1
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Erhardt J, Schmitt C, Eck P, Schmitt M, Keßler P, Lee K, Kim T, Cacho C, Cojocariu I, Baranowski D, Feyer V, Veyrat L, Sangiovanni G, Claessen R, Moser S. Bias-Free Access to Orbital Angular Momentum in Two-Dimensional Quantum Materials. PHYSICAL REVIEW LETTERS 2024; 132:196401. [PMID: 38804920 DOI: 10.1103/physrevlett.132.196401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 03/06/2024] [Accepted: 04/08/2024] [Indexed: 05/29/2024]
Abstract
The demonstration of a topological band inversion constitutes the most elementary proof of a quantum spin Hall insulator (QSHI). On a fundamental level, such an inverted band gap is intrinsically related to the bulk Berry curvature, a gauge-invariant fingerprint of the wave function's quantum geometric properties in Hilbert space. Intimately tied to orbital angular momentum (OAM), the Berry curvature can be, in principle, extracted from circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES), were it not for interfering final state photoelectron emission channels that obscure the initial state OAM signature. Here, we outline a full-experimental strategy to avoid such interference artifacts and isolate the clean OAM from the CD-ARPES response. Bench-marking this strategy for the recently discovered atomic monolayer system indenene, we demonstrate its distinct QSHI character and establish CD-ARPES as a scalable bulk probe to experimentally classify the topology of two-dimensional quantum materials with time reversal symmetry.
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Affiliation(s)
- Jonas Erhardt
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
| | - Cedric Schmitt
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
| | - Philipp Eck
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, Germany
| | - Matthias Schmitt
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, OX11 0DE, United Kingdom
| | - Philipp Keßler
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
| | - Kyungchan Lee
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
| | - Timur Kim
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, OX11 0DE, United Kingdom
| | - Cephise Cacho
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, OX11 0DE, United Kingdom
| | - Iulia Cojocariu
- Elettra-Sincrotrone, S.C.p.A, Trieste, 34149, Italy
- Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich GmbH, Jülich, 52428, Germany
- Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
| | - Daniel Baranowski
- Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich GmbH, Jülich, 52428, Germany
| | - Vitaliy Feyer
- Peter Grünberg Institute (PGI-6), Forschungszentrum Jülich GmbH, Jülich, 52428, Germany
- Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), Universität Duisburg-Essen, 47047 Duisburg, Germany
| | - Louis Veyrat
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
- Leibniz Institute for Solid State and Materials Research, IFW Dresden, D-01069 Dresden, Germany
- Laboratoire National des Champs Magnétiques Intenses, CNRS-INSA-UJF-UPS, UPR3228, 143 avenue de Rangueil, F-31400 Toulouse, France
| | - Giorgio Sangiovanni
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, Germany
| | - Ralph Claessen
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
| | - Simon Moser
- Physikalisches Institut, Universität Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, D-97074 Würzburg, Germany
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Liang J, Liu Z, Yang Z, Huang Y, Wurstbauer U, Dean CR, West KW, Pfeiffer LN, Du L, Pinczuk A. Evidence for chiral graviton modes in fractional quantum Hall liquids. Nature 2024; 628:78-83. [PMID: 38538799 DOI: 10.1038/s41586-024-07201-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Accepted: 02/16/2024] [Indexed: 04/01/2024]
Abstract
Exotic physics could emerge from interplay between geometry and correlation. In fractional quantum Hall (FQH) states1, novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of fluctuations of an internal quantum metric under a quantum geometry description2-5. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons. They are characterized by polarized states with chirality6-8 of +2 or -2, and energy gaps coinciding with the fundamental neutral collective excitations (namely, magnetorotons9,10) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here we observe chiral spin-2 long-wavelength magnetorotons using inelastic scattering of circularly polarized lights, providing strong evidence for CGMs in FQH liquids. At filling factor v = 1/3, a gapped mode identified as the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum S = -2, which persists at extremely long wavelength. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The modes have characteristic energies and sharp peaks with marked temperature and filling-factor dependence, corroborating the assignment of long-wavelength magnetorotons. The observations capture the essentials of CGMs and support the FQH geometrical description, paving the way to unveil rich physics of quantum metric effects in topological correlated systems.
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Affiliation(s)
- Jiehui Liang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Ziyu Liu
- Department of Physics, Columbia University, New York, NY, USA
| | - Zihao Yang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | - Yuelei Huang
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China
| | | | - Cory R Dean
- Department of Physics, Columbia University, New York, NY, USA
| | - Ken W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Loren N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ, USA
| | - Lingjie Du
- School of Physics, National Laboratory of Solid State Microstructures, and Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing, China.
- Shishan Laboratory, Suzhou Campus of Nanjing University, Suzhou, China.
| | - Aron Pinczuk
- Department of Physics, Columbia University, New York, NY, USA
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA
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3
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Hu J, Lorchat E, Chen X, Watanabe K, Taniguchi T, Heinz TF, Murthy PA, Chervy T. Quantum control of exciton wave functions in 2D semiconductors. SCIENCE ADVANCES 2024; 10:eadk6369. [PMID: 38507493 PMCID: PMC10954220 DOI: 10.1126/sciadv.adk6369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 02/15/2024] [Indexed: 03/22/2024]
Abstract
Excitons-bound electron-hole pairs-play a central role in light-matter interaction phenomena and are crucial for wide-ranging applications from light harvesting and generation to quantum information processing. A long-standing challenge in solid-state optics has been to achieve precise and scalable control over excitonic motion. We present a technique using nanostructured gate electrodes to create tailored potential landscapes for excitons in 2D semiconductors, enabling in situ wave function shaping at the nanoscale. Our approach forms electrostatic traps for excitons in various geometries, such as quantum dots, rings, and arrays thereof. We show independent spectral tuning of spatially separated quantum dots, achieving degeneracy despite material disorder. Owing to the strong light-matter coupling of excitons in 2D semiconductors, we observe unambiguous signatures of confined exciton wave functions in optical reflection and photoluminescence measurements. This work unlocks possibilities for engineering exciton dynamics and interactions at the nanometer scale, with implications for optoelectronic devices, topological photonics, and quantum nonlinear optics.
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Affiliation(s)
- Jenny Hu
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Etienne Lorchat
- NTT Research, Inc. Physics & Informatics Laboratories, 940 Stewart Dr, Sunnyvale, CA 94085, USA
| | - Xueqi Chen
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Tony F. Heinz
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Puneet A. Murthy
- Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Thibault Chervy
- NTT Research, Inc. Physics & Informatics Laboratories, 940 Stewart Dr, Sunnyvale, CA 94085, USA
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Yang Y, Yang B, Ma G, Li J, Zhang S, Chan CT. Non-Abelian physics in light and sound. Science 2024; 383:eadf9621. [PMID: 38386745 DOI: 10.1126/science.adf9621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 01/17/2024] [Indexed: 02/24/2024]
Abstract
Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.
