1
|
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.
Collapse
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.
| |
Collapse
|
2
|
Lebrat M, Xu M, Kendrick LH, Kale A, Gang Y, Seetharaman P, Morera I, Khatami E, Demler E, Greiner M. Observation of Nagaoka polarons in a Fermi-Hubbard quantum simulator. Nature 2024; 629:317-322. [PMID: 38720043 DOI: 10.1038/s41586-024-07272-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 03/06/2024] [Indexed: 05/12/2024]
Abstract
Quantum interference can deeply alter the nature of many-body phases of matter1. In the case of the Hubbard model, Nagaoka proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference2-4. However, a microscopic observation of this kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice5,6. Using quantum gas microscopy, we image these polarons as extended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. By contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants7. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation8-10.
Collapse
Affiliation(s)
- Martin Lebrat
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Muqing Xu
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Anant Kale
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Youqi Gang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Pranav Seetharaman
- Department of Physics and Astronomy, San José State University, San Jose, CA, USA
| | - Ivan Morera
- Departament de Física Quàntica i Astrofísica, Universitat de Barcelona, Barcelona, Spain
- Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland
| | - Ehsan Khatami
- Department of Physics and Astronomy, San José State University, San Jose, CA, USA
| | - Eugene Demler
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
3
|
Wang B, Aidelsburger M, Dalibard J, Eckardt A, Goldman N. Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:163402. [PMID: 38701474 DOI: 10.1103/physrevlett.132.163402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/05/2024]
Abstract
Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.
Collapse
Affiliation(s)
- Botao Wang
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Monika Aidelsburger
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| |
Collapse
|
4
|
Pasqualetti G, Bettermann O, Darkwah Oppong N, Ibarra-García-Padilla E, Dasgupta S, Scalettar RT, Hazzard KRA, Bloch I, Fölling S. Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2024; 132:083401. [PMID: 38457712 DOI: 10.1103/physrevlett.132.083401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Accepted: 01/09/2024] [Indexed: 03/10/2024]
Abstract
We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.
Collapse
Affiliation(s)
- G Pasqualetti
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - O Bettermann
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - N Darkwah Oppong
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - E Ibarra-García-Padilla
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
- Department of Physics and Astronomy, San José State University, San José, California 95192, USA
| | - S Dasgupta
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
| | - R T Scalettar
- Department of Physics, University of California, Davis, California 95616, USA
| | - K R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics, University of California, Davis, California 95616, USA
| | - I Bloch
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - S Fölling
- Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| |
Collapse
|
5
|
Wang CY, Ho TL. Interference of holon strings in 2D Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:175402. [PMID: 38232392 DOI: 10.1088/1361-648x/ad1f8d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 01/17/2024] [Indexed: 01/19/2024]
Abstract
The 2D Hubbard model with large repulsion is an important problem in condensed matter physics. At half filling, its ground state is an antiferromagnet (AMF). The dope AMF below half filling is believed to capture the physics of highTcsuperconductors. And the fermion excitation of this dope AMF is theorized as splitting up into holons and spinons that carry charge and spin separately. It is believed that these exotic holons and spinons are the origins of the unusual properties of highTcsuperconductors. Despite the interests in holons and spinons, the direct observations of these excitations remain difficult in solid state experiments. Here, we show that with the rapid advances in the experimental techniques in cold atoms, the direct observation of holons is possible in quantum quench dynamic processes in cold atom settings. We show that the well-known holon-strings generated by the motion of a holon as well as their interferences can be detected by the measurements spin-spin correlations and demonstrate the presence of the Marshall phase associated with a holon string reflecting an underlying AMF background. Moreover, we show that the interferences of the holon strings make a holon propagate anisotropically, with a diffusion pattern clearly distinct from that of spinless fermions. At the same time, we show that these interferences lead to a large suppression in magnetic order in the region swept through by the strings (even to about 95% for some bond). We further demonstrate the Marshall phase of the holon-strings by comparing the dynamics of holon in thetJmodel with that of the so-calledσtJ-model, which is thetJmodel with the Marshall phase removed. The holons in these models propagate entirely differently.
