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Shao HJ, Wang YX, Zhu DZ, Zhu YS, Sun HN, Chen SY, Zhang C, Fan ZJ, Deng Y, Yao XC, Chen YA, Pan JW. Antiferromagnetic phase transition in a 3D fermionic Hubbard model. Nature 2024; 632:267-272. [PMID: 38987606 DOI: 10.1038/s41586-024-07689-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 06/07/2024] [Indexed: 07/12/2024]
Abstract
The fermionic Hubbard model (FHM)1 describes a wide range of physical phenomena resulting from strong electron-electron correlations, including conjectured mechanisms for unconventional superconductivity. Resolving its low-temperature physics is, however, challenging theoretically or numerically. Ultracold fermions in optical lattices2,3 provide a clean and well-controlled platform offering a path to simulate the FHM. Doping the antiferromagnetic ground state of a FHM simulator at half-filling is expected to yield various exotic phases, including stripe order4, pseudogap5, and d-wave superfluid6, offering valuable insights into high-temperature superconductivity7-9. Although the observation of antiferromagnetic correlations over short10 and extended distances11 has been obtained, the antiferromagnetic phase has yet to be realized as it requires sufficiently low temperatures in a large and uniform quantum simulator. Here we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature and doping concentration are finely tuned to approach their respective critical values, a sharp increase in the spin structure factor is observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class12. At half-filling and with optimal interaction strength, the measured spin structure factor reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results provide opportunities for exploring the low-temperature phase diagram of the FHM.
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Affiliation(s)
- Hou-Ji Shao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Yu-Xuan Wang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - De-Zhi Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Yan-Song Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Hao-Nan Sun
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Si-Yuan Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Chi Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
| | - Zhi-Jie Fan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China
| | - Youjin Deng
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China
| | - Xing-Can Yao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei, China.
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, China.
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2
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Bohrdt A, Demler E, Grusdt F. Dichotomy of heavy and light pairs of holes in the t-J model. Nat Commun 2023; 14:8017. [PMID: 38049409 PMCID: PMC10695955 DOI: 10.1038/s41467-023-43453-2] [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: 01/06/2023] [Accepted: 11/09/2023] [Indexed: 12/06/2023] Open
Abstract
A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. Here we use state-of-the art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in four-legged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, meta-stable pair, which has a dispersion proportional to the hole hopping t, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. Understanding the pairing mechanism can on the one hand pave the way to boosting binding energies in related models, and on the other hand enable insights into the intricate competition of various phases of matter in strongly correlated electron systems.
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Affiliation(s)
- A Bohrdt
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - E Demler
- Institut für Theoretische Physik, ETH Zurich, 8093, Zurich, Switzerland
| | - F Grusdt
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, München, D-80333, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany.
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3
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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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4
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Shaffer D, Wang J, Santos LH. Unconventional self-similar Hofstadter superconductivity from repulsive interactions. Nat Commun 2022; 13:7785. [PMID: 36526619 PMCID: PMC9758186 DOI: 10.1038/s41467-022-35316-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 11/23/2022] [Indexed: 12/23/2022] Open
Abstract
Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number [Formula: see text]. The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.
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Affiliation(s)
- Daniel Shaffer
- grid.189967.80000 0001 0941 6502Department of Physics, Emory University, 400 Dowman Drive, Atlanta, GA 30322 USA
| | - Jian Wang
- grid.189967.80000 0001 0941 6502Department of Physics, Emory University, 400 Dowman Drive, Atlanta, GA 30322 USA
| | - Luiz H. Santos
- grid.189967.80000 0001 0941 6502Department of Physics, Emory University, 400 Dowman Drive, Atlanta, GA 30322 USA
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5
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Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.
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6
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Walsh C, Charlebois M, Sémon P, Sordi G, Tremblay AMS. Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator. Proc Natl Acad Sci U S A 2021; 118:e2104114118. [PMID: 34161286 PMCID: PMC8237656 DOI: 10.1073/pnas.2104114118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A key open issue in condensed-matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information-theory tools on the two-dimensional (2D) Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels and shows a broad peak versus doping, as a result of competing quantum and classical effects.
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Affiliation(s)
- Caitlin Walsh
- Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom
| | - Maxime Charlebois
- Département de Chimie, Biochimie et Physique, Institut de Recherche sur l'Hydrogène, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada
| | - Patrick Sémon
- Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973-5000
| | - Giovanni Sordi
- Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom;
| | - André-Marie S Tremblay
- Département de Physique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
- Institut Quantique, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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7
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Zaletel MP, Kaufman A, Stamper-Kurn DM, Yao NY. Preparation of Low Entropy Correlated Many-Body States via Conformal Cooling Quenches. PHYSICAL REVIEW LETTERS 2021; 126:103401. [PMID: 33784144 DOI: 10.1103/physrevlett.126.103401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
We propose and analyze a method for preparing low entropy many-body states in isolated quantum optical systems of atoms, ions, and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite-temperature, time-dependent matrix product state calculations reveal that even moderately sized bath regions can remove enough energy and entropy density to expose coherent low-temperature physics. The protocol is particularly natural in systems with long-range interactions, such as lattice-trapped polar molecules and Rydberg-excited atoms, where the magnitude of the Hamiltonian scales directly with the interparticle spacing. To this end, we propose simple, near-term implementations of conformal cooling quenches in systems of atoms or molecules, where signatures of low-temperature phases may be observed.