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Affiliation(s)
- Yi Yang
- Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Biao Yang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Jensen Li
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Shuang Zhang
- Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong, China
- New Cornerstone Science Laboratory, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - C T Chan
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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5
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Pang Z, Wong BTT, Hu J, Yang Y. Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2024; 132:043804. [PMID: 38335358 DOI: 10.1103/physrevlett.132.043804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Accepted: 11/27/2023] [Indexed: 02/12/2024]
Abstract
Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for vector potentials, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences. With SU(2) gauge fields, the braiding degrees that can be achieved are twice the highest hopping order of a lattice model, indicating the utility of spinful freedom to attain high-order nontrivial braiding. At both ends of an open chain, non-Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population can be effectively tuned near the exceptional points. Generalizing to two dimensions, the gauge invariance of Wilson loops can also break down in non-Hermitian lattices dressed with non-Abelian gauge fields. Toward realization, we present a concrete experimental proposal for non-Abelian gauge fields in non-Hermitian systems via the synthetic frequency dimension of a polarization-multiplexed fiber ring resonator.
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Affiliation(s)
- Zehai Pang
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Bengy Tsz Tsun Wong
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Jinbing Hu
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
- College of Optical-Electrical Information and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Yi Yang
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
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6
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Törmä P. Essay: Where Can Quantum Geometry Lead Us? PHYSICAL REVIEW LETTERS 2023; 131:240001. [PMID: 38181149 DOI: 10.1103/physrevlett.131.240001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Indexed: 01/07/2024]
Abstract
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry, including the amplitude distance characterized by the quantum metric, has started to receive attention in the last few years. Various quantum transport and interaction phenomena have been found to be critically influenced by quantum geometry. For example, quantum geometry allows counterintuitive flow of supercurrent in a flat band where single electrons are immobile. In this Essay, I will discuss my view of the important open problems and future applications of this research topic and will try to inspire the reader to come up with further ideas. At its best, quantum geometry can open a new chapter in band theory and lead to breakthroughs as transformative as room-temperature superconductivity. However, first, more experiments directly showing the effect of quantum geometry are needed. We also have to integrate quantum geometry analysis in our most advanced numerical methods. Further, the ramifications of quantum geometry should be studied in a wider range, including electric and electromagnetic responses and interaction phenomena in free- and correlated-electron materials, bosonic systems, optics, and other fields. Part of a series of Essays which concisely present author visions for the future of their field.
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Affiliation(s)
- Päivi Törmä
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
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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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Luo X, Cai Y, Yue X, Zhang Y, Yun F, Li F. Full characterization of vector eigenstates in symmetrically confined systems with photonic spin-orbit coupling. OPTICS EXPRESS 2023; 31:27749-27760. [PMID: 37710843 DOI: 10.1364/oe.495899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 07/22/2023] [Indexed: 09/16/2023]
Abstract
The photonic spin-orbit (SO) coupling is a widely investigated effect in optical microcavities leading to various interesting physical phenomena and potential applications. We report the full sets of eigenenergies and eigenstates in a symmetrically confined potential under the effect of SO coupling induced by the transverse-electric transverse-magnetic (TE-TM) splitting, which are derived analytically via the degenerate perturbation theory. We obtained the eigenenergies and the eigenstates from the 1st to the 6th orders of excited manifold, and demonstrate unambiguously that universal rules governing the mode formation exist in such complicated photonic systems, making the modes exhibiting the features of solid and hollow skyrmions as well as spin vortices. We show that these eigenstates can be described by the SO coupled hyperspheres that can be decomposed into a series of higher-order Poincare spheres. Our results significantly extend the area of microcavity spin-optronics to the general theory of eigenvalues in confined systems, and provide an efficient theoretical frame for the information processing using microcavity-based high-dimensional vector states.
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Martone GI, Cherroret N. Time Translation Symmetry Breaking in an Isolated Spin-Orbit-Coupled Fluid of Light. PHYSICAL REVIEW LETTERS 2023; 131:013803. [PMID: 37478429 DOI: 10.1103/physrevlett.131.013803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 05/14/2023] [Accepted: 06/08/2023] [Indexed: 07/23/2023]
Abstract
We study the interplay between intrinsic spin-orbit coupling and nonlinear photon-photon interactions in a nonparaxial, elliptically polarized fluid of light propagating in a bulk Kerr medium. We find that in situations where the nonlinear interactions induce birefringence, i.e., a polarization-dependent nonlinear refractive index, their interplay with spin-orbit coupling results in an interference between the two polarization components of the fluid traveling at different wave vectors, which entails the breaking of translation symmetry along the propagation direction. This phenomenon leads to a Floquet band structure in the Bogoliubov spectrum of the fluid, and to characteristic oscillations of its intensity correlations. We characterize these oscillations in detail and point out their exponential growth at large propagation distances, revealing the presence of parametric resonances.
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Affiliation(s)
- Giovanni I Martone
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
- CNR NANOTEC, Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
- INFN, Sezione di Lecce, 73100 Lecce, Italy
| | - Nicolas Cherroret
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
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Li Y, Li Y, Luo X, Guo C, Qin Y, Fu H, Zhang Y, Yun F, Liao Q, Li F. Elimination of Chirality in Three-Dimensionally Confined Open-Access Microcavities. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:1868. [PMID: 37368298 DOI: 10.3390/nano13121868] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Revised: 05/26/2023] [Accepted: 05/27/2023] [Indexed: 06/28/2023]
Abstract
The emergent optical activity (OA) caused by anisotropic light emitter in microcavities is an important physical mechanism discovered recently, which leads to Rashba-Dresselhaus photonic spin-orbit (SO) coupling. In this study, we report a sharp contrast of the roles of the emergent OA in free and confined cavity photons, by observing the optical chirality in a planar-planar microcavity and its elimination in a concave-planar microcavity, evidenced by polarization-resolved white-light spectroscopy, which agrees well with the theoretical predictions based on the degenerate perturbation theory. Moreover, we theoretically predict that a slight phase gradient in real space can partially restore the effect of the emergent OA in confined cavity photons. The results are significant additions to the field of cavity spinoptronics and provide a novel method for manipulating photonic SO coupling in confined optical systems.
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Affiliation(s)
- Yiming Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yuan Li
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, China
| | - Xiaoxuan Luo
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Chaowei Guo
- Center for Advancing Materials Performance from the Nanoscale (CAMP-Nano), State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yuanbin Qin
- Center for Advancing Materials Performance from the Nanoscale (CAMP-Nano), State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, China
| | - Yanpeng Zhang
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Feng Yun
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
- Solid-State Lighting Engineering Research Center, Xi'an Jiaotong University, Xi'an 710049, China
| | - Qing Liao
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, China
| | - Feng Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
- Solid-State Lighting Engineering Research Center, Xi'an Jiaotong University, Xi'an 710049, China
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11
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Gao A, Liu YF, Qiu JX, Ghosh B, V Trevisan T, Onishi Y, Hu C, Qian T, Tien HJ, Chen SW, Huang M, Bérubé D, Li H, Tzschaschel C, Dinh T, Sun Z, Ho SC, Lien SW, Singh B, Watanabe K, Taniguchi T, Bell DC, Lin H, Chang TR, Du CR, Bansil A, Fu L, Ni N, Orth PP, Ma Q, Xu SY. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 2023:eadf1506. [PMID: 37319246 DOI: 10.1126/science.adf1506] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Accepted: 06/06/2023] [Indexed: 06/17/2023]
Abstract
Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi2Te4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.