Collapse
Affiliation(s)
- Chang-Yan Wang
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
| | - Tin-Lun Ho
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
| |
Collapse
|
6
|
Shen K, Gelin MF, Sun K, Zhao Y. Dynamics of a Magnetic Polaron in an Antiferromagnet. MATERIALS (BASEL, SWITZERLAND) 2024; 17:469. [PMID: 38255636 PMCID: PMC10820380 DOI: 10.3390/ma17020469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Revised: 01/07/2024] [Accepted: 01/16/2024] [Indexed: 01/24/2024]
Abstract
The t-J model remains an indispensable construct in high-temperature superconductivity research, bridging the gap between charge dynamics and spin interactions within antiferromagnetic matrices. This study employs the multiple Davydov Ansatz method with thermo-field dynamics to dissect the zero-temperature and finite-temperature behaviors. We uncover the nuanced dependence of hole and spin deviation dynamics on the spin-spin coupling parameter J, revealing a thermally-activated landscape where hole mobilities and spin deviations exhibit a distinct temperature-dependent relationship. This numerically accurate thermal perspective augments our understanding of charge and spin dynamics in an antiferromagnet.
Collapse
Affiliation(s)
- Kaijun Shen
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Maxim F. Gelin
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Kewei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yang Zhao
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
| |
Collapse
|
7
|
Di Carli A, Parsonage C, La Rooij A, Koehn L, Ulm C, Duncan CW, Daley AJ, Haller E, Kuhr S. Commensurate and incommensurate 1D interacting quantum systems. Nat Commun 2024; 15:474. [PMID: 38212298 PMCID: PMC10784295 DOI: 10.1038/s41467-023-44610-3] [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: 10/19/2023] [Accepted: 12/19/2023] [Indexed: 01/13/2024] Open
Abstract
Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments.
Collapse
Affiliation(s)
- Andrea Di Carli
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Christopher Parsonage
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Arthur La Rooij
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Lennart Koehn
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Clemens Ulm
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Callum W Duncan
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Andrew J Daley
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Elmar Haller
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom
| | - Stefan Kuhr
- Department of Physics, SUPA, University of Strathclyde, Glasgow, G4 0NG, United Kingdom.
| |
Collapse
|
8
|
Xu M, Kendrick LH, Kale A, Gang Y, Ji G, Scalettar RT, Lebrat M, Greiner M. Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator. Nature 2023; 620:971-976. [PMID: 37532942 DOI: 10.1038/s41586-023-06280-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Accepted: 06/02/2023] [Indexed: 08/04/2023]
Abstract
Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids1-3. Promising candidate materials for such phases4-6 can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration7-11. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model12. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices8,13 and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials14.
Collapse
Affiliation(s)
- Muqing Xu
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Anant Kale
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Youqi Gang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Martin Lebrat
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Hales J, Bajpai U, Liu T, Baykusheva DR, Li M, Mitrano M, Wang Y. Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering. Nat Commun 2023; 14:3512. [PMID: 37316515 DOI: 10.1038/s41467-023-38540-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2022] [Accepted: 05/03/2023] [Indexed: 06/16/2023] Open
Abstract
Characterizing and controlling entanglement in quantum materials is crucial for the development of next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in macroscopic solids is theoretically and experimentally challenging. At equilibrium the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopic observables and a nonequilibrium extension of this method could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials with time-resolved resonant inelastic x-ray scattering. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced many-body entanglement due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via ultrafast spectroscopic measurements.
Collapse
Affiliation(s)
- Jordyn Hales
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Utkarsh Bajpai
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Tongtong Liu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | | | - Mingda Li
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Matteo Mitrano
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA.
| | - Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA.
| |
Collapse
|
11
|
Xiong R, Nie JH, Brantly SL, Hays P, Sailus R, Watanabe K, Taniguchi T, Tongay S, Jin C. Correlated insulator of excitons in WSe 2/WS 2 moiré superlattices. Science 2023; 380:860-864. [PMID: 37167352 DOI: 10.1126/science.add5574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
A panoply of unconventional electronic states has been observed in moiré superlattices. Engineering similar bosonic phases remains, however, largely unexplored. We report the observation of a bosonic correlated insulator in WSe2/WS2 moiré superlattices composed of excitons, i.e., tightly bound electron-hole pairs. We develop a pump probe spectroscopy method that we use to observe an exciton incompressible state at exciton filling νex = 1 and charge neutrality, indicating a correlated insulator of excitons. With varying charge density, the bosonic correlated insulator continuously transitions into an electron correlated insulator at charge filling νe = 1, suggesting a mixed correlated insulating state between the two limits. Our studies establish semiconducting moiré superlattices as an intriguing platform for engineering bosonic phases.