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Affiliation(s)
- Michael P Zaletel
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
| | - Adam Kaufman
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Dan M Stamper-Kurn
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
| | - Norman Y Yao
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
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8
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Sels D, Dashti H, Mora S, Demler O, Demler E. Quantum approximate Bayesian computation for NMR model inference. NAT MACH INTELL 2020; 2:396-402. [PMID: 33163858 PMCID: PMC7643990 DOI: 10.1038/s42256-020-0198-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 06/02/2020] [Indexed: 12/30/2022]
Abstract
Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to real world problems is a subject of active investigation. Analysis of many-body quantum system is particularly challenging for classical computers due to the exponential scaling of Hilbert space dimension with the number of particles. Hence, solving problems relevant to chemistry and condensed matter physics are expected to be the first successful applications of quantum computers. In this paper, we propose another class of problems from the quantum realm that can be solved efficiently on quantum computers: model inference for nuclear magnetic resonance (NMR) spectroscopy, which is important for biological and medical research. Our results are based on three interconnected studies. Firstly, we use methods from classical machine learning to analyze a dataset of NMR spectra of small molecules. We perform a stochastic neighborhood embedding and identify clusters of spectra, and demonstrate that these clusters are correlated with the covalent structure of the molecules. Secondly, we propose a simple and efficient method, aided by a quantum simulator, to extract the NMR spectrum of any hypothetical molecule described by a parametric Heisenberg model. Thirdly, we propose a simple variational Bayesian inference procedure for extracting Hamiltonian parameters of experimentally relevant NMR spectra.
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Affiliation(s)
- Dries Sels
- Department of Physics, Harvard University, 17 Oxford st., Cambridge, MA 02138, USA
- Theory of quantum and complex systems, Universiteit Antwerpen, B-2610 Antwerpen, Belgium
| | - Hesam Dashti
- Division of Preventive Medicine, Brigham and Womens Hospital, Harvard Medical School, 900 Commonwealth Ave., Boston, MA 02215, USA
| | - Samia Mora
- Division of Preventive Medicine, Brigham and Womens Hospital, Harvard Medical School, 900 Commonwealth Ave., Boston, MA 02215, USA
- Division of Cardiovascular Medicine, Brigham and Womens Hospital, Harvard Medical School, 900 Commonwealth Ave., Boston, MA 02215, USA
| | - Olga Demler
- Division of Preventive Medicine, Brigham and Womens Hospital, Harvard Medical School, 900 Commonwealth Ave., Boston, MA 02215, USA
| | - Eugene Demler
- Department of Physics, Harvard University, 17 Oxford st., Cambridge, MA 02138, USA
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9
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Yang B, Sun H, Huang CJ, Wang HY, Deng Y, Dai HN, Yuan ZS, Pan JW. Cooling and entangling ultracold atoms in optical lattices. Science 2020; 369:550-553. [DOI: 10.1126/science.aaz6801] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 06/05/2020] [Indexed: 11/02/2022]
Abstract
Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of 1.9−0.4+1.7×10−3kB. The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 ± 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement.
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Affiliation(s)
- Bing Yang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hui Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chun-Jiong Huang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Han-Yi Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Youjin Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Han-Ning Dai
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhen-Sheng Yuan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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10
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Gong Z, Yoshioka N, Shibata N, Hamazaki R. Universal Error Bound for Constrained Quantum Dynamics. PHYSICAL REVIEW LETTERS 2020; 124:210606. [PMID: 32530663 DOI: 10.1103/physrevlett.124.210606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Revised: 03/13/2020] [Accepted: 05/01/2020] [Indexed: 06/11/2023]
Abstract
It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to additional couplings that mix these states, and thus approximately lead to a constrained dynamics within the subspace. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. Here we establish an observable-based error bound for such a constrained-dynamics approximation in generic gapped quantum systems. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. We demonstrate that either the intercept or the slope in the bound is asymptotically saturable by simple models. We generalize the result to quantum many-body systems with local interactions, for which the coupling strength diverges in the thermodynamic limit while the error is found to grow no faster than a power law t^{d+1} in d dimensions. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.
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Affiliation(s)
- Zongping Gong
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Nobuyuki Yoshioka
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Reserach (CPR), Wako-shi, Saitama 351-0198, Japan
| | - Naoyuki Shibata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ryusuke Hamazaki
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
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11
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Lin J, Nan J, Luo Y, Yao XC, Li X. Quantum Adiabatic Doping with Incommensurate Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 123:233603. [PMID: 31868469 DOI: 10.1103/physrevlett.123.233603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
Quantum simulations of Fermi-Hubbard models have been attracting considerable effort in the optical lattice research, with the ultracold antiferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping is atomic localization in the incommensurate lattice, potentially causing an exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.
