1
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Valahu CH, Olaya-Agudelo VC, MacDonell RJ, Navickas T, Rao AD, Millican MJ, Pérez-Sánchez JB, Yuen-Zhou J, Biercuk MJ, Hempel C, Tan TR, Kassal I. Direct observation of geometric-phase interference in dynamics around a conical intersection. Nat Chem 2023; 15:1503-1508. [PMID: 37640849 DOI: 10.1038/s41557-023-01300-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 07/21/2023] [Indexed: 08/31/2023]
Abstract
Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analogue quantum simulators-such as those realized using trapped ions-to accurately describe nuclear quantum effects.
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Affiliation(s)
- C H Valahu
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
| | - V C Olaya-Agudelo
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
- School of Chemistry, University of Sydney, Sydney, New South Wales, Australia
| | - R J MacDonell
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
- School of Chemistry, University of Sydney, Sydney, New South Wales, Australia
- University of Sydney Nano Institute, University of Sydney, Sydney, New South Wales, Australia
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada
| | - T Navickas
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
| | - A D Rao
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
| | - M J Millican
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
| | - J B Pérez-Sánchez
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA
| | - J Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA
| | - M J Biercuk
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
| | - C Hempel
- School of Physics, University of Sydney, Sydney, New South Wales, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia
- Institute for Quantum Electronics, ETH Zürich, Zürich, Switzerland
- ETH Zurich-PSI Quantum Computing Hub, Paul Scherrer Institut, Villigen, Switzerland
| | - T R Tan
- School of Physics, University of Sydney, Sydney, New South Wales, Australia.
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia.
| | - I Kassal
- ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia.
- School of Chemistry, University of Sydney, Sydney, New South Wales, Australia.
- University of Sydney Nano Institute, University of Sydney, Sydney, New South Wales, Australia.
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2
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Chen C, Liu RZ, Wu J, Su ZE, Ding X, Qin J, Wang L, Zhang WW, He Y, Wang XL, Lu CY, Li L, Sanders BC, Liu XJ, Pan JW. Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands. PHYSICAL REVIEW LETTERS 2023; 131:133601. [PMID: 37831993 DOI: 10.1103/physrevlett.131.133601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 08/17/2023] [Indexed: 10/15/2023]
Abstract
Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.
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Affiliation(s)
- Chao Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Run-Ze Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jizhou Wu
- Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zu-En Su
- The Physics Department and the Solid State Institute, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Xing Ding
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian Qin
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Lin Wang
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
| | - Wei-Wei Zhang
- School of Computer Science, Northwestern Polytechnical University, Xi'an 710129, China
| | - Yu He
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xi-Lin Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Barry C Sanders
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- International Quantum Academy, Shenzhen 518048, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
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3
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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4
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Liu JY, Luo GQ, Wang XQ, Hemmerich A, Xu ZF. Experimental realization of a high precision tunable hexagonal optical lattice. OPTICS EXPRESS 2022; 30:44375-44384. [PMID: 36522863 DOI: 10.1364/oe.470742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 10/23/2022] [Indexed: 06/17/2023]
Abstract
Hexagonal optical lattices offer a tunable platform to study exotic orbital physics in solid state materials. Here, we present a versatile high-precision scheme to implement a hexagonal optical lattice potential, which is engineered by overlapping two independent triangular optical sublattices generated by laser beams with slightly different wavelengths around 1064 nm. This enables us to precisely control the detailed structure of the hexagonal lattice by adjusting the relative position and the relative lattice depth of the two triangular optical sublattices. Taking advantage of the sensitive dependence of the second Bloch band on small lattice deformations, we propose a strategy to optimize the optical lattice geometry with an extremely high precision. This method can also be extended to other lattice configurations involving more than two sublattices. Our work provides the experimental requirements in the search for novel orbital physics of ultracold atoms, for example, in the flat p-band of the hexagonal optical lattice.
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5
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Li JZ, Zou CJ, Du YX, Lv QX, Huang W, Liang ZT, Zhang DW, Yan H, Zhang S, Zhu SL. Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2022; 129:220402. [PMID: 36493448 DOI: 10.1103/physrevlett.129.220402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Revised: 09/24/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Topological vacua are a family of degenerate ground states of Yang-Mills fields with zero field strength but nontrivial topological structures. They play a fundamental role in particle physics and quantum field theory, but have not yet been experimentally observed. Here we report the first theoretical proposal and experimental realization of synthetic topological vacua with a cloud of atomic Bose-Einstein condensates. Our setup provides a promising platform to demonstrate the fundamental concept that a vacuum, rather than being empty, has rich spatial structures. The Hamiltonian for the vacuum of topological number n=1 is synthesized and the related Hopf index is measured. The vacuum of topological number n=2 is also realized, and we find that vacua with different topological numbers have distinctive spin textures and Hopf links. Our Letter opens up opportunities for exploring topological vacua and related long-sought-after instantons in tabletop experiments.