Collapse
Affiliation(s)
- Richen Xiong
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Jacob H Nie
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Samuel L Brantly
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Patrick Hays
- School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Renee Sailus
- School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Sefaattin Tongay
- School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Chenhao Jin
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| |
Collapse
|
12
|
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: 5] [Impact Index Per Article: 5.0] [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.
Collapse
|
13
|
Nielsen KK, Pohl T, Bruun GM. Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons. PHYSICAL REVIEW LETTERS 2022; 129:246601. [PMID: 36563255 DOI: 10.1103/physrevlett.129.246601] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Revised: 08/12/2022] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
Abstract
We develop a nonperturbative theory for hole dynamics in antiferromagnetic spin lattices, as described by the t-J model. This is achieved by generalizing the self-consistent Born approximation to nonequilibrium systems, making it possible to calculate the full time-dependent many-body wave function. Our approach reveals three distinct dynamical regimes, ultimately leading to the formation of magnetic polarons. Following the initial ballistic stage of the hole dynamics, coherent formation of string excitations gives rise to characteristic oscillations in the hole density. Their damping eventually leaves behind magnetic polarons that undergo ballistic motion with a greatly reduced velocity. The developed theory provides a rigorous framework for understanding nonequilibrium physics of defects in quantum magnets and quantitatively explains recent observations from cold-atom quantum simulations in the strong coupling regime.
Collapse
Affiliation(s)
- K Knakkergaard Nielsen
- Max-Planck Institute for Quantum Optics, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark
| | - T Pohl
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark
| | - G M Bruun
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| |
Collapse
|
14
|
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.
Collapse
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
| |
Collapse
|
15
|
Daley AJ, Bloch I, Kokail C, Flannigan S, Pearson N, Troyer M, Zoller P. Practical quantum advantage in quantum simulation. Nature 2022; 607:667-676. [PMID: 35896643 DOI: 10.1038/s41586-022-04940-6] [Citation(s) in RCA: 43] [Impact Index Per Article: 21.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 06/07/2022] [Indexed: 11/09/2022]
Abstract
The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as 'quantum advantage'. As a next step along the development of this technology, it is now important to discuss 'practical quantum advantage', the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital-analogue devices that exist today already promise substantial flexibility in near-term applications.
Collapse
Affiliation(s)
- Andrew J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK.
| | - Immanuel Bloch
- Max Planck Institute of Quantum Optics, Garching, Germany.,Ludwig Maximilians University, Munich, Germany.,Munich Center for Quantum Science and Technology, Munich, Germany
| | - Christian Kokail
- Universität Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria
| | - Stuart Flannigan
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK
| | - Natalie Pearson
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK
| | | | - Peter Zoller
- Universität Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria
| |
Collapse
|
16
|
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.
Collapse
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
| |
Collapse
|
17
|
Abstract
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
Collapse
|
18
|
Zhu JX. Multipole polaron roams the devil's staircase. NATURE MATERIALS 2022; 21:384-385. [PMID: 35361948 DOI: 10.1038/s41563-022-01218-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Affiliation(s)
- Jian-Xin Zhu
- Theoretical Division and Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, NM, USA.
| |
Collapse
|
19
|
de Hond J, Xiang J, Chung WC, Cruz-Colón E, Chen W, Burton WC, Kennedy CJ, Ketterle W. Preparation of the Spin-Mott State: A Spinful Mott Insulator of Repulsively Bound Pairs. PHYSICAL REVIEW LETTERS 2022; 128:093401. [PMID: 35302815 DOI: 10.1103/physrevlett.128.093401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 01/28/2022] [Indexed: 06/14/2023]
Abstract
We observe and study a special ground state of bosons with two spin states in an optical lattice: the spin-Mott insulator, a state that consists of repulsively bound pairs that is insulating for both spin and charge transport. Because of the pairing gap created by the interaction anisotropy, it can be prepared with low entropy and can serve as a starting point for adiabatic state preparation. We find that the stability of the spin-Mott state depends on the pairing energy, and observe two qualitatively different decay regimes, one of which exhibits protection by the gap.
