1
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Prichard ML, Spar BM, Morera I, Demler E, Yan ZZ, Bakr WS. Directly imaging spin polarons in a kinetically frustrated Hubbard system. Nature 2024; 629:323-328. [PMID: 38720039 DOI: 10.1038/s41586-024-07356-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 03/26/2024] [Indexed: 05/12/2024]
Abstract
The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions1-8. However, in kinetically frustrated lattices, itinerant spin polarons-bound states of a dopant and a spin flip-have been theoretically predicted even in the absence of superexchange coupling9-14. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect15,16. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems10,11. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials17-20.
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Affiliation(s)
- Max L Prichard
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Benjamin M Spar
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Ivan Morera
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Barcelona, Spain
- Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland
| | - Eugene Demler
- Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland
| | - Zoe Z Yan
- Department of Physics, Princeton University, Princeton, NJ, USA
- James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, NJ, USA.
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2
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Hartke T, Oreg B, Turnbaugh C, Jia N, Zwierlein M. Direct observation of nonlocal fermion pairing in an attractive Fermi-Hubbard gas. Science 2023; 381:82-86. [PMID: 37410819 DOI: 10.1126/science.ade4245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Accepted: 05/26/2023] [Indexed: 07/08/2023]
Abstract
The Hubbard model of attractively interacting fermions provides a paradigmatic setting for fermion pairing. It features a crossover between Bose-Einstein condensation of tightly bound pairs and Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs, and a "pseudo-gap" region where pairs form above the superfluid critical temperature. We directly observe the nonlocal nature of fermion pairing in a Hubbard lattice gas, using spin- and density-resolved imaging of [Formula: see text]1000 fermionic potassium-40 atoms under a bilayer microscope. Complete fermion pairing is revealed by the vanishing of global spin fluctuations with increasing attraction. In the strongly correlated regime, the fermion pair size is found to be on the order of the average interparticle spacing. Our study informs theories of pseudo-gap behavior in strongly correlated fermion systems.
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Affiliation(s)
- Thomas Hartke
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA
| | - Botond Oreg
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA
| | - Carter Turnbaugh
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA
| | - Ningyuan Jia
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA
| | - Martin Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, MA 02139, USA
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3
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Christakis L, Rosenberg JS, Raj R, Chi S, Morningstar A, Huse DA, Yan ZZ, Bakr WS. Probing site-resolved correlations in a spin system of ultracold molecules. Nature 2023; 614:64-69. [PMID: 36725998 DOI: 10.1038/s41586-022-05558-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 11/11/2022] [Indexed: 02/03/2023]
Abstract
Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties1-11. These include a large set of internal states with long coherence times12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids18, quantum spin liquids19, fractional Chern insulators20 and quantum magnets21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy23 to measure the site-resolved dynamics of quantum correlations of polar 23Na87Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation29,30 and metrology31.
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Affiliation(s)
| | | | - Ravin Raj
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Sungjae Chi
- Department of Physics, Princeton University, Princeton, NJ, USA
| | | | - David A Huse
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Zoe Z Yan
- Department of Physics, Princeton University, Princeton, NJ, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, NJ, USA.
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4
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Magnetically mediated hole pairing in fermionic ladders of ultracold atoms. Nature 2023; 613:463-467. [PMID: 36653561 PMCID: PMC9849138 DOI: 10.1038/s41586-022-05437-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 10/11/2022] [Indexed: 01/20/2023]
Abstract
Conventional superconductivity emerges from pairing of charge carriers-electrons or holes-mediated by phonons1. In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations2, as captured by models of mobile charges in doped antiferromagnets3. However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems4-8, in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions9. Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings10, we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole-hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.
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5
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Yan ZZ, Spar BM, Prichard ML, Chi S, Wei HT, Ibarra-García-Padilla E, Hazzard KRA, Bakr WS. Two-Dimensional Programmable Tweezer Arrays of Fermions. PHYSICAL REVIEW LETTERS 2022; 129:123201. [PMID: 36179199 DOI: 10.1103/physrevlett.129.123201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 06/27/2022] [Accepted: 07/29/2022] [Indexed: 06/16/2023]
Abstract
We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.
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Affiliation(s)
- Zoe Z Yan
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Benjamin M Spar
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Max L Prichard
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Sungjae Chi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Hao-Tian Wei
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Eduardo Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Kaden R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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6
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Spar BM, Guardado-Sanchez E, Chi S, Yan ZZ, Bakr WS. Realization of a Fermi-Hubbard Optical Tweezer Array. PHYSICAL REVIEW LETTERS 2022; 128:223202. [PMID: 35714242 DOI: 10.1103/physrevlett.128.223202] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
We use lithium-6 atoms in an optical tweezer array to realize an eight-site Fermi-Hubbard chain near half filling. We achieve single site detection by combining the tweezer array with a quantum gas microscope. By reducing disorder in the energy offsets to less than the tunneling energy, we observe Mott insulators with strong antiferromagnetic correlations. The measured spin correlations allow us to put an upper bound on the entropy of 0.26(4)k_{B} per atom, comparable to the lowest entropies achieved with optical lattices. Additionally, we establish the flexibility of the tweezer platform by initializing atoms on one tweezer and observing tunneling dynamics across the array for uniform and staggered 1D geometries.