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Affiliation(s)
- Jia-Zhen Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Cong-Jun Zou
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Yan-Xiong Du
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Qing-Xian Lv
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Wei Huang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Zhen-Tao Liang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Engineering Technology Research Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, China
| | - Shanchao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
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6
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Hasan M, Madasu CS, Rathod KD, Kwong CC, Miniatura C, Chevy F, Wilkowski D. Wave Packet Dynamics in Synthetic Non-Abelian Gauge Fields. PHYSICAL REVIEW LETTERS 2022; 129:130402. [PMID: 36206409 DOI: 10.1103/physrevlett.129.130402] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 04/10/2022] [Accepted: 07/29/2022] [Indexed: 06/16/2023]
Abstract
It is generally admitted that in quantum mechanics, the electromagnetic potentials have physical interpretations otherwise absent in classical physics as illustrated by the Aharonov-Bohm effect. In 1984, Berry interpreted this effect as a geometrical phase factor. The same year, Wilczek and Zee generalized the concept of Berry phases to degenerate levels and showed that a non-Abelian gauge field arises in these systems. In sharp contrast with the Abelian case, spatially uniform non-Abelian gauge fields can induce particle noninertial motion. We explore this intriguing phenomenon with a degenerated Fermionic atomic gas subject to a two-dimensional synthetic SU(2) non-Abelian gauge field. We reveal the spin Hall nature of the noninertial dynamic as well as its anisotropy in amplitude and frequency due to the spin texture of the system. We finally draw the similarities and differences of the observed wave packet dynamic and the celebrated Zitterbewegung effect of the relativistic Dirac equation.
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Affiliation(s)
- Mehedi Hasan
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
| | - Chetan Sriram Madasu
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
| | - Ketan D Rathod
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
| | - Chang Chi Kwong
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
| | - Christian Miniatura
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
- Université Côte d'Azur, CNRS, INPHYNI, 06108 Nice, France
| | - Frédéric Chevy
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - David Wilkowski
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore
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7
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Brown CD, Chang SW, Schwarz MN, Leung TH, Kozii V, Avdoshkin A, Moore JE, Stamper-Kurn D. Direct geometric probe of singularities in band structure. Science 2022; 377:1319-1322. [DOI: 10.1126/science.abm6442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
A quantum system’s energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system’s properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.
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Affiliation(s)
- Charles D. Brown
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, Berkeley, CA 94720, USA
- Department of Physics, Yale University, New Haven, CT 06520, USA
| | - Shao-Wen Chang
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Malte N. Schwarz
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Tsz-Him Leung
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Vladyslav Kozii
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Alexander Avdoshkin
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Joel E. Moore
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Dan Stamper-Kurn
- Department of Physics, University of California, Berkeley, Berkeley, CA 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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8
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Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.
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9
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Li F, Xue K, Yi X. Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice. ENTROPY 2021; 23:e23111404. [PMID: 34828102 PMCID: PMC8624070 DOI: 10.3390/e23111404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Revised: 10/13/2021] [Accepted: 10/14/2021] [Indexed: 11/16/2022]
Abstract
Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson-hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.
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10
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Lv QX, Du YX, Liang ZT, Liu HZ, Liang JH, Chen LQ, Zhou LM, Zhang SC, Zhang DW, Ai BQ, Yan H, Zhu SL. Measurement of Spin Chern Numbers in Quantum Simulated Topological Insulators. PHYSICAL REVIEW LETTERS 2021; 127:136802. [PMID: 34623865 DOI: 10.1103/physrevlett.127.136802] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wave functions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are nonvanished.
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Affiliation(s)
- Qing-Xian Lv
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Yan-Xiong Du
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Zhen-Tao Liang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Hong-Zhi Liu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Jia-Hao Liang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Lin-Qing Chen
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Li-Ming Zhou
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Shan-Chao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
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11
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Käming N, Dawid A, Kottmann K, Lewenstein M, Sengstock K, Dauphin A, Weitenberg C. Unsupervised machine learning of topological phase transitions from experimental data. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abffe7] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Abstract
Identifying phase transitions is one of the key challenges in quantum many-body physics. Recently, machine learning methods have been shown to be an alternative way of localising phase boundaries from noisy and imperfect data without the knowledge of the order parameter. Here, we apply different unsupervised machine learning techniques, including anomaly detection and influence functions, to experimental data from ultracold atoms. In this way, we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion. We show that these methods can successfully be applied to experimental data at finite temperatures and to the data of Floquet systems when post-processing the data to a single micromotion phase. Our work provides a benchmark for the unsupervised detection of new exotic phases in complex many-body systems.
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12
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St-Jean P, Dauphin A, Massignan P, Real B, Jamadi O, Milicevic M, Lemaître A, Harouri A, Le Gratiet L, Sagnes I, Ravets S, Bloch J, Amo A. Measuring Topological Invariants in a Polaritonic Analog of Graphene. PHYSICAL REVIEW LETTERS 2021; 126:127403. [PMID: 33834841 DOI: 10.1103/physrevlett.126.127403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 09/08/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g., graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D subspaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene where Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems and opens the door to the exploration of more complex topological effects, e.g., involving disorder and interactions.