Collapse
Affiliation(s)
- Julius de Hond
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jinggang Xiang
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Woo Chang Chung
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Enid Cruz-Colón
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wenlan Chen
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - William Cody Burton
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Colin J Kennedy
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wolfgang Ketterle
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
20
|
Frérot I, Acín A. Coarse-Grained Self-Testing. PHYSICAL REVIEW LETTERS 2021; 127:240401. [PMID: 34951817 DOI: 10.1103/physrevlett.127.240401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Revised: 09/28/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
Self-testing is a device-independent method that usually amounts to show that the maximal quantum violation of a Bell's inequality certifies a unique quantum state, up to some symmetries inherent to the device-independent framework. In this work, we enlarge this approach and show how a coarse-grained version of self-testing is possible in which physically relevant properties of a many-body system are certified. To this aim we study a Bell scenario consisting of an arbitrary number of parties and show that the membership to a set of (entangled) quantum states whose size grows exponentially with the number of parties can be self-tested. Specifically, we prove that a many-body generalization of the chained Bell inequality is maximally violated if and only if the underlying quantum state is equal, up to local isometries, to a many-body singlet. The maximal violation of the inequality therefore certifies any statistical mixture of the exponentially many orthogonal pure states spanning the singlet manifold.
Collapse
Affiliation(s)
- Irénée Frérot
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Antonio Acín
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA - Institucio Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys 23, 08010 Barcelona, Spain
| |
Collapse
|
21
|
Bohrdt A, Demler E, Grusdt F. Rotational Resonances and Regge-like Trajectories in Lightly Doped Antiferromagnets. PHYSICAL REVIEW LETTERS 2021; 127:197004. [PMID: 34797143 DOI: 10.1103/physrevlett.127.197004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 10/13/2021] [Indexed: 06/13/2023]
Abstract
Understanding the nature of charge carriers in doped Mott insulators holds the key to unravelling puzzling properties of strongly correlated electron systems, including cuprate superconductors. Several theoretical models suggested that dopants can be understood as bound states of partons, the analogues of quarks in high-energy physics. However, direct signatures of spinon-chargon bound states are lacking, both in experiment and theory. Here we propose a rotational variant of angle-resolved photo-emission spectroscopy (ARPES) and calculate rotational spectra numerically using the density-matrix renormalization group. We identify long-lived rotational resonances for an individual dopant, which we interpret as a direct indicator of the microscopic structure of spinon-chargon bound states. Similar to Regge trajectories reflecting the quark structure of mesons, we establish a linear dependence of the rotational energy on the superexchange coupling. The rotational peaks we find are strongly suppressed in standard ARPES spectra, but we suggest a multiphoton extension of ARPES which allows us to access rotational spectra. Our findings suggest that multiphoton spectroscopy experiments should provide new insights into emergent universal features of strongly correlated electron systems.
Collapse
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), Schellingstr. 4, D-80799 München, Germany
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - E Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, München D-80333, Germany
| |
Collapse
|
22
|
Wang F, Mathur N, Janes AN, Sheng H, He P, Zheng X, Yu P, DeRuiter AJ, Schmidt JR, He J, Jin S. Defect-mediated ferromagnetism in correlated two-dimensional transition metal phosphorus trisulfides. SCIENCE ADVANCES 2021; 7:eabj4086. [PMID: 34678059 PMCID: PMC8535790 DOI: 10.1126/sciadv.abj4086] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/31/2021] [Indexed: 06/02/2023]
Abstract
Controlling the magnetic spin states of two-dimensional (2D) van der Waals (vdW) materials with strong electronic or magnetic correlation is important for spintronic applications but challenging. Crystal defects that are often present in 2D materials such as transition metal phosphorus trisulfides (MPS3) could influence their physical properties. Here, we report the effect of sulfur vacancies on the magnetic exchange interactions and spin ordering of few-layered vdW magnetic Ni1−xCoxPS3 nanosheets. Magnetic and structural characterization in corroboration with theoretical calculations reveal that sulfur vacancies effectively suppress the strong intralayer antiferromagnetic correlation, giving rise to a weak ferromagnetic ground state in Ni1−xCoxPS3 nanosheets. Notably, the magnetic field required to tune this ferromagnetic state (<300 Oe) is much lower than the value needed to tune a typical vdW antiferromagnet (> several thousand oersted). These findings provide a previously unexplored route for controlling competing correlated states and magnetic ordering by defect engineering in vdW materials.