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Affiliation(s)
- Jian Lin
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jue Nan
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuchen Luo
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
| | - Xing-Can Yao
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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12
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Li Y, Yuan J, Hemmerich A, Li X. Rotation-Symmetry-Enforced Coupling of Spin and Angular Momentum for p-Orbital Bosons. PHYSICAL REVIEW LETTERS 2018; 121:093401. [PMID: 30230858 DOI: 10.1103/physrevlett.121.093401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2018] [Indexed: 06/08/2023]
Abstract
Intrinsic spin angular-momentum coupling of an electron has a relativistic quantum origin with the coupling arising from charged orbits, which does not carry over to charge-neutral atoms. Here, we propose a mechanism of spontaneous generation of spin angular-momentum coupling with spinor atomic bosons loaded into p-orbital bands of a two-dimensional optical lattice. This spin angular-momentum coupling originates from many-body correlations and spontaneous symmetry breaking in a superfluid, with the key ingredients attributed to spin-channel quantum fluctuations and an approximate rotation symmetry. The resultant spin angular-momentum intertwined superfluid has Dirac excitations. In the presence of a chemical potential difference for adjacent sites, it provides a bosonic analogue of a symmetry-protected-topological insulator. Through a dynamical mean-field calculation, this novel superfluid is found to be a generic low-temperature phase, and it gives way to Mott localization only at strong interactions and even-integer fillings. We show the temperature to reach this order is accessible with present experiments.
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Affiliation(s)
- Yongqiang Li
- Department of Physics, National University of Defense Technology, Changsha 410073, People's Republic of China
- Department of Physics, Graduate School of China Academy of Engineering Physics, Beijing 100193, People's Republic of China
| | - Jianmin Yuan
- Department of Physics, National University of Defense Technology, Changsha 410073, People's Republic of China
- Department of Physics, Graduate School of China Academy of Engineering Physics, Beijing 100193, People's Republic of China
| | - Andreas Hemmerich
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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13
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Nayak S, Kumar S. Exotic superconducting states in the extended attractive Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:135601. [PMID: 29437156 DOI: 10.1088/1361-648x/aaaefe] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We show that the extended attractive Hubbard model on a square lattice allows for a variety of superconducting phases, including exotic mixed-symmetry phases with [Formula: see text] and [Formula: see text] symmetries, and a novel [Formula: see text] state. The calculations are performed within the Hartree-Fock Bardeen-Cooper-Schrieffer framework. The ground states of the mean-field Hamiltonian are obtained via a minimization scheme that relaxes the symmetry constraints on the superconducting solutions, hence allowing for a mixing of s-, p- and d-wave order parameters. The results are obtained within the assumption of uniform-density states. Our results show that extended attractive Hubbard model can serve as an effective model for investigating properties of exotic superconductors.
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Affiliation(s)
- Swagatam Nayak
- Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, Manauli PO 140306, India
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14
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Marti GE, Hutson RB, Goban A, Campbell SL, Poli N, Ye J. Imaging Optical Frequencies with 100 μHz Precision and 1.1 μm Resolution. PHYSICAL REVIEW LETTERS 2018; 120:103201. [PMID: 29570334 DOI: 10.1103/physrevlett.120.103201] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Indexed: 06/08/2023]
Abstract
We implement imaging spectroscopy of the optical clock transition of lattice-trapped degenerate fermionic Sr in the Mott-insulating regime, combining micron spatial resolution with submillihertz spectral precision. We use these tools to demonstrate atomic coherence for up to 15 s on the clock transition and reach a record frequency precision of 2.5×10^{-19}. We perform the most rapid evaluation of trapping light shifts and record a 150 mHz linewidth, the narrowest Rabi line shape observed on a coherent optical transition. The important emerging capability of combining high-resolution imaging and spectroscopy will improve the clock precision, and provide a path towards measuring many-body interactions and testing fundamental physics.
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Affiliation(s)
- G Edward Marti
- JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
| | - Ross B Hutson
- JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
| | - Akihisa Goban
- JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
| | - Sara L Campbell
- JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
| | - Nicola Poli
- Dipartimento di Fisica e Astronomia and LENS-Università di Firenze, INFN-Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (INO-CNR), Largo Enrico Fermi, 6, 50125 Firenze, Italy
| | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
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15
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Abstract
Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom-based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.