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Affiliation(s)
- P St-Jean
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Dauphin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - P Massignan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, 08034 Barcelona, Spain
| | - B Real
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - O Jamadi
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M Milicevic
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Harouri
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - L Le Gratiet
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - I Sagnes
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - S Ravets
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - J Bloch
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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13
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Topological features without a lattice in Rashba spin-orbit coupled atoms. Nat Commun 2021; 12:593. [PMID: 33500408 PMCID: PMC7838279 DOI: 10.1038/s41467-020-20762-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 12/18/2020] [Indexed: 11/08/2022] Open
Abstract
Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for creating quantized channels for transporting electrical current, light, and atmospheric disturbances. These topological effects are quantified in terms of integer-valued 'invariants', such as the Chern number, applicable to the quantum Hall effect, or the [Formula: see text] invariant suitable for topological insulators. Here, we report the engineering of Rashba spin-orbit coupling for a cold atomic gas giving non-trivial topology, without the underlying crystalline structure that conventionally yields integer Chern numbers. We validated our procedure by spectroscopically measuring both branches of the Rashba dispersion relation which touch at a single Dirac point. We then measured the quantum geometry underlying the dispersion relation using matter-wave interferometry to implement a form of quantum state tomography, giving a Berry's phase with magnitude π. This implies that opening a gap at the Dirac point would give two dispersions (bands) each with half-integer Chern number, potentially implying new forms of topological transport.
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14
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Di Liberto M, Goldman N, Palumbo G. Non-Abelian Bloch oscillations in higher-order topological insulators. Nat Commun 2020; 11:5942. [PMID: 33230167 PMCID: PMC7684321 DOI: 10.1038/s41467-020-19518-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 10/13/2020] [Indexed: 11/09/2022] Open
Abstract
Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.
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Affiliation(s)
- M Di Liberto
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium.
| | - N Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
| | - G Palumbo
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
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15
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Huang B, Liu WV. Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization. PHYSICAL REVIEW LETTERS 2020; 124:216601. [PMID: 32530681 DOI: 10.1103/physrevlett.124.216601] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Accepted: 05/11/2020] [Indexed: 06/11/2023]
Abstract
Higher-order topological insulators (HOTIs) have emerged as a new class of phases, whose robust in-gap "corner" modes arise from the bulk higher-order multipoles beyond the dipoles in conventional topological insulators. Here, we incorporate Floquet driving into HOTIs, and report for the first time a dynamical polarization theory with anomalous nonequilibrium multipoles. Further, a proposal to detect not only corner states but also their dynamical origin in cold atoms is demonstrated, with the latter one never achieved before. Experimental determination of anomalous Floquet corner modes is also proposed.
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Affiliation(s)
- Biao Huang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA 15260, USA
| | - W Vincent Liu
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA 15260, USA
- Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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16
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Universal momentum-to-real-space mapping of topological singularities. Nat Commun 2020; 11:1586. [PMID: 32221307 PMCID: PMC7101314 DOI: 10.1038/s41467-020-15374-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/04/2020] [Indexed: 11/26/2022] Open
Abstract
Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams. Topological properties of materials are typically presented in momentum space. Here, the authors show a universal mapping of topological singularities from momentum to real space, potentially applicable to a wide range of systems.
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17
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Gou W, Chen T, Xie D, Xiao T, Deng TS, Gadway B, Yi W, Yan B. Tunable Nonreciprocal Quantum Transport through a Dissipative Aharonov-Bohm Ring in Ultracold Atoms. PHYSICAL REVIEW LETTERS 2020; 124:070402. [PMID: 32142332 DOI: 10.1103/physrevlett.124.070402] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2019] [Accepted: 02/03/2020] [Indexed: 06/10/2023]
Abstract
We report the experimental observation of tunable, nonreciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parameters. We demonstrate that the nonreciprocity originates from the interplay of the synthetic magnetic flux and the laser-induced loss, which simultaneously breaks the inversion and the time-reversal symmetries. Our results open up the avenue for investigating nonreciprocal dynamics in cold atoms, and highlight the dissipative AB ring as a flexible building element for applications in quantum simulation and quantum information.
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Affiliation(s)
- Wei Gou
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tao Chen
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Dizhou Xie
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Teng Xiao
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tian-Shu Deng
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Bo Yan
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
- Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
- Key Laboratory of Quantum Optics, Chinese Academy of Sciences, Shanghai, 200800, China
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18
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Yu M, Yang P, Gong M, Cao Q, Lu Q, Liu H, Zhang S, Plenio MB, Jelezko F, Ozawa T, Goldman N, Cai J. Experimental measurement of the quantum geometric tensor using coupled qubits in diamond. Natl Sci Rev 2020; 7:254-260. [PMID: 34692040 PMCID: PMC8288884 DOI: 10.1093/nsr/nwz193] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2019] [Revised: 11/17/2019] [Accepted: 11/18/2019] [Indexed: 12/03/2022] Open
Abstract
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
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Affiliation(s)
- Min Yu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Pengcheng Yang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Musang Gong
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qingyun Cao
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qiuyu Lu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Haibin Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shaoliang Zhang
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Martin B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fedor Jelezko
- Institut für Quantenoptik & IQST, Albert-Einstein Allee 11, Universität Ulm, D-89081 Ulm, Germany.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Tomoki Ozawa
- Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium
| | - Jianming Cai
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
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19
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Matsyshyn O, Sodemann I. Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule. PHYSICAL REVIEW LETTERS 2019; 123:246602. [PMID: 31922840 DOI: 10.1103/physrevlett.123.246602] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 10/07/2019] [Indexed: 06/10/2023]
Abstract
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects.