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Affiliation(s)
- Anyuan Gao
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Yu-Fei Liu
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Jian-Xiang Qiu
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Barun Ghosh
- Department of Physics, Northeastern University, Boston, MA 02115, USA
| | - Thaís V Trevisan
- Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
- Ames National Laboratory, Ames, IA 50011, USA
| | - Yugo Onishi
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chaowei Hu
- Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Tiema Qian
- Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Hung-Ju Tien
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Shao-Wen Chen
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Mengqi Huang
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Damien Bérubé
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Houchen Li
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Christian Tzschaschel
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Thao Dinh
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Zhe Sun
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Sheng-Chin Ho
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
| | - Shang-Wei Lien
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Bahadur Singh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Colaba, Mumbai, India
| | - Kenji Watanabe
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - David C Bell
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Center for Nanoscale Systems, Harvard University, Cambridge, MA 02138, USA
| | - Hsin Lin
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Tay-Rong Chang
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Chunhui Rita Du
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Arun Bansil
- Department of Physics, Northeastern University, Boston, MA 02115, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Ni Ni
- Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Peter P Orth
- Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
- Ames National Laboratory, Ames, IA 50011, USA
| | - Qiong Ma
- Department of Physics, Boston College, Chestnut Hill, MA, USA
| | - Su-Yang Xu
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA
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12
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Lovett S, Walker PM, Osipov A, Yulin A, Naik PU, Whittaker CE, Shelykh IA, Skolnick MS, Krizhanovskii DN. Observation of Zitterbewegung in photonic microcavities. LIGHT, SCIENCE & APPLICATIONS 2023; 12:126. [PMID: 37221208 DOI: 10.1038/s41377-023-01162-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 04/12/2023] [Accepted: 04/14/2023] [Indexed: 05/25/2023]
Abstract
We present and experimentally study the effects of the photonic spin-orbit coupling on the real space propagation of polariton wavepackets in planar semiconductor microcavities and polaritonic analogues of graphene. In particular, we demonstrate the appearance of an analogue Zitterbewegung effect, a term which translates as 'trembling motion' in English, which was originally proposed for relativistic Dirac electrons and consisted of the oscillations of the centre of mass of a wavepacket in the direction perpendicular to its propagation. For a planar microcavity, we observe regular Zitterbewegung oscillations whose amplitude and period depend on the wavevector of the polaritons. We then extend these results to a honeycomb lattice of coupled microcavity resonators. Compared to the planar cavity, such lattices are inherently more tuneable and versatile, allowing simulation of the Hamiltonians of a wide range of important physical systems. We observe an oscillation pattern related to the presence of the spin-split Dirac cones in the dispersion. In both cases, the experimentally observed oscillations are in good agreement with theoretical modelling and independently measured bandstructure parameters, providing strong evidence for the observation of Zitterbewegung.
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Affiliation(s)
- Seth Lovett
- Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK
| | - Paul M Walker
- Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK.
| | - Alexey Osipov
- Department of Physics and Technology, ITMO University, St. Petersburg, 197101, Russia
| | - Alexey Yulin
- Department of Physics and Technology, ITMO University, St. Petersburg, 197101, Russia
| | - Pooja Uday Naik
- Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK
| | - Charles E Whittaker
- Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK
| | - Ivan A Shelykh
- Department of Physics and Technology, ITMO University, St. Petersburg, 197101, Russia
- Science Institute, University of Iceland, Dunhagi 3, IS-107, Reykjavik, Iceland
| | - Maurice S Skolnick
- Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, UK
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13
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Cheng D, Wang K, Fan S. Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension. PHYSICAL REVIEW LETTERS 2023; 130:083601. [PMID: 36898123 DOI: 10.1103/physrevlett.130.083601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non-Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.
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Affiliation(s)
- Dali Cheng
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
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14
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Liang Q, Ma X, Long T, Yao J, Liao Q, Fu H. Circularly Polarized Lasing from a Microcavity Filled with Achiral Single-Crystalline Microribbons. Angew Chem Int Ed Engl 2023; 62:e202213229. [PMID: 36494879 DOI: 10.1002/anie.202213229] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 11/23/2022] [Accepted: 12/09/2022] [Indexed: 12/14/2022]
Abstract
Organic circularly polarized (CP) lasers have received increasing attention due to their future photoelectric applications. Here, we demonstrate a CP laser from a pure organic crystal-filled microcavity without any chiral molecules or chiral structures. Benefited from the giant anisotropy and excellent laser gain of organic crystals, optical Rashba-Dresselhaus spin-orbit coupling effect can be induced and is conductive to the CP laser in such microcavities. The maximum dissymmetry factor of the CP lasing with opposite helicities reachs 1.2. Our strategy may provide a new idea for the design of CP lasers towards future 3D laser displays, information storage and other fields.
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Affiliation(s)
- Qian Liang
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, China
| | - Xuekai Ma
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098, Paderborn, Germany
| | - Teng Long
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, China
| | - Jiannian Yao
- Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of chemistry, Chinese Academy of Sciences, Beijing, 100190, China
| | - Qing Liao
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing, 100048, China
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15
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Mazzola F, Ghosh B, Fujii J, Acharya G, Mondal D, Rossi G, Bansil A, Farias D, Hu J, Agarwal A, Politano A, Vobornik I. Discovery of a Magnetic Dirac System with a Large Intrinsic Nonlinear Hall Effect. NANO LETTERS 2023; 23:902-907. [PMID: 36689192 PMCID: PMC10064332 DOI: 10.1021/acs.nanolett.2c04194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 01/17/2023] [Indexed: 06/17/2023]
Abstract
Magnetic materials exhibiting topological Dirac fermions are attracting significant attention for their promising technological potential in spintronics. In these systems, the combined effect of the spin-orbit coupling and magnetic order enables the realization of novel topological phases with exotic transport properties, including the anomalous Hall effect and magneto-chiral phenomena. Herein, we report experimental signature of topological Dirac antiferromagnetism in TaCoTe2 via angle-resolved photoelectron spectroscopy and first-principles density functional theory calculations. In particular, we find the existence of spin-orbit coupling-induced gaps at the Fermi level, consistent with the manifestation of a large intrinsic nonlinear Hall conductivity. Remarkably, we find that the latter is extremely sensitive to the orientation of the Néel vector, suggesting TaCoTe2 as a suitable candidate for the realization of non-volatile spintronic devices with an unprecedented level of intrinsic tunability.