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Affiliation(s)
- Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany. .,Germany Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany
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16
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Mazurenko A, Chiu CS, Ji G, Parsons MF, Kanász-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M. A cold-atom Fermi–Hubbard antiferromagnet. Nature 2017; 545:462-466. [DOI: 10.1038/nature22362] [Citation(s) in RCA: 419] [Impact Index Per Article: 59.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Accepted: 04/03/2017] [Indexed: 11/09/2022]
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17
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Drewes JH, Miller LA, Cocchi E, Chan CF, Wurz N, Gall M, Pertot D, Brennecke F, Köhl M. Antiferromagnetic Correlations in Two-Dimensional Fermionic Mott-Insulating and Metallic Phases. PHYSICAL REVIEW LETTERS 2017; 118:170401. [PMID: 28498688 DOI: 10.1103/physrevlett.118.170401] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Indexed: 06/07/2023]
Abstract
We experimentally study the emergence of antiferromagnetic correlations between ultracold fermionic atoms in a two-dimensional optical lattice with decreasing temperature. We determine the uniform magnetic susceptibility of the two-dimensional Hubbard model from simultaneous measurements of the in situ density distribution of both spin components. At half filling and strong interactions our data approach the Heisenberg model of localized spins with antiferromagnetic correlations. Moreover, we observe a fast decay of magnetic correlations when doping the system away from half filling.
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Affiliation(s)
- J H Drewes
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - L A Miller
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - E Cocchi
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - C F Chan
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - N Wurz
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - M Gall
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - D Pertot
- Physikalisches Institut, University of Bonn, Wegelerstrasse 8, 53115 Bonn, Germany
| | - F Brennecke
- 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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18
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Raum PT, Scarola VW. Thermometry for Laughlin States of Ultracold Atoms. PHYSICAL REVIEW LETTERS 2017; 118:115302. [PMID: 28368627 DOI: 10.1103/physrevlett.118.115302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2016] [Indexed: 06/07/2023]
Abstract
Cooling atomic gases into strongly correlated quantum phases requires estimates of the entropy to perform thermometry and establish viability. We construct an ansatz partition function for models of Laughlin states of atomic gases by combining high temperature series expansions with exact diagonalization. Using the ansatz we find that entropies required to observe Laughlin correlations with bosonic gases are within reach of current cooling capabilities.
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Affiliation(s)
- P T Raum
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - V W Scarola
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
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19
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Fedorov AK, Matveenko SI, Yudson VI, Shlyapnikov GV. Novel p-wave superfluids of fermionic polar molecules. Sci Rep 2016; 6:27448. [PMID: 27278711 PMCID: PMC4899692 DOI: 10.1038/srep27448] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Accepted: 05/18/2016] [Indexed: 11/09/2022] Open
Abstract
Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry.
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Affiliation(s)
- A K Fedorov
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia.,LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay 91405, France
| | - S I Matveenko
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay 91405, France.,L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow 119334, Russia
| | - V I Yudson
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia.,Institute for Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 142190, Russia
| | - G V Shlyapnikov
- Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia.,LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Orsay 91405, France.,Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.,Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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20
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Rosenberg P, Chiesa S, Zhang S. FFLO order in ultra-cold atoms in three-dimensional optical lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:225601. [PMID: 25984657 DOI: 10.1088/0953-8984/27/22/225601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate different ground-state phases of attractive spin-imbalanced populations of fermions in three-dimensional optical lattices. Detailed numerical calculations are performed using Hartree-Fock-Bogoliubov theory to determine the ground-state properties systematically for different values of density, spin polarization and interaction strength. We first consider the high density and low polarization regime, in which the effect of the optical lattice is most evident. We then proceed to the low density and high polarization regime where the effects of the underlying lattice are less significant and the system begins to resemble a continuum Fermi gas. We explore the effects of density, polarization and interaction on the character of the phases in each regime and highlight the qualitative differences between the two regimes. In the high-density regime, the order is found to be of Larkin-Ovchinnikov type, linearly oriented with one characteristic wave vector but varying in its direction with the parameters. At lower densities the order parameter develops more structures involving multiple wave vectors.
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Affiliation(s)
- Peter Rosenberg
- Department of Physics, College of William and Mary, Williamsburg, VA 23188, USA
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21
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Lin HF, Liu HD, Tao HS, Liu WM. Phase transitions of the ionic Hubbard model on the honeycomb lattice. Sci Rep 2015; 5:9810. [PMID: 25961417 PMCID: PMC5386193 DOI: 10.1038/srep09810] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Accepted: 03/06/2015] [Indexed: 11/12/2022] Open
Abstract
Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction Uc, then increases upturn. At Uc, there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.
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Affiliation(s)
- Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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22
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Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms. Nature 2015; 519:211-4. [DOI: 10.1038/nature14223] [Citation(s) in RCA: 276] [Impact Index Per Article: 30.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2014] [Accepted: 12/04/2014] [Indexed: 11/08/2022]
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23
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Duarte PM, Hart RA, Yang TL, Liu X, Paiva T, Khatami E, Scalettar RT, Trivedi N, Hulet RG. Compressibility of a fermionic mott insulator of ultracold atoms. PHYSICAL REVIEW LETTERS 2015; 114:070403. [PMID: 25763942 DOI: 10.1103/physrevlett.114.070403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Indexed: 06/04/2023]
Abstract
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in situ imaging to extract the central density of the gas and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling.