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Affiliation(s)
- O Matsyshyn
- Max Planck Institute for the Physics of Complex Systems, Dresden 01187, Germany
| | - I Sodemann
- Max Planck Institute for the Physics of Complex Systems, Dresden 01187, Germany
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20
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Ünal FN, Seradjeh B, Eckardt A. How to Directly Measure Floquet Topological Invariants in Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 122:253601. [PMID: 31347903 DOI: 10.1103/physrevlett.122.253601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 06/10/2023]
Abstract
The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the gaps. We propose a feasible scheme for measuring these winding numbers in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a by-product, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.
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Affiliation(s)
- F Nur Ünal
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Babak Seradjeh
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Department of Physics, Indiana University, 727 E Third Street, Bloomington, Indiana 47405, USA
| | - André Eckardt
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
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21
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Tan X, Zhang DW, Yang Z, Chu J, Zhu YQ, Li D, Yang X, Song S, Han Z, Li Z, Dong Y, Yu HF, Yan H, Zhu SL, Yu Y. Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit. PHYSICAL REVIEW LETTERS 2019; 122:210401. [PMID: 31283314 DOI: 10.1103/physrevlett.122.210401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Indexed: 06/09/2023]
Abstract
A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system. The work opens up a unique approach to explore the topology of quantum states with the QGT.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Zhen Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Ji Chu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Danyu Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Xiaopei Yang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Shuqing Song
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhikun Han
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhiyuan Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yuqian Dong
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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22
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Song D, Leykam D, Su J, Liu X, Tang L, Liu S, Zhao J, Efremidis NK, Xu J, Chen Z. Valley Vortex States and Degeneracy Lifting via Photonic Higher-Band Excitation. PHYSICAL REVIEW LETTERS 2019; 122:123903. [PMID: 30978034 DOI: 10.1103/physrevlett.122.123903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Indexed: 06/09/2023]
Abstract
We demonstrate valley-dependent vortex generation in photonic graphene. Without breaking inversion symmetry, the excitation of two valleys leads to the formation of an optical vortex upon Bragg reflection to the third equivalent valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without a synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase-mediated topological phenomena in other systems.
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Affiliation(s)
- Daohong Song
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Daniel Leykam
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Jing Su
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Xiuying Liu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Liqin Tang
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Sheng Liu
- The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and School of Science, Northwestern Polytechnical University, Xi'an 710072, China
| | - Jianlin Zhao
- The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and School of Science, Northwestern Polytechnical University, Xi'an 710072, China
| | - Nikolaos K Efremidis
- Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion, Crete, Greece
| | - Jingjun Xu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Zhigang Chen
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, and TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
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23
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Schine N, Chalupnik M, Can T, Gromov A, Simon J. Electromagnetic and gravitational responses of photonic Landau levels. Nature 2019; 565:173-179. [DOI: 10.1038/s41586-018-0817-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Accepted: 10/31/2018] [Indexed: 11/09/2022]
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24
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Cooper NR, Dalibard J, Spielman IB. Topological bands for ultracold atoms. REVIEWS OF MODERN PHYSICS 2019; 91:10.1103/revmodphys.91.015005. [PMID: 32189812 PMCID: PMC7079706 DOI: 10.1103/revmodphys.91.015005] [Citation(s) in RCA: 123] [Impact Index Per Article: 24.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.
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Affiliation(s)
- N R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 place Marcelin Berthelot, 75005, Paris, France
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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Abstract
We construct a generalized system by introducing an additional long-range hopping to the well-known Su-Schrieffer-Heeger (SSH) model. This system exhibits richer topological properties including non-trivial topological phases and associated localized edge states. We study the zero-energy edge states in detail and derive the edge-state wave functions using two different methods. Furthermore, we propose a possible setup using octupole moments optically excited on an array of dielectric particles for the realization of the system, and by adjusting the coupling strengths between neighboring particles we can control the hotspots (near-field enhancement) in such structures.
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26
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Xie BY, Wang HF, Zhu XY, Lu MH, Wang ZD, Chen YF. Photonics meets topology. OPTICS EXPRESS 2018; 26:24531-24550. [PMID: 30469568 DOI: 10.1364/oe.26.024531] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2018] [Accepted: 08/20/2018] [Indexed: 06/09/2023]
Abstract
The topological phases in materials have been studied in recent decades for their unique boundary states and transport properties. Photonic systems with band structures embrace the topological phases closely, where they not only provide platforms to testify the topological band theory, but also shed light on designing novel optical devices. In this review, we present exciting developments, supported by brief descriptions of prominent milestones of topological phases in photonic systems in recent years. These studies may sustain further developments of optical devices and offer novel methods for light manipulations.
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27
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Mukherjee S, Di Liberto M, Öhberg P, Thomson RR, Goldman N. Experimental Observation of Aharonov-Bohm Cages in Photonic Lattices. PHYSICAL REVIEW LETTERS 2018; 121:075502. [PMID: 30169066 DOI: 10.1103/physrevlett.121.075502] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2018] [Indexed: 06/08/2023]
Abstract
We report on the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in photonic lattices. Considering a rhombic array of optical waveguides, we engineer modulation-assisted tunneling processes that effectively produce nonzero magnetic flux per plaquette. This synthetic magnetic field for light can be tuned at will by varying the phase of the modulation. In the regime where half a flux quantum is realized in each plaquette, all the energy bands dramatically collapse into nondispersive (flat) bands and all eigenstates are completely localized. We demonstrate this Aharonov-Bohm caging by studying the propagation of light in the bulk of the photonic lattice. Besides, we explore the dynamics on the edge of the lattice and discuss how the corresponding edge states can be continuously connected to the topological edge states of the Creutz ladder. Our photonic lattice constitutes an appealing platform where the interplay between engineered gauge fields, frustration, localization, and topological properties can be finely studied.