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Affiliation(s)
- Federico Mazzola
- CNR-IOM
TASC Laboratory, Area Science Park, 34149Trieste, Italy
- Department
of Molecular Sciences and Nanosystems, Ca’
Foscari University of Venice, 30172Venice, Italy
| | - Barun Ghosh
- Department
of Physics, Northeastern University, Boston, Massachusetts02115, United States
| | - Jun Fujii
- CNR-IOM
TASC Laboratory, Area Science Park, 34149Trieste, Italy
| | - Gokul Acharya
- Department
of Physics, University of Arkansas, Fayetteville, Arkansas72701, United States
| | - Debashis Mondal
- CNR-IOM
TASC Laboratory, Area Science Park, 34149Trieste, Italy
| | | | - Arun Bansil
- Department
of Physics, Northeastern University, Boston, Massachusetts02115, United States
| | - Daniel Farias
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, 28049Madrid, Spain
- Instituto
“Nicolás Cabrera” and Condensed Matter Physics
Center (IFIMAC), Universidad Autónoma
de Madrid, 28049Madrid, Spain
| | - Jin Hu
- Department
of Physics, University of Arkansas, Fayetteville, Arkansas72701, United States
| | - Amit Agarwal
- Department
of Physics, Indian Institute of Technology
Kanpur, Kanpur208016, India
| | - Antonio Politano
- Department
of Physical and Chemical Sciences, University
of L’Aquila, Via
Vetoio, 67100L’Aquila, Italy
| | - Ivana Vobornik
- CNR-IOM
TASC Laboratory, Area Science Park, 34149Trieste, Italy
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16
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Wei M, Wang L, Wang B, Xiang L, Xu F, Wang B, Wang J. Quantum Fluctuation of the Quantum Geometric Tensor and Its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems. PHYSICAL REVIEW LETTERS 2023; 130:036202. [PMID: 36763382 DOI: 10.1103/physrevlett.130.036202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 12/13/2022] [Indexed: 06/18/2023]
Abstract
In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying the quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects; so do their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of the quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.
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Affiliation(s)
- Miaomiao Wei
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Luyang Wang
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Bin Wang
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Longjun Xiang
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Fuming Xu
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Baigeng Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
| | - Jian Wang
- College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
- Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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17
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Arora A, Rudner MS, Song JCW. Quantum Plasmonic Nonreciprocity in Parity-Violating Magnets. NANO LETTERS 2022; 22:9351-9357. [PMID: 36383645 DOI: 10.1021/acs.nanolett.2c03126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The optical responses of metals are often dominated by plasmonic resonances, that is, the collective oscillations of interacting electron liquids. Here we unveil a new class of plasmons─quantum metric plasmons (QMPs)─that arise in a wide range of parity-violating magnetic metals. In these materials, a dipolar distribution of the quantum metric (a fundamental characteristic of Bloch wave functions) produces intrinsic nonreciprocal bulk plasmons. Strikingly, QMP nonreciprocity manifests even when the single-particle dispersion is symmetric: QMPs are sensitive to time-reversal and parity violations hidden in the Bloch wave function. In materials with asymmetric single-particle dispersions, quantum metric dipole induced nonreciprocity can continue to dominate at large frequencies. We anticipate that QMPs can be realized in a wide range of parity-violating magnets, including twisted bilayer graphene heterostructures, where quantum geometric quantities can achieve large values.
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Affiliation(s)
- Arpit Arora
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore637371
| | - Mark S Rudner
- Department of Physics, University of Washington, SeattleWashington98195, United States
| | - Justin C W Song
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore637371
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18
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Kokhanchik P, Solnyshkov D, Stöferle T, Piętka B, Szczytko J, Malpuech G. Modulated Rashba-Dresselhaus Spin-Orbit Coupling for Topology Control and Analog Simulations. PHYSICAL REVIEW LETTERS 2022; 129:246801. [PMID: 36563269 DOI: 10.1103/physrevlett.129.246801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 10/28/2022] [Indexed: 06/17/2023]
Abstract
We show theoretically that Rashba-Dresselhaus spin-orbit coupling (RDSOC) in lattices acts as a synthetic gauge field. This allows us to control both the phase and the magnitude of tunneling coefficients between sites, which is the key ingredient to implement topological Hamitonians and spin lattices useful for simulation perpectives. We use liquid crystal based microcavities in which RDSOC can be switched on and off as a model platform. We propose a realistic scheme for implementation of a Su-Schrieffer-Heeger chain in which the edge states existence can be tuned, and a Harper-Hofstadter model with a tunable contrasted flux for each (pseudo)spin component. We further show that a transverse-field Ising model and classical XY Hamiltonian with tunable parameters can be implemented, opening up prospects for analog physics, simulations, and optimization.
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Affiliation(s)
- Pavel Kokhanchik
- Institut Pascal, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
| | - Dmitry Solnyshkov
- Institut Pascal, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
- Institut Universitaire de France (IUF), 75231 Paris, France
| | - Thilo Stöferle
- IBM Research Europe-Zurich, CH-8803 Rüschlikon, Switzerland
| | - Barbara Piętka
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Jacek Szczytko
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Guillaume Malpuech
- Institut Pascal, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
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19
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Room-temperature polariton quantum fluids in halide perovskites. Nat Commun 2022; 13:7388. [DOI: 10.1038/s41467-022-34987-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Accepted: 11/14/2022] [Indexed: 12/02/2022] Open
Abstract
AbstractQuantum fluids exhibit quantum mechanical effects at the macroscopic level, which contrast strongly with classical fluids. Gain-dissipative solid-state exciton-polaritons systems are promising emulation platforms for complex quantum fluid studies at elevated temperatures. Recently, halide perovskite polariton systems have emerged as materials with distinctive advantages over other room-temperature systems for future studies of topological physics, non-Abelian gauge fields, and spin-orbit interactions. However, the demonstration of nonlinear quantum hydrodynamics, such as superfluidity and Čerenkov flow, which is a consequence of the renormalized elementary excitation spectrum, remains elusive in halide perovskites. Here, using homogenous halide perovskites single crystals, we report, in both one- and two-dimensional cases, the complete set of quantum fluid phase transitions from normal classical fluids to scatterless polariton superfluids and supersonic fluids—all at room temperature, clear consequences of the Landau criterion. Specifically, the supersonic Čerenkov wave pattern was observed at room temperature. The experimental results are also in quantitative agreement with theoretical predictions from the dissipative Gross-Pitaevskii equation. Our results set the stage for exploring the rich non-equilibrium quantum fluid many-body physics at room temperature and also pave the way for important polaritonic device applications.
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20
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Łempicka-Mirek K, Król M, Sigurdsson H, Wincukiewicz A, Morawiak P, Mazur R, Muszyński M, Piecek W, Kula P, Stefaniuk T, Kamińska M, De Marco L, Lagoudakis PG, Ballarini D, Sanvitto D, Szczytko J, Piętka B. Electrically tunable Berry curvature and strong light-matter coupling in liquid crystal microcavities with 2D perovskite. SCIENCE ADVANCES 2022; 8:eabq7533. [PMID: 36197989 PMCID: PMC9534495 DOI: 10.1126/sciadv.abq7533] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
The field of spinoptronics is underpinned by good control over photonic spin-orbit coupling in devices that have strong optical nonlinearities. Such devices might hold the key to a new era of optoelectronics where momentum and polarization degrees of freedom of light are interwoven and interfaced with electronics. However, manipulating photons through electrical means is a daunting task given their charge neutrality. In this work, we present electrically tunable microcavity exciton-polariton resonances in a Rashba-Dresselhaus spin-orbit coupling field. We show that different spin-orbit coupling fields and the reduced cavity symmetry lead to tunable formation of the Berry curvature, the hallmark of quantum geometrical effects. For this, we have implemented an architecture of a photonic structure with a two-dimensional perovskite layer incorporated into a microcavity filled with nematic liquid crystal. Our work interfaces spinoptronic devices with electronics by combining electrical control over both the strong light-matter coupling conditions and artificial gauge fields.