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Affiliation(s)
- Pedro M Duarte
- Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, Texas 77005, USA
| | - Russell A Hart
- Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, Texas 77005, USA
| | - Tsung-Lin Yang
- Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, Texas 77005, USA
| | - Xinxing Liu
- Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, Texas 77005, USA
| | - Thereza Paiva
- Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68.528, 21941-972 Rio de Janeiro, RJ, Brazil
| | - Ehsan Khatami
- Department of Physics and Astronomy, San Jose State University, San Jose, California 95192, USA
| | - Richard T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - Nandini Trivedi
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Randall G Hulet
- Department of Physics and Astronomy and Rice Quantum Institute, Rice University, Houston, Texas 77005, USA
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24
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Scheurer MS, Rachel S, Orth PP. Dimensional crossover and cold-atom realization of topological Mott insulators. Sci Rep 2015; 5:8386. [PMID: 25669431 PMCID: PMC4323638 DOI: 10.1038/srep08386] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2014] [Accepted: 01/19/2015] [Indexed: 11/25/2022] Open
Abstract
Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.
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Affiliation(s)
- Mathias S Scheurer
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Stephan Rachel
- Institute for Theoretical Physics, TU Dresden, 01062 Dresden, Germany
| | - Peter P Orth
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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25
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Tao HS, Chen YH, Lin HF, Liu HD, Liu WM. Layer anti-ferromagnetism on bilayer honeycomb lattice. Sci Rep 2014; 4:5367. [PMID: 24947369 PMCID: PMC4064339 DOI: 10.1038/srep05367] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2013] [Accepted: 05/29/2014] [Indexed: 11/09/2022] Open
Abstract
Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.
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Affiliation(s)
- Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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26
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Bauer J, Salomon C, Demler E. Realizing a Kondo-correlated state with ultracold atoms. PHYSICAL REVIEW LETTERS 2013; 111:215304. [PMID: 24313499 DOI: 10.1103/physrevlett.111.215304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2013] [Revised: 09/30/2013] [Indexed: 06/02/2023]
Abstract
We propose a novel realization of Kondo physics with ultracold atomic gases. It is based on a Fermi sea of two different hyperfine states of one atom species forming bound states with a different species, which is spatially confined in a trapping potential. We show that different situations displaying Kondo physics can be realized when Feshbach resonances between the species are tuned by a magnetic field and the trapping frequency is varied. We illustrate that a mixture of 40K and 23Na atoms can be used to generate a Kondo-correlated state and that momentum resolved radio frequency spectroscopy can provide unambiguous signatures of the formation of Kondo resonances at the Fermi energy. We discuss how tools of atomic physics can be used to investigate open questions for Kondo physics, such as the extension of the Kondo screening cloud.
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Affiliation(s)
- Johannes Bauer
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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27
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Romero-Isart O, Navau C, Sanchez A, Zoller P, Cirac JI. Superconducting vortex lattices for ultracold atoms. PHYSICAL REVIEW LETTERS 2013; 111:145304. [PMID: 24138251 DOI: 10.1103/physrevlett.111.145304] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2013] [Revised: 07/25/2013] [Indexed: 06/02/2023]
Abstract
We propose and analyze a nanoengineered vortex array in a thin-film type-II superconductor as a magnetic lattice for ultracold atoms. This proposal addresses several of the key questions in the development of atomic quantum simulators. By trapping atoms close to the surface, tools of nanofabrication and structuring of lattices on the scale of few tens of nanometers become available with a corresponding benefit in energy scales and temperature requirements. This can be combined with the possibility of magnetic single site addressing and manipulation together with a favorable scaling of superconducting surface-induced decoherence.
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Affiliation(s)
- O Romero-Isart
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
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28
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Schmidt B, Bakhtiari MR, Titvinidze I, Schneider U, Snoek M, Hofstetter W. Dynamical arrest of ultracold lattice fermions. PHYSICAL REVIEW LETTERS 2013; 110:075302. [PMID: 25166379 DOI: 10.1103/physrevlett.110.075302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2012] [Revised: 11/05/2012] [Indexed: 06/03/2023]
Abstract
We theoretically investigate the thermodynamics of an interacting inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a recent experiment by L. Hackermüller et al., Science 327, 1621 (2010), we study the effect of the interplay between thermodynamics and strong correlations on the size of the fermionic cloud. We use dynamical mean-field theory to compute the cloud size, which in the experiment shows an anomalous expansion behavior upon increasing attractive interaction. We confirm this qualitative effect but, assuming adiabaticity, we find quantitative agreement only for weak interactions. For strong interactions we observe significant nonequilibrium effects which we attribute to a dynamical arrest of the particles due to increasing correlations.