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Affiliation(s)
- Sebabrata Mukherjee
- Scottish Universities Physics Alliance (SUPA), Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Marco Di Liberto
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Patrik Öhberg
- Scottish Universities Physics Alliance (SUPA), Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Robert R Thomson
- Scottish Universities Physics Alliance (SUPA), Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
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28
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Sun Y, Leykam D, Nenni S, Song D, Chen H, Chong YD, Chen Z. Observation of Valley Landau-Zener-Bloch Oscillations and Pseudospin Imbalance in Photonic Graphene. PHYSICAL REVIEW LETTERS 2018; 121:033904. [PMID: 30085826 DOI: 10.1103/physrevlett.121.033904] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2017] [Revised: 05/04/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate intervalley Bloch oscillation (BO) and Landau-Zener tunneling (LZT) in an optically induced honeycomb lattice with a refractive-index gradient. Unlike previously observed BO in a gapped square lattice, we show nonadiabatic beam dynamics that are highly sensitive to the direction of the index gradient and the choice of the Dirac cones. In particular, a symmetry-preserving potential leads to nearly perfect LZT and coherent BO between the inequivalent valleys, whereas a symmetry-breaking potential generates asymmetric scattering, imperfect LZT, and valley-sensitive generation of vortices mediated by a pseudospin imbalance. This clearly indicates that, near the Dirac points, the transverse gradient does not always act as a simple scalar force, as commonly assumed, and the LZT probability is strongly affected by the sublattice symmetry as analyzed from an effective Landau-Zener Hamiltonian. Our results illustrate the anisotropic response of an otherwise isotropic Dirac platform to real-space potentials acting as strong driving fields, which may be useful for manipulation of pseudospin and valley degrees of freedom in graphenelike systems.
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Affiliation(s)
- Yong Sun
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Daniel Leykam
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Stephen Nenni
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Daohong Song
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Y D Chong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Zhigang Chen
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
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29
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Liu B, Zhang P, Gao H, Li F. Chiral Orbital Magnetism of p-Orbital Bosons in Optical Lattices. PHYSICAL REVIEW LETTERS 2018; 121:015303. [PMID: 30028178 DOI: 10.1103/physrevlett.121.015303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2017] [Indexed: 06/08/2023]
Abstract
Chiral magnetism is a fascinating quantum phenomena that has been found in low-dimensional magnetic materials. It is not only interesting for understanding the concept of chirality, but also important for potential applications in spintronics. Past studies show that chiral magnets require both a lack of inversion symmetry and spin-orbit coupling to induce the Dzyaloshinskii-Moriya interaction. Here we report that the combination of inversion symmetry breaking and quantum degeneracy of orbital degrees of freedom will provide a new paradigm to achieve chiral orbital magnetism. By means of density matrix renormalization group calculation, we demonstrate that chiral orbital magnetism can be found when considering bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The high tunability of our scheme is also illustrated through simply manipulating the inversion symmetry of the system for cold atom experimental conditions.
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Affiliation(s)
- Bo Liu
- Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
| | - Peng Zhang
- Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
| | - Hong Gao
- Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
| | - Fuli Li
- Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
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30
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Yan Y, Zhou Q. Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons. PHYSICAL REVIEW LETTERS 2018; 120:235302. [PMID: 29932699 DOI: 10.1103/physrevlett.120.235302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2017] [Indexed: 06/08/2023]
Abstract
The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.
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Affiliation(s)
- Yangqian Yan
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47906, USA
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47906, USA
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31
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Geiger ZA, Fujiwara KM, Singh K, Senaratne R, Rajagopal SV, Lipatov M, Shimasaki T, Driben R, Konotop VV, Meier T, Weld DM. Observation and Uses of Position-Space Bloch Oscillations in an Ultracold Gas. PHYSICAL REVIEW LETTERS 2018; 120:213201. [PMID: 29883162 DOI: 10.1103/physrevlett.120.213201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Indexed: 05/22/2023]
Abstract
We report the observation and characterization of position-space Bloch oscillations using cold atoms in a tilted optical lattice. While momentum-space Bloch oscillations are a common feature of optical lattice experiments, the real-space center-of-mass dynamics are typically unresolvable. In a regime of rapid tunneling and low force, we observe real-space Bloch oscillation amplitudes of hundreds of lattice sites, in both ground and excited bands. We demonstrate two unique capabilities enabled by tracking of Bloch dynamics in position space: measurement of the full position-momentum phase-space evolution during a Bloch cycle, and direct imaging of the lattice band structure. These techniques, along with the ability to exert long-distance coherent control of quantum gases without modulation, may open up new possibilities for quantum control and metrology.
