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Yamamoto D, Morita K. Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using Cold Atoms with SU(N)-Symmetric Interactions. PHYSICAL REVIEW LETTERS 2024; 132:213401. [PMID: 38856247 DOI: 10.1103/physrevlett.132.213401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 03/02/2024] [Accepted: 04/04/2024] [Indexed: 06/11/2024]
Abstract
An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems. This study theoretically demonstrates a cooling method employing multicomponent Fermi gases with SU(N)-symmetric interactions, focusing on the case of ^{173}Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-entropy region, exclusively composed of two specific spin components, acts as a quantum simulator for strongly correlated electron systems, while the surrounding N-component mixture retains a significant portion of the entropy of the system. The total particle numbers for each component are good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics.
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Affiliation(s)
- Daisuke Yamamoto
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui, Setagaya, Tokyo 156-8550, Japan
| | - Katsuhiro Morita
- Department of Physics and Astronomy, Faculty of Science and Technology, Tokyo University of Science, Chiba 278-8510, Japan
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2
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Pasqualetti G, Bettermann O, Darkwah Oppong N, Ibarra-García-Padilla E, Dasgupta S, Scalettar RT, Hazzard KRA, Bloch I, Fölling S. Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2024; 132:083401. [PMID: 38457712 DOI: 10.1103/physrevlett.132.083401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 01/09/2024] [Indexed: 03/10/2024]
Abstract
We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.
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Affiliation(s)
- G Pasqualetti
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - O Bettermann
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - N Darkwah Oppong
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - E Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
| | - S Dasgupta
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - K R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
| | - I Bloch
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - S Fölling
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
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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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Competing magnetic orders in a bilayer Hubbard model with ultracold atoms. Nature 2021; 589:40-43. [PMID: 33408376 DOI: 10.1038/s41586-020-03058-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2020] [Accepted: 10/02/2020] [Indexed: 11/09/2022]
Abstract
Fermionic atoms in optical lattices have served as a useful model system in which to study and emulate the physics of strongly correlated matter. Driven by the advances of high-resolution microscopy, the current research focus is on two-dimensional systems1-3, in which several quantum phases-such as antiferromagnetic Mott insulators for repulsive interactions4-7 and charge-density waves for attractive interactions8-have been observed. However, the lattice structure of real materials, such as bilayer graphene, is composed of coupled layers and is therefore not strictly two-dimensional, which must be taken into account in simulations. Here we realize a bilayer Fermi-Hubbard model using ultracold atoms in an optical lattice, and demonstrate that the interlayer coupling controls a crossover between a planar antiferromagnetically ordered Mott insulator and a band insulator of spin-singlets along the bonds between the layers. We probe the competition of the magnetic ordering by measuring spin-spin correlations both within and between the two-dimensional layers. Our work will enable the exploration of further properties of coupled-layer Hubbard models, such as theoretically predicted superconducting pairing mechanisms9,10.
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Hartke T, Oreg B, Jia N, Zwierlein M. Doublon-Hole Correlations and Fluctuation Thermometry in a Fermi-Hubbard Gas. PHYSICAL REVIEW LETTERS 2020; 125:113601. [PMID: 32975995 DOI: 10.1103/physrevlett.125.113601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 07/19/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the single atom and single site-resolved detection of the total density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence imaging of doublons is achieved by splitting each lattice site into a double well, thereby separating atom pairs. Full density readout yields a direct measurement of the equation of state, including direct thermometry via the fluctuation-dissipation theorem. Site-resolved density correlations reveal the Pauli hole at low filling, and strong doublon-hole correlations near half filling. These are shown to account for the difference between local and nonlocal density fluctuations in the Mott insulator. Our technique enables the study of atom-resolved charge transport in the Fermi-Hubbard model, the site-resolved observation of molecules, and the creation of bilayer Fermi-Hubbard systems.
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Affiliation(s)
- Thomas Hartke
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Botond Oreg
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ningyuan Jia
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Martin Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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6
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Gall M, Chan CF, Wurz N, Köhl M. Simulating a Mott Insulator Using Attractive Interaction. PHYSICAL REVIEW LETTERS 2020; 124:010403. [PMID: 31976738 DOI: 10.1103/physrevlett.124.010403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2019] [Indexed: 06/10/2023]
Abstract
We study the particle-hole symmetry in the Hubbard model using ultracold fermionic atoms in an optical lattice. We demonstrate the mapping between charge and spin degrees of freedom and, in particular, show the occurrence of a state with "incompressible" magnetization for attractive interactions. Our results present a novel approach to quantum simulation by giving access to strongly correlated phases of matter through an experimental mapping to easier detectable observables.