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Affiliation(s)
- Bernd Schmidt
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt/Main, Germany
| | - M Reza Bakhtiari
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt/Main, Germany and I. Institut für Theoretische Physik, Universität Hamburg, 20355 Hamburg, Germany
| | - Irakli Titvinidze
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt/Main, Germany and I. Institut für Theoretische Physik, Universität Hamburg, 20355 Hamburg, Germany
| | - Ulrich Schneider
- Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
| | - Michiel Snoek
- Institute for Theoretical Physics, Universiteit van Amsterdam, 1090 GL Amsterdam, The Netherlands
| | - Walter Hofstetter
- Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt/Main, Germany
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29
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Xu Z, Li L, Xianlong G, Chen S. Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:055601. [PMID: 23262414 DOI: 10.1088/0953-8984/25/5/055601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The ground state properties of the Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interactions are investigated by means of the exact diagonalization method. We show that the appearance of N-crests in the density profile of a trapped N-fermion system is a natural result of 'fermionization' between antiparallel-spin fermions in the strongly repulsive limit and cannot be taken as the only signature of the Wigner crystal phase, as the static structure factor does not show any signature of crystallization. In contrast, both the density distribution and the static structure factor of the Hubbard model with strong long-range interactions display clear signatures of the Wigner crystal phase. Our results indicate the important role of long-range interaction in the formation of the Wigner crystal phase.
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Affiliation(s)
- Zhihao Xu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
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30
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Volčko D, Quader KF. Signatures of fermion pairing with unconventional symmetry around the BCS-BEC crossover in a quasi-2D lattice. PHYSICAL REVIEW LETTERS 2012; 109:235303. [PMID: 23368217 DOI: 10.1103/physrevlett.109.235303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2012] [Indexed: 06/01/2023]
Abstract
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, d(x(2)-y(2)) and extended-s (s(*)), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, v(k)(2), the ratio of the Bogoliubov coefficients, v(k)/u(k), and the Fourier transform of v(k)(2) are strikingly different for d and s(*) symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.
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Affiliation(s)
- Dušan Volčko
- Department of Physics, Kent State University, Kent, Ohio 44242, USA
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31
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Sotnikov A, Cocks D, Hofstetter W. Advantages of mass-imbalanced ultracold fermionic mixtures for approaching quantum magnetism in optical lattices. PHYSICAL REVIEW LETTERS 2012; 109:065301. [PMID: 23006278 DOI: 10.1103/physrevlett.109.065301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2012] [Indexed: 06/01/2023]
Abstract
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a directly observable signature of the ordered state. For the trapped system, we compare our results obtained by real-space DMFT to a local-density approximation. We calculate the entropy for a wide range of parameters and identify regions, in which mass-imbalanced mixtures could have clear advantages over balanced ones for the purpose of obtaining and detecting quantum magnetism.
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Affiliation(s)
- Andrii Sotnikov
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt/Main, Germany
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32
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Baranov MA, Dalmonte M, Pupillo G, Zoller P. Condensed Matter Theory of Dipolar Quantum Gases. Chem Rev 2012; 112:5012-61. [DOI: 10.1021/cr2003568] [Citation(s) in RCA: 480] [Impact Index Per Article: 40.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. A. Baranov
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- RRC “Kurchatov Institute”,
Kurchatov Square 1, 123182, Moscow, Russia
| | - M. Dalmonte
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Dipartimento di Fisica dell’Università
di Bologna, via Irnerio 46, 40126 Bologna, Italy
| | - G. Pupillo
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- ISIS (UMR 7006) and IPCMS (UMR
7504), Université de Strasbourg and CNRS, Strasbourg, France
| | - P. Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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33
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Chen YH, Tao HS, Yao DX, Liu WM. Kondo metal and ferrimagnetic insulator on the triangular kagome lattice. PHYSICAL REVIEW LETTERS 2012; 108:246402. [PMID: 23004298 DOI: 10.1103/physrevlett.108.246402] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2012] [Indexed: 06/01/2023]
Abstract
We obtain the rich phase diagrams in the Hubbard model on the triangular kagome lattice as a function of interaction, temperature, and asymmetry by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in the Mott transition of two sublattices on the triangular kagome lattice and produces two novel phases called plaquette insulator with a clearly visible gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value U(c), a short range paramagnetic insulating state, which is a candidate for the short rang resonating valence-bond spin liquid, emerges before the ferrimagnetic order is formed independent of asymmetry. Furthermore, we discuss how to measure these phases in future experiments.
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Affiliation(s)
- Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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34
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Zhang X, Chen Y, Liu G, Wu W, Wen L, Liu W. Quantum information and many body physics with cold atoms. CHINESE SCIENCE BULLETIN-CHINESE 2012. [DOI: 10.1007/s11434-012-5095-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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35
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Li X, Corcovilos TA, Wang Y, Weiss DS. 3D projection sideband cooling. PHYSICAL REVIEW LETTERS 2012; 108:103001. [PMID: 22463405 DOI: 10.1103/physrevlett.108.103001] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Indexed: 05/31/2023]
Abstract
We demonstrate 3D microwave projection sideband cooling of trapped, neutral atoms. The technique employs state-dependent potentials that enable microwave photons to drive vibration-number reducing transitions. The particular cooling sequence we employ uses minimal spontaneous emission, and works even for relatively weakly bound atoms. We cool 76% of atoms to their 3D vibrational ground states in a site-resolvable 3D optical lattice.