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Affiliation(s)
- Zachary A Geiger
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Kurt M Fujiwara
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Kevin Singh
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Ruwan Senaratne
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Shankari V Rajagopal
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Mikhail Lipatov
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Toshihiko Shimasaki
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
| | - Rodislav Driben
- Department of Physics and CeOPP, University of Paderborn, D-33098 Paderborn, Germany
| | - Vladimir V Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, Lisboa 1749-016, Portugal
| | - Torsten Meier
- Department of Physics and CeOPP, University of Paderborn, D-33098 Paderborn, Germany
| | - David M Weld
- University of California and California Institute for Quantum Emulation, Santa Barbara, California 93105, USA
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32
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Tan X, Zhang DW, Liu Q, Xue G, Yu HF, Zhu YQ, Yan H, Zhu SL, Yu Y. Topological Maxwell Metal Bands in a Superconducting Qutrit. PHYSICAL REVIEW LETTERS 2018; 120:130503. [PMID: 29694203 DOI: 10.1103/physrevlett.120.130503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Revised: 01/01/2018] [Indexed: 06/08/2023]
Abstract
We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Threefold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Qiang Liu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Guangming Xue
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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33
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Liu S, Shao LB, Hou QZ, Xue ZY. Quantum anomalous Hall phase in a one-dimensional optical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:124001. [PMID: 29380747 DOI: 10.1088/1361-648x/aaab89] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
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Affiliation(s)
- Sheng Liu
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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34
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Abstract
Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom-based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.
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Affiliation(s)
- Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany. .,Germany Fakultät für Physik, Ludwig-Maximilians-Universität, 80799 Munich, Germany
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35
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Luu TT, Wörner HJ. Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat Commun 2018; 9:916. [PMID: 29500349 PMCID: PMC5834542 DOI: 10.1038/s41467-018-03397-4] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2017] [Accepted: 02/08/2018] [Indexed: 11/09/2022] Open
Abstract
Berry phase and Berry curvature have become ubiquitous concepts in physics, relevant to a variety of phenomena, such as polarization, various Hall effects, etc. Studies of these phenomena call for characterization of Berry phase or curvature which is largely limited to theory, and a few measurements in optical lattices. In this work, we report polarimetry of high-harmonic emission from solids and exploit this novel capability to directly retrieve the Berry curvature of α-quartz. We show that the two manifestations of broken inversion symmetry in solids lead to perpendicular or parallel polarization of even harmonics with respect to the driving field. Using semiclassical transport theory, we retrieve the Berry curvature from spectra measured in perpendicular polarization, the results being supported by ab initio calculation. Our work demonstrates an approach for the direct measurement of Berry curvature in solids, which could serve as a benchmark for theoretical studies.
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Affiliation(s)
- Tran Trung Luu
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093, Zürich, Switzerland.
| | - Hans Jakob Wörner
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093, Zürich, Switzerland
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36
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Zhao S, Wu Y, Zhang K, Ding H, Du D, Zhao J, Pan N, Wang X. Manipulating the quantum interference effect and magnetotransport of ZnO nanowires through interfacial doping. NANOSCALE 2017; 9:17610-17616. [PMID: 29114687 DOI: 10.1039/c7nr05917e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We carefully prepared interfacial Al-doped (IAD) and interfacial natively-doped (IND) ZnO nanowires (NWs) by introducing atomic-layer interfacial Δ-doping between the two steps of CVD growth. Variable-temperature electron transport as well as magnetotransport behaviours of these NWs were systematically investigated. By virtue of the unique architecture and the quality-guaranteed growth technique, a series of quantum interference effects were clearly observed in the IAD ZnO NWs, including weak localization, universal conductance fluctuation and Altshuler-Aronov-Spivak oscillations. The phase-coherence length (Lφ) of electrons exceeds 100 nm in the IAD ZnO NWs, much longer than those in the IND ones and most conventionally doped ZnO NWs. This ability to efficiently manipulate a variety of quantum interference effects in ZnO NWs is very desirable for applications in nano-optoelectronics, nano- & quantum-electronics and solid-state quantum computing.
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Affiliation(s)
- Siwen Zhao
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, P.R. China.
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37
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Zhang WW, Sanders BC, Apers S, Goyal SK, Feder DL. Detecting Topological Transitions in Two Dimensions by Hamiltonian Evolution. PHYSICAL REVIEW LETTERS 2017; 119:197401. [PMID: 29219504 DOI: 10.1103/physrevlett.119.197401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Indexed: 06/07/2023]
Abstract
We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing of the band gap, a prerequisite for a quantum phase transition between topological phases. Furthermore, for realistic and experimentally motivated Hamiltonians, the density profile in topologically nontrivial phases displays characteristic rings in the vicinity of the origin that are absent in trivial phases. The results are expected to have an immediate application to systems of ultracold atoms and photonic lattices.