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Affiliation(s)
- Karolina Łempicka-Mirek
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Mateusz Król
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Helgi Sigurdsson
- Science Institute, University of Iceland, Dunhagi 3, IS-107 Reykjavik, Iceland
- Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
| | - Adam Wincukiewicz
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Przemysław Morawiak
- Institute of Applied Physics, Military University of Technology, Warsaw, Poland
| | - Rafał Mazur
- Institute of Applied Physics, Military University of Technology, Warsaw, Poland
| | - Marcin Muszyński
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Wiktor Piecek
- Institute of Applied Physics, Military University of Technology, Warsaw, Poland
| | - Przemysław Kula
- Institute of Chemistry, Military University of Technology, Warsaw, Poland
| | - Tomasz Stefaniuk
- Institute of Geophysics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
| | - Maria Kamińska
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Luisa De Marco
- CNR-Nanotec, Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Pavlos G. Lagoudakis
- Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
- Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, 6 Bolshoy Boulevard 30, Building 1, 121205 Moscow, Russia
| | - Dario Ballarini
- CNR-Nanotec, Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Daniele Sanvitto
- CNR-Nanotec, Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
| | - Jacek Szczytko
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
| | - Barbara Piętka
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, PL-02-093 Warsaw, Poland
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21
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Long T, Ma X, Ren J, Li F, Liao Q, Schumacher S, Malpuech G, Solnyshkov D, Fu H. Helical Polariton Lasing from Topological Valleys in an Organic Crystalline Microcavity. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2203588. [PMID: 35989095 PMCID: PMC9561778 DOI: 10.1002/advs.202203588] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 08/01/2022] [Indexed: 06/15/2023]
Abstract
Topological photonics provides an important platform for the development of photonic devices with robust disorder-immune light transport and controllable helicity. Mixing photons with excitons (or polaritons) gives rise to nontrivial polaritonic bands with chiral modes, allowing the manipulation of helical lasers in strongly coupled light-matter systems. In this work, helical polariton lasing from topological valleys of an organic anisotropic microcrystalline cavity based on tailored local nontrivial band geometry is demonstrated. This polariton laser emits light of different helicity along different angular directions. The significantly enhanced chiral characteristics are achieved by the nonlinear relaxation process. Helical topological polariton lasers may provide a perfect platform for the exploration of novel topological phenomena that involve light-matter interaction and the development of polariton-based spintronic devices.
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Affiliation(s)
- Teng Long
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal UniversityBeijing100048P. R. China
| | - Xuekai Ma
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP)Universität PaderbornWarburger Strasse 10033098PaderbornGermany
| | - Jiahuan Ren
- Tianjin Key Laboratory of Molecular Optoelectronic ScienceSchool of Chemical Engineering and TechnologyCollaborative Innovation Center of Chemical Science and Engineering (Tianjin)Tianjin UniversityTianjin300072P. R. China
| | - Feng Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic TechniqueSchool of Electronic Science and EngineeringFaculty of Electronic and Information EngineeringXi'an Jiaotong UniversityXi'an710049China
| | - Qing Liao
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal UniversityBeijing100048P. R. China
| | - Stefan Schumacher
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP)Universität PaderbornWarburger Strasse 10033098PaderbornGermany
- Wyant College of Optical SciencesUniversity of ArizonaTucsonAZ85721United States
| | - Guillaume Malpuech
- Institut PascalPHOTON‐N2Université Clermont AuvergneCNRSClermont INPClermont‐FerrandF‐63000France
| | - Dmitry Solnyshkov
- Institut PascalPHOTON‐N2Université Clermont AuvergneCNRSClermont INPClermont‐FerrandF‐63000France
- Institut Universitaire de France (IUF)Paris75231France
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic DevicesDepartment of ChemistryCapital Normal UniversityBeijing100048P. R. China
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22
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Król M, Septembre I, Oliwa P, Kędziora M, Łempicka-Mirek K, Muszyński M, Mazur R, Morawiak P, Piecek W, Kula P, Bardyszewski W, Lagoudakis PG, Solnyshkov DD, Malpuech G, Piętka B, Szczytko J. Annihilation of exceptional points from different Dirac valleys in a 2D photonic system. Nat Commun 2022; 13:5340. [PMID: 36096889 PMCID: PMC9468178 DOI: 10.1038/s41467-022-33001-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 08/26/2022] [Indexed: 12/03/2022] Open
Abstract
Topological physics relies on Hamiltonian’s eigenstate singularities carrying topological charges, such as Dirac points, and – in non-Hermitian systems – exceptional points (EPs), lines or surfaces. So far, the reported non-Hermitian topological transitions were related to the creation of a pair of EPs connected by a Fermi arc out of a single Dirac point by increasing non-Hermiticity. Such EPs can annihilate by reducing non-Hermiticity. Here, we demonstrate experimentally that an increase of non-Hermiticity can lead to the annihilation of EPs issued from different Dirac points (valleys). The studied platform is a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Non-Hermiticity is provided by polarization-dependent losses. By increasing the non-Hermiticity degree, we control the position of the EPs. After the intervalley annihilation, the system becomes free of any band singularity. Our results open the field of non-Hermitian valley-physics and illustrate connections between Hermitian topology and non-Hermitian phase transitions. The authors study a liquid crystal microcavity with polarization-dependent absorption, a source of non-Hermiticity. The transition in the Hermitian topology of the spin-orbit coupling makes possible the annihilation of exceptional points.
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23
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Solnyshkov DD, Leblanc C, Septembre I, Malpuech G. Domain-Wall Topology Induced by Spontaneous Symmetry Breaking in Polariton Graphene. PHYSICAL REVIEW LETTERS 2022; 129:066802. [PMID: 36018632 DOI: 10.1103/physrevlett.129.066802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2023]
Abstract
We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s band. The condensation occurs at the kinetically favorable negative mass extrema (K and K^{'} valleys) of the valence band. Considering attractive polariton-polariton interaction allows us to generate a spatially extended condensate. The symmetry breaking occurring during the condensate buildup leads to the formation of valley-polarized domains. This process can either be spontaneous, following the Kibble-Zurek scenario, or triggered, leading to a controlled spatial distribution of valley-polarized domains. The selection of a single valley breaks time-reversal symmetry, and the walls separating domains exhibit a reconfigurable topologically protected chiral current. This current emerges as a result of the interplay between the nontrivial valley topology and the condensation-induced symmetry breaking.