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Affiliation(s)
- Xiao Li
- Physics Department, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802, USA
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36
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Iazzi M, Bassan N, Trombettoni A, Schmidt KE, Fantoni S. Vortex lines distribution in inhomogeneous lattices. Mol Phys 2011. [DOI: 10.1080/00268976.2011.637083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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37
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Kitagawa T, Aspect A, Greiner M, Demler E. Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry. PHYSICAL REVIEW LETTERS 2011; 106:115302. [PMID: 21469872 DOI: 10.1103/physrevlett.106.115302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2010] [Revised: 05/29/2010] [Indexed: 05/30/2023]
Abstract
Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.
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Affiliation(s)
- Takuya Kitagawa
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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38
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Diehl S, Yi W, Daley AJ, Zoller P. Dissipation-induced d-wave pairing of fermionic atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2010; 105:227001. [PMID: 21231414 DOI: 10.1103/physrevlett.105.227001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2010] [Indexed: 05/30/2023]
Abstract
We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a parent Liouvillian operator so that a BCS-type state of a given symmetry, e.g., a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number-conserving and quasilocal processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.
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Affiliation(s)
- S Diehl
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
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39
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DeSalvo BJ, Yan M, Mickelson PG, Martinez de Escobar YN, Killian TC. Degenerate Fermi gas of (87)Sr. PHYSICAL REVIEW LETTERS 2010; 105:030402. [PMID: 20867747 DOI: 10.1103/physrevlett.105.030402] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2010] [Indexed: 05/29/2023]
Abstract
We report quantum degeneracy in a gas of ultracold fermionic (87)Sr atoms. By evaporatively cooling a mixture of spin states in an optical dipole trap for 10.5 s, we obtain samples well into the degenerate regime with T/T(F)=0.26(-0.06)(+0.05). The main signature of degeneracy is a change in the momentum distribution as measured by time-of-flight imaging, and we also observe a decrease in evaporation efficiency below T/T(F) ∼0.5.
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Affiliation(s)
- B J DeSalvo
- Department of Physics and Astronomy, Rice University, Houston, Texas, 77251, USA
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40
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Kantian A, Daley AJ, Zoller P. η condensate of fermionic atom pairs via adiabatic state preparation. PHYSICAL REVIEW LETTERS 2010; 104:240406. [PMID: 20867286 DOI: 10.1103/physrevlett.104.240406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2009] [Indexed: 05/29/2023]
Abstract
We discuss how an η condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalization group methods, we analyze a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
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Affiliation(s)
- A Kantian
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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41
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Jördens R, Tarruell L, Greif D, Uehlinger T, Strohmaier N, Moritz H, Esslinger T, De Leo L, Kollath C, Georges A, Scarola V, Pollet L, Burovski E, Kozik E, Troyer M. Quantitative determination of temperature in the approach to magnetic order of ultracold fermions in an optical lattice. PHYSICAL REVIEW LETTERS 2010; 104:180401. [PMID: 20482156 DOI: 10.1103/physrevlett.104.180401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2009] [Revised: 03/23/2010] [Indexed: 05/29/2023]
Abstract
We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Néel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy.
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Affiliation(s)
- R Jördens
- Department of Physics, ETH Zurich, 8093 Zurich, Switzerland
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42
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Hackermüller L, Schneider U, Moreno-Cardoner M, Kitagawa T, Best T, Will S, Demler E, Altman E, Bloch I, Paredes B. Anomalous expansion of attractively interacting fermionic atoms in an optical lattice. Science 2010; 327:1621-4. [PMID: 20339067 DOI: 10.1126/science.1184565] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The interplay of thermodynamics and quantum correlations can give rise to counterintuitive phenomena in many-body systems. We report on an isentropic effect in a spin mixture of attractively interacting fermionic atoms in an optical lattice. As we adiabatically increase the attraction between the atoms, we observe that the gas expands instead of contracting. This unexpected behavior demonstrates the crucial role of the lattice potential in the thermodynamics of the fermionic Hubbard model.
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Affiliation(s)
- Lucia Hackermüller
- Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz, Germany
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43
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Paiva T, Scalettar R, Randeria M, Trivedi N. Fermions in 2D optical lattices: temperature and entropy scales for observing antiferromagnetism and superfluidity. PHYSICAL REVIEW LETTERS 2010; 104:066406. [PMID: 20366841 DOI: 10.1103/physrevlett.104.066406] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2009] [Indexed: 05/29/2023]
Abstract
One of the major challenges in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine constraints on the entropy for observing these phases in two-dimensional Hubbard models using determinantal quantum Monte Carlo simulations. We find that an entropy per particle approximately = ln2 is sufficient to observe the insulating gap in the repulsive Hubbard model at half-filling, or the pairing pseudogap in the attractive case. Observing antiferromagnetic correlations or superfluidity in 2D systems requires a further reduction in entropy by a factor of 3 or more. In contrast with higher dimensions, we find that adiabatic cooling is not useful to achieve the required low temperatures. We also show that double-occupancy measurements are useful for thermometry for temperatures greater than the nearest-neighbor hopping energy.