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Affiliation(s)
- Wei-Wei Zhang
- State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
- Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
| | - Barry C Sanders
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1, Canada
| | - Simon Apers
- SYSTeMS, Ghent University IR08, Technologiepark 913, B-9052 Zwijnaarde, Belgium
| | - Sandeep K Goyal
- Indian Institute of Science Education and Research, Mohali, Punjab 140306, India
| | - David L Feder
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
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38
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Velasco CG, Paredes B. Realizing and Detecting a Topological Insulator in the AIII Symmetry Class. PHYSICAL REVIEW LETTERS 2017; 119:115301. [PMID: 28949240 DOI: 10.1103/physrevlett.119.115301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Indexed: 06/07/2023]
Abstract
Topological insulators in the AIII (chiral unitary) symmetry class lack experimental realization. Moreover, fractionalization in one-dimensional topological insulators has not been yet directly observed. Our work might open possibilities for both challenges. We propose a one-dimensional model realizing the AIII symmetry class which can be realized in current experiments with ultracold atomic gases. We further report on a distinctive property of topological edge modes in the AIII class: in contrast to those in the well-studied BDI (chiral orthogonal) class, they have nonzero momentum. Exploiting this feature we propose a path for the detection of fractionalization. A fermion added to an AIII system splits into two halves localized at opposite momenta, which can be detected by imaging the momentum distribution.
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Affiliation(s)
- Carlos G Velasco
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany and Instituto de Física Teórica CSIC/UAM, C/Nicolás Cabrera, 13-15 Cantoblanco, 28049 Madrid, Spain
| | - Belén Paredes
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany and Instituto de Física Teórica CSIC/UAM, C/Nicolás Cabrera, 13-15 Cantoblanco, 28049 Madrid, Spain
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39
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Tran DT, Dauphin A, Grushin AG, Zoller P, Goldman N. Probing topology by "heating": Quantized circular dichroism in ultracold atoms. SCIENCE ADVANCES 2017; 3:e1701207. [PMID: 28835930 PMCID: PMC5562418 DOI: 10.1126/sciadv.1701207] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2017] [Accepted: 07/16/2017] [Indexed: 05/30/2023]
Abstract
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ2, where h = 2π ℏ is Planck's constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.
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Affiliation(s)
- Duc Thanh Tran
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Alexandre Dauphin
- ICFO–Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Adolfo G. Grushin
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Institut Néel, CNRS and Université Grenoble Alpes, F-38042 Grenoble, France
| | - Peter Zoller
- International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine, B-1050 Brussels, Belgium
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
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40
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Tarnowski M, Nuske M, Fläschner N, Rem B, Vogel D, Freystatzky L, Sengstock K, Mathey L, Weitenberg C. Observation of Topological Bloch-State Defects and Their Merging Transition. PHYSICAL REVIEW LETTERS 2017; 118:240403. [PMID: 28665652 DOI: 10.1103/physrevlett.118.240403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Indexed: 06/07/2023]
Abstract
Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.
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Affiliation(s)
- Matthias Tarnowski
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Marlon Nuske
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Nick Fläschner
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Benno Rem
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Dominik Vogel
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
| | - Lukas Freystatzky
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Klaus Sengstock
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Ludwig Mathey
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Christof Weitenberg
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
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41
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Zhang P, Gallardo D, Liu S, Gao Y, Li T, Wang Y, Chen Z, Zhang X. Vortex degeneracy lifting and Aharonov-Bohm-like interference in deformed photonic graphene. OPTICS LETTERS 2017; 42:915-918. [PMID: 28248330 DOI: 10.1364/ol.42.000915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Photonic graphene, a honeycomb lattice of evanescently coupled waveguides, has provided a superior platform for investigating a host of fundamental phenomena such as unconventional edge states, synthetic magnetic fields, photonic Landau levels, Floquet topological insulators, and pseudospin effects. Here, we demonstrate both experimentally and numerically, topological vortex degeneracy lifting and Aharonov-Bohm-like interference from local deformation in a photonic honeycomb lattice. When a single valley is excited, lattice deformation leads to the generation of a vortex pair due to the lifting of degeneracy associated with pseudospin states. In the case of double-valley excitation, we observe the Aharonov-Bohm-like interference merely due to the deformation of the graphene lattice, which gives rise to an artificial gauge field. Our results may provide insight into the understanding of similar phenomena in other graphene-like materials and structures.
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42
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Livi LF, Cappellini G, Diem M, Franchi L, Clivati C, Frittelli M, Levi F, Calonico D, Catani J, Inguscio M, Fallani L. Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition. PHYSICAL REVIEW LETTERS 2016; 117:220401. [PMID: 27925719 DOI: 10.1103/physrevlett.117.220401] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron ^{173}Yb atoms. By mapping the electronic states onto effective sites along a synthetic "electronic" dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.