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Affiliation(s)
- D D Solnyshkov
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
- Institut Universitaire de France (IUF), F-75231 Paris, France
| | - C Leblanc
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
| | - I Septembre
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
| | - G Malpuech
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, Clermont INP, F-63000 Clermont-Ferrand, France
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24
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Tao R, Peng K, Haeberlé L, Li Q, Jin D, Fleming GR, Kéna-Cohen S, Zhang X, Bao W. Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature. NATURE MATERIALS 2022; 21:761-766. [PMID: 35681064 DOI: 10.1038/s41563-022-01276-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
Exciton polaritons, the part-light and part-matter quasiparticles in semiconductor optical cavities, are promising for exploring Bose-Einstein condensation, non-equilibrium many-body physics and analogue simulation at elevated temperatures. However, a room-temperature polaritonic platform on par with the GaAs quantum wells grown by molecular beam epitaxy at low temperatures remains elusive. The operation of such a platform calls for long-lifetime, strongly interacting excitons in a stringent material system with large yet nanoscale-thin geometry and homogeneous properties. Here, we address this challenge by adopting a method based on the solution synthesis of excitonic halide perovskites grown under nanoconfinement. Such nanoconfinement growth facilitates the synthesis of smooth and homogeneous single-crystalline large crystals enabling the demonstration of XY Hamiltonian lattices with sizes up to 10 × 10. With this demonstration, we further establish perovskites as a promising platform for room temperature polaritonic physics and pave the way for the realization of robust mode-disorder-free polaritonic devices at room temperature.
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Affiliation(s)
- Renjie Tao
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, USA
| | - Kai Peng
- Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Louis Haeberlé
- Department of Engineering Physics, École Polytechnique de Montréal, Montréal, Quebec, Canada
| | - Quanwei Li
- Department of Chemistry, University of California, Berkeley, CA, USA
| | - Dafei Jin
- Center for Nanoscale Materials, Argonne National Laboratory, Lemont, IL, USA
| | - Graham R Fleming
- Department of Chemistry, University of California, Berkeley, CA, USA
| | - Stéphane Kéna-Cohen
- Department of Engineering Physics, École Polytechnique de Montréal, Montréal, Quebec, Canada
| | - Xiang Zhang
- Nanoscale Science and Engineering Center, University of California, Berkeley, CA, USA.
- Faculty of Science and Faculty of Engineering, The University of Hong Kong, Hong Kong, China.
| | - Wei Bao
- Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA.
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25
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Ness G, Lam MR, Alt W, Meschede D, Sagi Y, Alberti A. Observing crossover between quantum speed limits. SCIENCE ADVANCES 2021; 7:eabj9119. [PMID: 34936463 PMCID: PMC8694601 DOI: 10.1126/sciadv.abj9119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds, which relate the maximum speed of evolution to the system’s energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multilevel system by following the motion of a single atom in an optical trap using fast matter wave interferometry. We find two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the quantum evolution deviates from the geodesic path in the Hilbert space of the multilevel system. Our results are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.
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Affiliation(s)
- Gal Ness
- Physics Department, Technion-Israel Institute of Technology, IL-32000 Haifa, Israel
| | - Manolo R. Lam
- Institut für Angewandte Physik, Universität Bonn, 53115 Bonn, Germany
| | - Wolfgang Alt
- Institut für Angewandte Physik, Universität Bonn, 53115 Bonn, Germany
| | - Dieter Meschede
- Institut für Angewandte Physik, Universität Bonn, 53115 Bonn, Germany
| | - Yoav Sagi
- Physics Department, Technion-Israel Institute of Technology, IL-32000 Haifa, Israel
| | - Andrea Alberti
- Institut für Angewandte Physik, Universität Bonn, 53115 Bonn, Germany
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26
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Spencer MS, Fu Y, Schlaus AP, Hwang D, Dai Y, Smith MD, Gamelin DR, Zhu XY. Spin-orbit-coupled exciton-polariton condensates in lead halide perovskites. SCIENCE ADVANCES 2021; 7:eabj7667. [PMID: 34851673 PMCID: PMC8635445 DOI: 10.1126/sciadv.abj7667] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
Spin-orbit coupling (SOC) is responsible for a range of spintronic and topological processes in condensed matter. Here, we show photonic analogs of SOCs in exciton-polaritons and their condensates in microcavities composed of birefringent lead halide perovskite single crystals. The presence of crystalline anisotropy coupled with splitting in the optical cavity of the transverse electric and transverse magnetic modes gives rise to a non-Abelian gauge field, which can be described by the Rashba-Dresselhaus Hamiltonian near the degenerate points of the two polarization modes. With increasing density, the exciton-polaritons with pseudospin textures undergo phase transitions to competing condensates with orthogonal polarizations. Unlike their pure photonic counterparts, these exciton-polaritons and condensates inherit nonlinearity from their excitonic components and may serve as quantum simulators of many-body SOC processes.
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Affiliation(s)
| | - Yongping Fu
- Department of Chemistry, Columbia University, New York, NY 10027, USA
| | - Andrew P. Schlaus
- Department of Chemistry, Columbia University, New York, NY 10027, USA
| | - Doyk Hwang
- Department of Chemistry, Columbia University, New York, NY 10027, USA
| | - Yanan Dai
- Department of Chemistry, Columbia University, New York, NY 10027, USA
| | - Matthew D. Smith
- Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA
| | - Daniel R. Gamelin
- Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA
| | - X.-Y. Zhu
- Department of Chemistry, Columbia University, New York, NY 10027, USA
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27
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Polimeno L, Lerario G, De Giorgi M, De Marco L, Dominici L, Todisco F, Coriolano A, Ardizzone V, Pugliese M, Prontera CT, Maiorano V, Moliterni A, Giannini C, Olieric V, Gigli G, Ballarini D, Xiong Q, Fieramosca A, Solnyshkov DD, Malpuech G, Sanvitto D. Tuning of the Berry curvature in 2D perovskite polaritons. NATURE NANOTECHNOLOGY 2021; 16:1349-1354. [PMID: 34675412 DOI: 10.1038/s41565-021-00977-2] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 08/09/2021] [Indexed: 06/13/2023]
Abstract
The engineering of the energy dispersion of polaritons in microcavities through nanofabrication or through the exploitation of intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields such as the anomalous quantum Hall and Rashba effects. Here we show how we can obtain different Berry curvature distributions of polariton bands in a strongly coupled organic-inorganic two-dimensional perovskite single-crystal microcavity. The spatial anisotropy of the perovskite crystal combined with photonic spin-orbit coupling produce two Hamilton diabolical points in the dispersion. An external magnetic field breaks time-reversal symmetry owing to the exciton Zeeman splitting and lifts the degeneracy of the diabolical points. As a result, the bands possess non-zero integral Berry curvatures, which we directly measure by state tomography. In addition to the determination of the different Berry curvatures of the multimode microcavity dispersions, we can also modify the Berry curvature distribution, the so-called band geometry, within each band by tuning external parameters, such as temperature, magnetic field and sample thickness.