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Affiliation(s)
- M Gall
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - 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 Köhl
- Physikalisches Institut, University of Bonn, Wegelerstraße 8, 53115 Bonn, Germany
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7
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Schauss P. Polarons leave a trace. Science 2019; 365:218. [DOI: 10.1126/science.aax6486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Spin and charge interplay leads to stringlike excitations in the 2D Hubbard model
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Affiliation(s)
- Peter Schauss
- Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA
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8
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Mazurenko A, Blatt S, Huber F, Parsons MF, Chiu CS, Ji G, Greif D, Greiner M. Implementation of a stable, high-power optical lattice for quantum gas microscopy. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:033101. [PMID: 30927819 DOI: 10.1063/1.5066623] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2018] [Accepted: 02/08/2019] [Indexed: 06/09/2023]
Abstract
We describe the design and implementation of a stable high-power 1064 nm laser system to generate optical lattices for experiments with ultracold quantum gases. The system is based on a low-noise laser amplified by an array of four heavily modified, high-power fiber amplifiers. The beam intensity is stabilized and controlled with a nonlinear feedback loop. Using real-time monitoring of the resulting optical lattice, we find the stability of the lattice site positions to be well below the lattice spacing over the course of hours. The position of the harmonic trap produced by the Gaussian envelope of the lattice beams is stable to about one lattice spacing and the long-term (six-month) relative root-mean-square stability of the lattice spacing itself is 0.5%.
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Affiliation(s)
- A Mazurenko
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S Blatt
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Huber
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M F Parsons
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - C S Chiu
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - G Ji
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D Greif
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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9
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Salomon G, Koepsell J, Vijayan J, Hilker TA, Nespolo J, Pollet L, Bloch I, Gross C. Direct observation of incommensurate magnetism in Hubbard chains. Nature 2018; 565:56-60. [DOI: 10.1038/s41586-018-0778-7] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2018] [Accepted: 10/12/2018] [Indexed: 11/10/2022]
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10
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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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11
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Loida K, Bernier JS, Citro R, Orignac E, Kollath C. Probing the Bond Order Wave Phase Transitions of the Ionic Hubbard Model by Superlattice Modulation Spectroscopy. PHYSICAL REVIEW LETTERS 2017; 119:230403. [PMID: 29286701 DOI: 10.1103/physrevlett.119.230403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2017] [Indexed: 06/07/2023]
Abstract
An exotic phase, the bond order wave, characterized by the spontaneous dimerization of the hopping, has been predicted to exist sandwiched between the band and Mott insulators in systems described by the ionic Hubbard model. Despite growing theoretical evidence, this phase still evades experimental detection. Given the recent realization of the ionic Hubbard model in ultracold atomic gases, we propose here to detect the bond order wave using superlattice modulation spectroscopy. We demonstrate, with the help of time-dependent density-matrix renormalization group and bosonization, that this spectroscopic approach reveals characteristics of both the Ising and Kosterlitz-Thouless transitions signaling the presence of the bond order wave phase. This scheme also provides insights into the excitation spectra of both the band and Mott insulators.
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Affiliation(s)
- Karla Loida
- HISKP, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
| | | | - Roberta Citro
- Dipartimento di Fisica "E.R. Caianiello" and CNR-SPIN, Università degli Studi di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (Sa), Italy
| | - Edmond Orignac
- Université de Lyon, École Normale Supérieure de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Corinna Kollath
- HISKP, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
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12
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Brown PT, Mitra D, Guardado-Sanchez E, Schauß P, Kondov SS, Khatami E, Paiva T, Trivedi N, Huse DA, Bakr WS. Spin-imbalance in a 2D Fermi-Hubbard system. Science 2017; 357:1385-1388. [DOI: 10.1126/science.aam7838] [Citation(s) in RCA: 97] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Accepted: 08/24/2017] [Indexed: 11/02/2022]
Abstract
The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.
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13
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Rossi R. Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit. PHYSICAL REVIEW LETTERS 2017; 119:045701. [PMID: 29341772 DOI: 10.1103/physrevlett.119.045701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Indexed: 06/07/2023]
Abstract
We present a simple trick that allows us to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models, such that the thermodynamic limit can be taken analytically. With our approach one can achieve superior performance compared to conventional diagrammatic Monte Carlo algorithm, while rendering the algorithmic part dramatically simpler. By considering the sum of all connected diagrams at once, we allow for massive cancellations between different diagrams, greatly reducing the sign problem. In the end, the computational effort increases only exponentially with the order of the expansion, which should be contrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model.
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Affiliation(s)
- Riccardo Rossi
- Laboratoire de Physique Statistique de l'École Normale Supérieure, 75005 Paris, France
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14
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Lingua F, Capogrosso-Sansone B, Minardi F, Penna V. Thermometry of bosonic mixtures in Optical Lattices via Demixing. Sci Rep 2017; 7:5105. [PMID: 28698563 PMCID: PMC5506072 DOI: 10.1038/s41598-017-05353-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2017] [Accepted: 05/26/2017] [Indexed: 11/16/2022] Open
Abstract
Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected.
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Affiliation(s)
- F Lingua
- Department of Applied Science and Technology and u.d.r. CNISM, Politecnico di Torino, I-10129, Torino, Italy.
| | | | - F Minardi
- Istituto Nazionale di Ottica (INO-CNR), I-50019 Sesto Fiorentino, Italy.,European Laboratory for Non-Linear Spectroscopy (LENS) and Dipartimento di Fisica, Università di Firenze, I-50019, Sesto Fiorentino, Italy
| | - V Penna
- Department of Applied Science and Technology and u.d.r. CNISM, Politecnico di Torino, I-10129, Torino, Italy
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15
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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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