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Affiliation(s)
- L F Livi
- LENS European Laboratory for Nonlinear Spectroscopy, I-50019 Sesto Fiorentino, Italy
- INO-CNR Istituto Nazionale di Ottica del CNR, Sezione di Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
| | - G Cappellini
- Department of Physics and Astronomy, University of Florence, I-50019 Sesto Fiorentino, Italy
- INO-CNR Istituto Nazionale di Ottica del CNR, Sezione di Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
| | - M Diem
- ILP Institut für Laserphysik, Universität Hamburg, D-20355 Hamburg, Germany
- INRIM Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy
| | - L Franchi
- Department of Physics and Astronomy, University of Florence, I-50019 Sesto Fiorentino, Italy
| | - C Clivati
- INRIM Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy
| | - M Frittelli
- INRIM Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy
| | - F Levi
- INRIM Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy
| | - D Calonico
- INRIM Istituto Nazionale di Ricerca Metrologica, I-10135 Torino, Italy
| | - J Catani
- LENS European Laboratory for Nonlinear Spectroscopy, I-50019 Sesto Fiorentino, Italy
- INO-CNR Istituto Nazionale di Ottica del CNR, Sezione di Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
- INFN Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
| | - M Inguscio
- LENS European Laboratory for Nonlinear Spectroscopy, I-50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, I-50019 Sesto Fiorentino, Italy
- INO-CNR Istituto Nazionale di Ottica del CNR, Sezione di Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
| | - L Fallani
- LENS European Laboratory for Nonlinear Spectroscopy, I-50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, I-50019 Sesto Fiorentino, Italy
- INO-CNR Istituto Nazionale di Ottica del CNR, Sezione di Sesto Fiorentino, I-50019 Sesto Fiorentino, Italy
- INFN Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
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43
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Photo-electrons unveil topological transitions in graphene-like systems. Sci Rep 2016; 6:36577. [PMID: 27833125 PMCID: PMC5105119 DOI: 10.1038/srep36577] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2016] [Accepted: 10/12/2016] [Indexed: 11/12/2022] Open
Abstract
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature Ωkn whose integral on the Brillouin zone is a topological invariant known as the Chern number. The bulk-boundary correspondence states that these numbers define the number of edge or surface topologically protected states. It is then of primary interest to find experimental techniques able to measure the Berry curvature. However, up to now, there are no spectroscopic experiments that proved to be capable to obtain information on Ωkn to distinguish different topological structures of the bulk wavefunctions of semiconducting materials. Based on experimental results of the dipolar matrix elements for graphene, here we show that ARPES experiments with the appropriate x-ray energies and polarization can unambiguously detect changes of the Chern numbers in dynamically driven graphene and graphene-like materials opening new routes towards the experimental study of topological properties of condensed matter systems.
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44
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Xu ZF, You L, Hemmerich A, Liu WV. π-Flux Dirac Bosons and Topological Edge Excitations in a Bosonic Chiral p-Wave Superfluid. PHYSICAL REVIEW LETTERS 2016; 117:085301. [PMID: 27588862 DOI: 10.1103/physrevlett.117.085301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Indexed: 06/06/2023]
Abstract
We study the topological properties of elementary excitations in a staggered p_{x}±ip_{y} Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous p_{x}+ip_{y} momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the p_{x}+ip_{y} and p_{x}-ip_{y} condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.
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Affiliation(s)
- Zhi-Fang Xu
- MOE Key Laboratory of Fundamental Physical Quantities Measurements, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Andreas Hemmerich
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Wilczek Quantum Center, Zhejiang University of Technology, Hangzhou 310023, China
| | - W Vincent Liu
- Wilczek Quantum Center, Zhejiang University of Technology, Hangzhou 310023, China
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
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45
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Abstract
We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in 1D and 2D lattices. In our scheme, two internal atomic states represent a pseudospin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin-spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom-atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom-atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce nontrivial Berry phases in the spin lattice, thus opening new avenues for realizing topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well-known spin models.
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46
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Interferometric measurements of many-body topological invariants using mobile impurities. Nat Commun 2016; 7:11994. [PMID: 27312285 PMCID: PMC4915020 DOI: 10.1038/ncomms11994] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2015] [Accepted: 05/16/2016] [Indexed: 11/08/2022] Open
Abstract
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable.
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47
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Li T, Duca L, Reitter M, Grusdt F, Demler E, Endres M, Schleier-Smith M, Bloch I, Schneider U. Bloch state tomography using Wilson lines. Science 2016; 352:1094-7. [DOI: 10.1126/science.aad5812] [Citation(s) in RCA: 117] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2015] [Accepted: 04/15/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Tracy Li
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Lucia Duca
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Martin Reitter
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Fabian Grusdt
- Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany
- Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, 67663 Kaiserslautern, Germany
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Manuel Endres
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | | | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Ulrich Schneider
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
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48
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Flaschner N, Rem BS, Tarnowski M, Vogel D, Luhmann DS, Sengstock K, Weitenberg C. Experimental reconstruction of the Berry curvature in a Floquet Bloch band. Science 2016; 352:1091-4. [DOI: 10.1126/science.aad4568] [Citation(s) in RCA: 313] [Impact Index Per Article: 39.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Accepted: 03/23/2016] [Indexed: 11/02/2022]
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49
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Lu HI, Schemmer M, Aycock LM, Genkina D, Sugawa S, Spielman IB. Geometrical Pumping with a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2016; 116:200402. [PMID: 27258857 PMCID: PMC5100700 DOI: 10.1103/physrevlett.116.200402] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Indexed: 05/30/2023]
Abstract
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization.
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Affiliation(s)
- H.-I Lu
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
| | - M. Schemmer
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
- École Normale Supérieure de Lyon, F-69364 Lyon, France
| | - L. M. Aycock
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
- Cornell University, Ithaca, New York, 14850, USA
| | - D. Genkina
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
| | - S. Sugawa
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
| | - I. B. Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
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50
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Chen W. Scaling theory of topological phase transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:055601. [PMID: 26790004 DOI: 10.1088/0953-8984/28/5/055601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
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Affiliation(s)
- Wei Chen
- Institut für Theoretische Physik, ETH Zürich, 8093 Zürich, Switzerland
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