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Affiliation(s)
- Laura Polimeno
- Dipartimento di Matematica e Fisica, 'Ennio de Giorgi', Università del Salento, Lecce, Italy
- CNR NANOTEC, Institute of Nanotechnology, Lecce, Italy
- INFN Istituto Nazionale di Fisica Nucleare, Lecce, Italy
| | | | | | | | | | | | - Annalisa Coriolano
- Dipartimento di Matematica e Fisica, 'Ennio de Giorgi', Università del Salento, Lecce, Italy
- CNR NANOTEC, Institute of Nanotechnology, Lecce, Italy
| | | | - Marco Pugliese
- Dipartimento di Matematica e Fisica, 'Ennio de Giorgi', Università del Salento, Lecce, Italy
- CNR NANOTEC, Institute of Nanotechnology, Lecce, Italy
| | | | | | | | | | | | - Giuseppe Gigli
- Dipartimento di Matematica e Fisica, 'Ennio de Giorgi', Università del Salento, Lecce, Italy
- CNR NANOTEC, Institute of Nanotechnology, Lecce, Italy
| | | | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, P. R. China
- Beijing Academy of Quantum Information Sciences, Beijing, P.R. China
| | - Antonio Fieramosca
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Nanyang, Singapore
| | - Dmitry D Solnyshkov
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Clermont-Ferrand, France.
- Institut Universitaire de France (IUF), Paris, France.
| | - Guillaume Malpuech
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Clermont-Ferrand, France
| | - Daniele Sanvitto
- CNR NANOTEC, Institute of Nanotechnology, Lecce, Italy
- INFN Istituto Nazionale di Fisica Nucleare, Lecce, Italy
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28
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Su R, Estrecho E, Biegańska D, Huang Y, Wurdack M, Pieczarka M, Truscott AG, Liew TCH, Ostrovskaya EA, Xiong Q. Direct measurement of a non-Hermitian topological invariant in a hybrid light-matter system. SCIENCE ADVANCES 2021; 7:eabj8905. [PMID: 34731010 PMCID: PMC8565900 DOI: 10.1126/sciadv.abj8905] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 09/13/2021] [Indexed: 05/31/2023]
Abstract
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterized by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant—fractional spectral winding. Our work represents an essential step toward realization of non-Hermitian topological phases in a condensed matter system.
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Affiliation(s)
- Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Eliezer Estrecho
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Dąbrówka Biegańska
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
- Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Yuqing Huang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Matthias Wurdack
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Maciej Pieczarka
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
- Department of Experimental Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Andrew G. Truscott
- Laser Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Timothy C. H. Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore, Singapore
| | - Elena A. Ostrovskaya
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Qihua Xiong
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P.R. China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
- Beijing Innovation Center for Future Chips, Tsinghua University, Beijing 100084, P.R. China
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29
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Biegańska D, Pieczarka M, Estrecho E, Steger M, Snoke DW, West K, Pfeiffer LN, Syperek M, Truscott AG, Ostrovskaya EA. Collective Excitations of Exciton-Polariton Condensates in a Synthetic Gauge Field. PHYSICAL REVIEW LETTERS 2021; 127:185301. [PMID: 34767383 DOI: 10.1103/physrevlett.127.185301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 07/24/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
Collective (elementary) excitations of quantum bosonic condensates, including condensates of exciton polaritons in semiconductor microcavities, are a sensitive probe of interparticle interactions. In anisotropic microcavities with momentum-dependent transverse-electric-transverse-magnetic splitting of the optical modes, the excitations' dispersions are predicted to be strongly anisotropic, which is a consequence of the synthetic magnetic gauge field of the cavity, as well as the interplay between different interaction strengths for polaritons in the singlet and triplet spin configurations. Here, by directly measuring the dispersion of the collective excitations in a high-density optically trapped exciton-polariton condensate, we observe excellent agreement with the theoretical predictions for spinor polariton excitations. We extract the interaction constants for polaritons of the same and opposite spin and map out the characteristic spin textures in an interacting spinor condensate of exciton polaritons.
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Affiliation(s)
- D Biegańska
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
- Department of Experimental Physics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - M Pieczarka
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
- Department of Experimental Physics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - E Estrecho
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - M Steger
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - D W Snoke
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - K West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Syperek
- Department of Experimental Physics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - A G Truscott
- Laser Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - E A Ostrovskaya
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
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30
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Julku A, Bruun GM, Törmä P. Quantum Geometry and Flat Band Bose-Einstein Condensation. PHYSICAL REVIEW LETTERS 2021; 127:170404. [PMID: 34739285 DOI: 10.1103/physrevlett.127.170404] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 09/24/2021] [Indexed: 06/13/2023]
Abstract
We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.
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Affiliation(s)
- Aleksi Julku
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
| | - Georg M Bruun
- Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Päivi Törmä
- Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland
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31
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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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32
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Quantum fluids of light in all-optical scatterer lattices. Nat Commun 2021; 12:5571. [PMID: 34552069 PMCID: PMC8458361 DOI: 10.1038/s41467-021-25845-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 09/02/2021] [Indexed: 11/08/2022] Open
Abstract
One of the recently established paradigms in condensed matter physics is examining a system's behaviour in artificial potentials, giving insight into phenomena of quantum fluids in hard-to-reach settings. A prominent example is the matter-wave scatterer lattice, where high energy matter waves undergo transmission and reflection through narrow width barriers leading to stringent phase matching conditions with lattice band formation. In contrast to evanescently coupled lattice sites, the realisation of a scatterer lattice for macroscopic matter-wave fluids has remained elusive. Here, we implement a system of exciton-polariton condensates in a non-Hermitian Lieb lattice of scatterer potentials. By fine tuning the lattice parameters, we reveal a nonequilibrium phase transition between distinct regimes of polariton condensation: a scatterer lattice of gain guided polaritons condensing on the lattice potential maxima, and trapped polaritons condensing in the potential minima. Our results pave the way towards unexplored physics of non-Hermitian fluids in non-stationary mixtures of confined and freely expanding waves.
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33
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Liao Q, Leblanc C, Ren J, Li F, Li Y, Solnyshkov D, Malpuech G, Yao J, Fu H. Experimental Measurement of the Divergent Quantum Metric of an Exceptional Point. PHYSICAL REVIEW LETTERS 2021; 127:107402. [PMID: 34533335 DOI: 10.1103/physrevlett.127.107402] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT), containing both the Berry curvature, central to the description of topological matter, and the quantum metric. So far, the full QGT has been measured only in Hermitian systems, where the role of the quantum metric is mostly limited to corrections. On the contrary, in non-Hermitian systems, and, in particular, near exceptional points, the quantum metric is expected to diverge and to often play a dominant role, for example, in the enhanced sensing and in wave packet dynamics. In this Letter, we report the first experimental measurement of the quantum metric in a non-Hermitian system. The specific platform under study is an organic microcavity with exciton-polariton eigenstates, which demonstrate exceptional points. We measure the quantum metric's divergence, and we determine the scaling exponent n=-1.01±0.08, which is in agreement with the theoretical description of second-order exceptional points.