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Affiliation(s)
- Benjamin M Spar
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | | | - Sungjae Chi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Zoe Z Yan
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Waseem S Bakr
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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7
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Observation of Cooper pairs in a mesoscopic two-dimensional Fermi gas. Nature 2022; 606:287-291. [PMID: 35676427 DOI: 10.1038/s41586-022-04678-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Accepted: 03/23/2022] [Indexed: 11/08/2022]
Abstract
The formation of strongly correlated fermion pairs is fundamental for the emergence of fermionic superfluidity and superconductivity1. For instance, Cooper pairs made of two electrons of opposite spin and momentum at the Fermi surface of the system are a key ingredient of Bardeen-Cooper-Schrieffer (BCS) theory-the microscopic explanation of the emergence of conventional superconductivity2. Understanding the mechanism behind pair formation is an ongoing challenge in the study of many strongly correlated fermionic systems3. Controllable many-body systems that host Cooper pairs would thus be desirable. Here we directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We apply an imaging scheme that enables us to extract the full in situ momentum distribution of a strongly interacting Fermi gas with single-particle and spin resolution4. Our ultracold gas enables us to freely tune between a completely non-interacting, unpaired system and weak attractions, where we find Cooper pair correlations at the Fermi surface. When increasing the attractive interactions even further, the pairs gradually turn into deeply bound molecules that break up the Fermi surface. Our mesoscopic system is closely related to the physics of nuclei, superconducting grains or quantum dots5-7. With the precise control over the interactions, particle number and potential landscape in our experiment, the observables we establish in this work provide an approach for answering longstanding questions concerning not only such mesoscopic systems but also their connection to the macroscopic world.
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8
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Realizing the symmetry-protected Haldane phase in Fermi-Hubbard ladders. Nature 2022; 606:484-488. [PMID: 35650440 PMCID: PMC9200636 DOI: 10.1038/s41586-022-04688-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 03/24/2022] [Indexed: 11/30/2022]
Abstract
Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain1,2. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter3,4. More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement5–7. Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi–Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator. A ladder-like arrangement of an ultracold gas of lithium atoms trapped in an optical lattice enables the observation of a symmetry-protected topological phase.
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9
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Koepsell J, Bourgund D, Sompet P, Hirthe S, Bohrdt A, Wang Y, Grusdt F, Demler E, Salomon G, Gross C, Bloch I. Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid. Science 2021; 374:82-86. [PMID: 34591626 DOI: 10.1126/science.abe7165] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Joannis Koepsell
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Dominik Bourgund
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Pimonpan Sompet
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Sarah Hirthe
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Annabelle Bohrdt
- Munich Center for Quantum Science and Technology, 80799 München, Germany.,Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Yao Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Department of Physics and Astronomy, Clemson University, Clemson, SC 29631, USA
| | - Fabian Grusdt
- Munich Center for Quantum Science and Technology, 80799 München, Germany.,Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Guillaume Salomon
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany.,The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, 22761 Hamburg, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology, 80799 München, Germany.,Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
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10
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Miles C, Bohrdt A, Wu R, Chiu C, Xu M, Ji G, Greiner M, Weinberger KQ, Demler E, Kim EA. Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data. Nat Commun 2021; 12:3905. [PMID: 34162847 PMCID: PMC8222395 DOI: 10.1038/s41467-021-23952-w] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 05/27/2021] [Indexed: 11/09/2022] Open
Abstract
Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data.
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Affiliation(s)
- Cole Miles
- Department of Physics, Cornell University, Ithaca, NY, USA
| | - Annabelle Bohrdt
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics and Institute for Advanced Study, Technical University of Munich, Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), München, Germany
| | - Ruihan Wu
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Christie Chiu
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
- Princeton Center for Complex Materials, Princeton University, Princeton, NJ, USA
| | - Muqing Xu
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Eun-Ah Kim
- Department of Physics, Cornell University, Ithaca, NY, USA.
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11
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Bohrdt A, Wang Y, Koepsell J, Kánasz-Nagy M, Demler E, Grusdt F. Dominant Fifth-Order Correlations in Doped Quantum Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 126:026401. [PMID: 33512175 DOI: 10.1103/physrevlett.126.026401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t-J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T_{c} superconductivity.
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Affiliation(s)
- A Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
| | - Y Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - J Koepsell
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - M Kánasz-Nagy
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
| | - E Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstrasse 37, München D-80333, Germany
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12
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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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13
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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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