strinati GC. Extracting the condensate density from projection experiments with Fermi gases. PHYSICAL REVIEW LETTERS 2005; 95:010407. [PMID: 16090593 DOI: 10.1103/physrevlett.95.010407] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2005] [Indexed: 05/03/2023]
Abstract
A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the Bose-Einstein condensation (BEC) sides, thus "projecting" the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of the mean field.
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Affiliation(s)
- A Perali
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
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27
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Kinast J, Turlapov A, Thomas JE. Damping of a unitary Fermi gas. PHYSICAL REVIEW LETTERS 2005; 94:170404. [PMID: 15904273 DOI: 10.1103/physrevlett.94.170404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2005] [Indexed: 05/02/2023]
Abstract
We measure the temperature dependence of the radial breathing mode in an optically trapped, unitary Fermi gas of 6Li, just above the center of a broad Feshbach resonance. The damping rate reveals a clear change in behavior which we interpret as arising from a superfluid transition. We suggest pair breaking as a mechanism for an increase in the damping rate which occurs at temperatures well above the transition. In contrast to the damping, the frequency varies smoothly and remains close to the unitary hydrodynamic value. At low temperature T, the damping depends on the atom number only through the reduced temperature, and extrapolates to 0 at T = 0.
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Affiliation(s)
- J Kinast
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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28
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Stajic J, Chen Q, Levin K. Density profiles of strongly interacting trapped fermi gases. PHYSICAL REVIEW LETTERS 2005; 94:060401. [PMID: 15783708 DOI: 10.1103/physrevlett.94.060401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2004] [Revised: 11/10/2004] [Indexed: 05/24/2023]
Abstract
We study density profiles in trapped fermionic gases, near Feshbach resonances, at all T< or =Tc and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.
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Affiliation(s)
- Jelena Stajic
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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29
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Feder DL. Vortex arrays in a rotating superfluid Fermi gas. PHYSICAL REVIEW LETTERS 2004; 93:200406. [PMID: 15600906 DOI: 10.1103/physrevlett.93.200406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2004] [Indexed: 05/24/2023]
Abstract
The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.
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Affiliation(s)
- David L Feder
- Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada
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30
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Batchelor MT, Guan XW, McGuire JB. Ground state of 1D bosons with delta interaction: link to the BCS model. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/42/l01] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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31
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Perali A, Pieri P, Strinati GC. Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover. PHYSICAL REVIEW LETTERS 2004; 93:100404. [PMID: 15447391 DOI: 10.1103/physrevlett.93.100404] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2004] [Indexed: 05/24/2023]
Abstract
Theoretical predictions for the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.
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Affiliation(s)
- A Perali
- Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
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32
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Chin C, Bartenstein M, Altmeyer A, Riedl S, Jochim S, Denschlag JH, Grimm R. Observation of the Pairing Gap in a Strongly Interacting Fermi Gas. Science 2004; 305:1128-30. [PMID: 15272125 DOI: 10.1126/science.1100818] [Citation(s) in RCA: 169] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We studied fermionic pairing in an ultracold two-component gas of 6Li atoms by observing an energy gap in the radio-frequency excitation spectra. With control of the two-body interactions through a Feshbach resonance, we demonstrated the dependence of the pairing gap on coupling strength, temperature, and Fermi energy. The appearance of an energy gap with moderate evaporative cooling suggests that our full evaporation brought the strongly interacting system deep into a superfluid state.
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Affiliation(s)
- C Chin
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
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