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Affiliation(s)
- Qing Liao
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, People's Republic of China
| | - Charly Leblanc
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000 Clermont-Ferrand, France
| | - Jiahuan Ren
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, People's Republic of China
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, People's Republic of China
| | - Feng Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Shaanxi Key Lab of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Yiming Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Shaanxi Key Lab of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Dmitry Solnyshkov
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000 Clermont-Ferrand, France
- Institut Universitaire de France (IUF), 75231 Paris, France
| | - Guillaume Malpuech
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut Pascal, F-63000 Clermont-Ferrand, France
| | - Jiannian Yao
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, People's Republic of China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, Beijing 100048, People's Republic of China
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, Tianjin 300072, People's Republic of China
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34
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Sedov E, Sedova I, Arakelian S, Kavokin A. Polygonal patterns of confined light. OPTICS LETTERS 2021; 46:1836-1839. [PMID: 33857082 DOI: 10.1364/ol.418337] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 03/10/2021] [Indexed: 06/12/2023]
Abstract
We propose a technique for the generation of polygonal optical patterns in real space using a combined effect of the spin-orbit interaction and confinement of light in the plane of a dielectric optical microcavity. The spin-orbit interaction emerging from the splitting in transverse electric (TE) and transverse magnetic (TM) optical modes of the microcavity gives rise to oscillations in space of propagating macroscopic wave packets of polarized photons. Confined in a harmonic potential, the latter follow closed trajectories of a polygonal form. We demonstrate the possibility of excitation by a continuous wave resonant optical pumping of polygonal optical patterns with a controllable (both even and odd) number of vertices.
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35
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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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Ren J, Liao Q, Li F, Li Y, Bleu O, Malpuech G, Yao J, Fu H, Solnyshkov D. Nontrivial band geometry in an optically active system. Nat Commun 2021; 12:689. [PMID: 33514702 PMCID: PMC7846789 DOI: 10.1038/s41467-020-20845-2] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Accepted: 11/17/2020] [Indexed: 11/09/2022] Open
Abstract
Optical activity, also called circular birefringence, is known for two hundred years, but its applications for topological photonics remain unexplored. Unlike the Faraday effect, the optical activity provokes rotation of the linear polarization of light without magnetic effects, thus preserving the time-reversal symmetry. In this work, we report a direct measurement of the Berry curvature and quantum metric of the photonic modes of a planar cavity, containing a birefringent organic microcrystal (perylene) and exhibiting emergent optical activity. This experiment, performed at room temperature and at visible wavelength, establishes the potential of organic materials for implementing non-magnetic and low-cost topological photonic devices.
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Affiliation(s)
- Jiahuan Ren
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, 100048, Beijing, China
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, 300072, Tianjin, China
| | - Qing Liao
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, 100048, Beijing, China.
| | - Feng Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China.
- Department of Physics and Astronomy, University of Sheffield, Sheffield, UK.
| | - Yiming Li
- Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Olivier Bleu
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, F-63000, Clermont-Ferrand, France
| | - Guillaume Malpuech
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, F-63000, Clermont-Ferrand, France
| | - Jiannian Yao
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, 300072, Tianjin, China
| | - Hongbing Fu
- Beijing Key Laboratory for Optical Materials and Photonic Devices, Department of Chemistry, Capital Normal University, 100048, Beijing, China.
- Tianjin Key Laboratory of Molecular Optoelectronic Sciences, Department of Chemistry, School of Sciences, Tianjin University, Collaborative Innovation Center of Chemical Science and Engineering, 300072, Tianjin, China.
| | - Dmitry Solnyshkov
- Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, F-63000, Clermont-Ferrand, France.
- Institut Universitaire de France (IUF), 75231, Paris, France.
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37
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Tan X, Zhang DW, Zheng W, Yang X, Song S, Han Z, Dong Y, Wang Z, Lan D, Yan H, Zhu SL, Yu Y. Experimental Observation of Tensor Monopoles with a Superconducting Qudit. PHYSICAL REVIEW LETTERS 2021; 126:017702. [PMID: 33480777 DOI: 10.1103/physrevlett.126.017702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 12/09/2020] [Indexed: 06/12/2023]
Abstract
Monopoles play a center role in gauge theories and topological matter. There are two fundamental types of monopoles in physics: vector monopoles and tensor monopoles. Examples of vector monopoles include the Dirac monopole in three dimensions and Yang monopole in five dimensions, which have been extensively studied and observed in condensed matter or artificial systems. However, tensor monopoles are less studied, and their observation has not been reported. Here we experimentally construct a tunable spin-1 Hamiltonian to generate a tensor monopole and then measure its unique features with superconducting quantum circuits. The energy structure of a 4D Weyl-like Hamiltonian with threefold degenerate points acting as tensor monopoles is imaged. Through quantum-metric measurements, we report the first experiment that measures the Dixmier-Douady invariant, the topological charge of the tensor monopole. Moreover, we observe topological phase transitions characterized by the topological Dixmier-Douady invariant, rather than the Chern numbers as used for conventional monopoles in odd-dimensional spaces.
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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, 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
| | - Wen Zheng
- 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
| | - Yuqian Dong
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Zhimin Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dong Lan
- 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, 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
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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38
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Yang Y, Zhen B, Joannopoulos JD, Soljačić M. Non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly pairs. LIGHT, SCIENCE & APPLICATIONS 2020; 9:177. [PMID: 33088494 PMCID: PMC7572376 DOI: 10.1038/s41377-020-00384-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2020] [Revised: 07/28/2020] [Accepted: 08/02/2020] [Indexed: 06/11/2023]
Abstract
The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.
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Affiliation(s)
- Yi Yang
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
| | - Bo Zhen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 USA
| | - John D. Joannopoulos
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
| | - Marin Soljačić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
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39
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Glazov MM, Golub LE. Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals. PHYSICAL REVIEW LETTERS 2020; 125:157403. [PMID: 33095628 DOI: 10.1103/physrevlett.125.157403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 09/03/2020] [Indexed: 06/11/2023]
Abstract
Exciton valley Hall effect is the spatial separation of the valley-tagged excitons by a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering. We develop a microscopic theory of the exciton valley Hall effect in the presence of a synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current also demonstrating the cancellation of the anomalous velocity. The sensitivity of the effect to the origin of the drag force and to the scattering processes is shown. We extend the drift-diffusion model to account for the valley Hall effect and calculate the exciton density and valley polarization profiles.
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Affiliation(s)
- M M Glazov
- Ioffe Institute, 194021 St. Petersburg, Russia
| | - L E Golub
- Ioffe Institute, 194021 St. Petersburg, Russia
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40
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Quantum distance and anomalous Landau levels of flat bands. Nature 2020; 584:59-63. [PMID: 32760047 DOI: 10.1038/s41586-020-2540-1] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 05/18/2020] [Indexed: 11/09/2022]
Abstract
Semiclassical quantization of electronic states under a magnetic field, as proposed by Onsager, describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field1-5. Even in graphene with relativistic energy dispersion, Onsager's rule correctly describes the π Berry phase, as well as the unusual Landau level spectrum of Dirac particles6,7. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of dispersionless flat bands called 'singular flat bands'8. The singular flat band has a band crossing with another dispersive band that is enforced by the band-flatness condition, and shows anomalous magnetic responses. The Landau levels of a singular flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual 1/n dependence on the Landau level index n, which results in diverging orbital magnetic susceptibility. The total energy spread of the Landau levels of a singular flat band is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert-Schmidt quantum distance. We show that there is a universal and simple relationship between the total Landau level spread of a flat band and the maximum Hilbert-Schmidt quantum distance, which can be verified in various candidate materials. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.
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41
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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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