Collapse
Affiliation(s)
- Fengmei Wang
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, P. R. China
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - Nitish Mathur
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - Aurora N. Janes
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - Hongyuan Sheng
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - Peng He
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, P. R. China
| | - Xueli Zheng
- Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA
| | - Peng Yu
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, P. R. China
| | - Andrew J. DeRuiter
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - J. R. Schmidt
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| | - Jun He
- CAS Center for Excellence in Nanoscience, CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing 100190, P. R. China
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, P. R. China
| | - Song Jin
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, WI 53706, USA
| |
Collapse
|
23
|
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: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
Collapse
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
| |
Collapse
|
24
|
Masi L, Petrucciani T, Ferioli G, Semeghini G, Modugno G, Inguscio M, Fattori M. Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice. PHYSICAL REVIEW LETTERS 2021; 127:020601. [PMID: 34296908 DOI: 10.1103/physrevlett.127.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 03/17/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.
Collapse
Affiliation(s)
- L Masi
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - T Petrucciani
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - G Ferioli
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Semeghini
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Modugno
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - M Fattori
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
| |
Collapse
|
25
|
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.
Collapse
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.
| |
Collapse
|
26
|
Guzelturk B, Winkler T, Van de Goor TWJ, Smith MD, Bourelle SA, Feldmann S, Trigo M, Teitelbaum SW, Steinrück HG, de la Pena GA, Alonso-Mori R, Zhu D, Sato T, Karunadasa HI, Toney MF, Deschler F, Lindenberg AM. Visualization of dynamic polaronic strain fields in hybrid lead halide perovskites. NATURE MATERIALS 2021; 20:618-623. [PMID: 33398119 DOI: 10.1038/s41563-020-00865-5] [Citation(s) in RCA: 52] [Impact Index Per Article: 17.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
Excitation localization involving dynamic nanoscale distortions is a central aspect of photocatalysis1, quantum materials2 and molecular optoelectronics3. Experimental characterization of such distortions requires techniques sensitive to the formation of point-defect-like local structural rearrangements in real time. Here, we visualize excitation-induced strain fields in a prototypical member of the lead halide perovskites4 via femtosecond resolution diffuse X-ray scattering measurements. This enables momentum-resolved phonon spectroscopy of the locally distorted structure and reveals radially expanding nanometre-scale strain fields associated with the formation and relaxation of polarons in photoexcited perovskites. Quantitative estimates of the magnitude and shape of this polaronic distortion are obtained, providing direct insights into the dynamic structural distortions that occur in these materials5-9. Optical pump-probe reflection spectroscopy corroborates these results and shows how these large polaronic distortions transiently modify the carrier effective mass, providing a unified picture of the coupled structural and electronic dynamics that underlie the optoelectronic functionality of the hybrid perovskites.
Collapse
Affiliation(s)
- Burak Guzelturk
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA
- X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA
| | - Thomas Winkler
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Department of Physics and Astronomy, Aarhus University, Aarhus C, Denmark
| | | | - Matthew D Smith
- Department of Chemistry, Stanford University, Stanford, CA, USA
| | - Sean A Bourelle
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Sascha Feldmann
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Mariano Trigo
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Samuel W Teitelbaum
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Hans-Georg Steinrück
- Stanford Synchrotron Radiation Laboratory Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- Department of Chemistry, Paderborn University, Paderborn, Germany
| | - Gilberto A de la Pena
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Roberto Alonso-Mori
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Diling Zhu
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Takahiro Sato
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Hemamala I Karunadasa
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
- Department of Chemistry, Stanford University, Stanford, CA, USA
| | - Michael F Toney
- Stanford Synchrotron Radiation Laboratory Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Felix Deschler
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Walter Schottky Institute, Department of Physics, Technical University of Munich, Garching, Germany
| | - Aaron M Lindenberg
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA.
- Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA.
- PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA.
| |
Collapse
|
27
|
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.
Collapse
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
| |
Collapse
|
28
|
Grusdt F, Pollet L. Z_{2} Parton Phases in the Mixed-Dimensional t-J_{z} Model. PHYSICAL REVIEW LETTERS 2020; 125:256401. [PMID: 33416402 DOI: 10.1103/physrevlett.125.256401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t-J_{z} model can be understood in terms of spinless chargons coupled to a Z_{2} lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z_{2} electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J_{z}, i.e., well within reach of current experiments.
Collapse
Affiliation(s)
- Fabian 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
| | - Lode Pollet
- 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
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| |
Collapse
|
29
|
Hartke T, Oreg B, Jia N, Zwierlein M. Doublon-Hole Correlations and Fluctuation Thermometry in a Fermi-Hubbard Gas. PHYSICAL REVIEW LETTERS 2020; 125:113601. [PMID: 32975995 DOI: 10.1103/physrevlett.125.113601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 07/19/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the single atom and single site-resolved detection of the total density in a cold atom realization of the 2D Fermi-Hubbard model. Fluorescence imaging of doublons is achieved by splitting each lattice site into a double well, thereby separating atom pairs. Full density readout yields a direct measurement of the equation of state, including direct thermometry via the fluctuation-dissipation theorem. Site-resolved density correlations reveal the Pauli hole at low filling, and strong doublon-hole correlations near half filling. These are shown to account for the difference between local and nonlocal density fluctuations in the Mott insulator. Our technique enables the study of atom-resolved charge transport in the Fermi-Hubbard model, the site-resolved observation of molecules, and the creation of bilayer Fermi-Hubbard systems.
Collapse
Affiliation(s)
- Thomas Hartke
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Botond Oreg
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ningyuan Jia
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Martin Zwierlein
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
30
|
Koepsell J, Hirthe S, Bourgund D, Sompet P, Vijayan J, Salomon G, Gross C, Bloch I. Robust Bilayer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy. PHYSICAL REVIEW LETTERS 2020; 125:010403. [PMID: 32678648 DOI: 10.1103/physrevlett.125.010403] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 06/09/2020] [Indexed: 06/11/2023]
Abstract
Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly stable vertical superlattice and subsequent charge pumping to separate the layers by 21 μm. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods, or the realization of tunable bilayer systems.
Collapse
Affiliation(s)
- Joannis Koepsell
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Sarah Hirthe
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Dominik Bourgund
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Pimonpan Sompet
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Jayadev Vijayan
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Guillaume Salomon
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 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 (MCQST), 80799 München, Germany
- Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 München, Germany
| |
Collapse
|
31
|
Chiu CS, Ji G, Bohrdt A, Xu M, Knap M, Demler E, Grusdt F, Greiner M, Greif D. String patterns in the doped Hubbard model. Science 2020; 365:251-256. [PMID: 31320533 DOI: 10.1126/science.aav3587] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 06/05/2019] [Indexed: 11/02/2022]
Abstract
Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.
Collapse
Affiliation(s)
- Christie S Chiu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Geoffrey Ji
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Annabelle Bohrdt
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Muqing Xu
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Eugene Demler
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| | - Fabian Grusdt
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Markus Greiner
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA.
| | - Daniel Greif
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
| |
Collapse
|
32
|
Vijayan J, Sompet P, Salomon G, Koepsell J, Hirthe S, Bohrdt A, Grusdt F, Bloch I, Gross C. Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains. Science 2020; 367:186-189. [DOI: 10.1126/science.aay2354] [Citation(s) in RCA: 55] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Accepted: 11/14/2019] [Indexed: 11/02/2022]
Abstract
Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
Collapse
Affiliation(s)
- Jayadev Vijayan
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Pimonpan Sompet
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Guillaume Salomon
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Joannis Koepsell
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Sarah Hirthe
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - Annabelle Bohrdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Fabian Grusdt
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 München, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
- Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| |
Collapse
|