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Affiliation(s)
- Thereza Paiva
- Instituto de Fisica, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro RJ, Brazil
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44
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Byczuk K, Hofstetter W, Vollhardt D. Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder. PHYSICAL REVIEW LETTERS 2009; 102:146403. [PMID: 19392461 DOI: 10.1103/physrevlett.102.146403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2008] [Indexed: 05/27/2023]
Abstract
The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.
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Affiliation(s)
- Krzysztof Byczuk
- Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, D-86135 Augsburg, Germany
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45
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Scarola VW, Pollet L, Oitmaa J, Troyer M. Discerning incompressible and compressible phases of cold atoms in optical lattices. PHYSICAL REVIEW LETTERS 2009; 102:135302. [PMID: 19392366 DOI: 10.1103/physrevlett.102.135302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2008] [Revised: 03/01/2009] [Indexed: 05/27/2023]
Abstract
Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made.
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Affiliation(s)
- V W Scarola
- Department of Chemistry and Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720, USA
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46
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Schneider U, Hackermuller L, Will S, Best T, Bloch I, Costi TA, Helmes RW, Rasch D, Rosch A. Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice. Science 2008; 322:1520-5. [DOI: 10.1126/science.1165449] [Citation(s) in RCA: 579] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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47
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De Leo L, Kollath C, Georges A, Ferrero M, Parcollet O. Trapping and cooling fermionic atoms into Mott and Néel states. PHYSICAL REVIEW LETTERS 2008; 101:210403. [PMID: 19113396 DOI: 10.1103/physrevlett.101.210403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2008] [Revised: 09/12/2008] [Indexed: 05/27/2023]
Abstract
We perform a theoretical study of a fermionic gas with two hyperfine states confined to an optical lattice. We derive a generic state diagram as a function of interaction strength, particle number, and confining potential. We discuss the central density, the double occupancy, and their derivatives as probes for the Mott state, connecting our findings to the recent experiment of Jördens et al. [Nature (London) 455, 204 (2008)10.1038/nature07244]. Using entropic arguments we compare two different strategies to reach the antiferromagnetic state in the presence of a trapping potential.
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Affiliation(s)
- Lorenzo De Leo
- Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
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48
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Ottenstein TB, Lompe T, Kohnen M, Wenz AN, Jochim S. Collisional stability of a three-component degenerate fermi gas. PHYSICAL REVIEW LETTERS 2008; 101:203202. [PMID: 19113336 DOI: 10.1103/physrevlett.101.203202] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2008] [Indexed: 05/27/2023]
Abstract
We report on the creation of a degenerate Fermi gas consisting of a balanced mixture of atoms in three different hyperfine states of 6Li. This new system consists of three distinguishable fermions with different and tunable interparticle scattering lengths a_{12}, a_{13}, and a_{23}. We are able to prepare samples containing 5x10;{4} atoms in each state at a temperature of about 215 nK, which corresponds to T/T_{F} approximately 0.37. We investigated the collisional stability of the gas for magnetic fields between 0 and 600 G and found a prominent loss feature at 130 G. From lifetime measurements, we determined three-body loss coefficients, which vary over nearly 3 orders of magnitude.
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Affiliation(s)
- T B Ottenstein
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany.
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49
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Peterson MR, Zhang C, Tewari S, Sarma SD. Realizing the strongly correlated d-wave Mott-insulator state in a fermionic cold-atom optical lattice. PHYSICAL REVIEW LETTERS 2008; 101:150406. [PMID: 18999579 DOI: 10.1103/physrevlett.101.150406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2008] [Indexed: 05/27/2023]
Abstract
We show that a new state of matter, the d-wave Mott-insulator state (d-Mott state) (introduced recently by [H. Yao, W. F. Tsai, and S. A. Kivelson, Phys. Rev. B 76, 161104 (2007)]), which is characterized by a nonzero expectation value of a local plaquette operator embedded in an insulating state, can be engineered using ultracold atomic fermions in two-dimensional double-well optical lattices. We characterize and analyze the parameter regime where the d-Mott state is stable. We predict the testable signatures of the state in the time-of-flight measurements.
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Affiliation(s)
- Michael R Peterson
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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50
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Sandvik AW. Quantum Monte Carlo simulations of bosonic and fermionic impurities in a two-dimensional hard-core boson system. PHYSICAL REVIEW LETTERS 2008; 101:120405. [PMID: 18851347 DOI: 10.1103/physrevlett.101.120405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2007] [Revised: 07/15/2008] [Indexed: 05/26/2023]
Abstract
A two-dimensional lattice hard-core boson system with a small fraction of bosonic or fermionic impurities is studied. The impurity hopping and interactions are identical to those of the dominant bosons, so that effects due to quantum statistics can be isolated. A quantum Monte Carlo scheme is developed in which bosonic paths are sampled and the impurities are introduced at the level of summing over permutation cycles. For both types of impurities, an anomaly in the effective impurity interaction energy is found at the Kosterlitz-Thouless temperature; it changes from attractive for T>T(KT) to repulsive for T<T(KT), suggesting that impurities strongly affect the vortex physics.
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
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