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Ren M, Yu Y, Wu B, Qi X, Wang Y, Yao X, Ren J, Guo Z, Jiang H, Chen H, Liu XJ, Chen Z, Sun Y. Realization of Gapped and Ungapped Photonic Topological Anderson Insulators. PHYSICAL REVIEW LETTERS 2024; 132:066602. [PMID: 38394559 DOI: 10.1103/physrevlett.132.066602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 01/03/2024] [Indexed: 02/25/2024]
Abstract
It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.
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Affiliation(s)
- Mina Ren
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Ye Yu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Bintao Wu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xin Qi
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Yiwei Wang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiaogang Yao
- Information Materials and Devices Research Center, Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 201800, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Zhiwei Guo
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Haitao Jiang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- International Quantum Academy, Shenzhen 518048, China
| | - Zhigang Chen
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Yong Sun
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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2
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Meng Y, Lin S, Shi BJ, Wei B, Yang L, Yan B, Zhu Z, Xi X, Wang Y, Ge Y, Yuan SQ, Chen J, Liu GG, Sun HX, Chen H, Yang Y, Gao Z. Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry. PHYSICAL REVIEW LETTERS 2023; 130:026101. [PMID: 36706409 DOI: 10.1103/physrevlett.130.026101] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 12/09/2022] [Indexed: 06/18/2023]
Abstract
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.
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Affiliation(s)
- Yan Meng
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Shuxin Lin
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bin-Jie Shi
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Bin Wei
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
- Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Linyun Yang
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bei Yan
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhenxiao Zhu
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiang Xi
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yin Wang
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yong Ge
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Shou-Qi Yuan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Jingming Chen
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Hong-Xiang Sun
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
- State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Zhen Gao
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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3
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Xue H, Wang Z, Huang YX, Cheng Z, Yu L, Foo YX, Zhao YX, Yang SA, Zhang B. Projectively Enriched Symmetry and Topology in Acoustic Crystals. PHYSICAL REVIEW LETTERS 2022; 128:116802. [PMID: 35363008 DOI: 10.1103/physrevlett.128.116802] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z_{2} gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.
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Affiliation(s)
- Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Zihao Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yue-Xin Huang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Letian Yu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Y X Foo
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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4
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Schulz J, Jörg C, von Freymann G. Geometric control of next-nearest-neighbor coupling in evanescently coupled dielectric waveguides. OPTICS EXPRESS 2022; 30:9869-9877. [PMID: 35299400 DOI: 10.1364/oe.447921] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2021] [Accepted: 01/09/2022] [Indexed: 06/14/2023]
Abstract
We experimentally demonstrate that the next-nearest-neighbor-coupling (NNN-coupling) in an array of waveguides can naturally be negative. To do so, dielectric zig-zag shaped waveguide arrays are fabricated with direct laser writing (DLW). By changing the angle of the zig-zag shape it is possible to tune between positive and negative ratios of nearest and next-nearest-neighbor coupling, which also allows to reduce the impact of the NNN-coupling to zero at the correct respective angle. We confirm the existence of negative NNN-couplings experimentally and show the improved accuracy of a refined tight-binding model. Our results are also of importance for other discrete systems in which the tight-binding model is often used.
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5
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Shao LB, Liu Q, Xiao R, Yang SA, Zhao YX. Gauge-Field Extended k·p Method and Novel Topological Phases. PHYSICAL REVIEW LETTERS 2021; 127:076401. [PMID: 34459642 DOI: 10.1103/physrevlett.127.076401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 07/01/2021] [Indexed: 06/13/2023]
Abstract
Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i) The little co-group must include the translations with nontrivial algebraic relations. (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.
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Affiliation(s)
- L B Shao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Q Liu
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - R Xiao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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6
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Ehrhardt M, Keil R, Maczewsky LJ, Dittel C, Heinrich M, Szameit A. Exploring complex graphs using three-dimensional quantum walks of correlated photons. SCIENCE ADVANCES 2021; 7:7/9/eabc5266. [PMID: 33637523 PMCID: PMC7909875 DOI: 10.1126/sciadv.abc5266] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
Graph representations are a powerful concept for solving complex problems across natural science, as patterns of connectivity can give rise to a multitude of emergent phenomena. Graph-based approaches have proven particularly fruitful in quantum communication and quantum search algorithms in highly branched quantum networks. Here, we introduce a previously unidentified paradigm for the direct experimental realization of excitation dynamics associated with three-dimensional networks by exploiting the hybrid action of spatial and polarization degrees of freedom of photon pairs in complex waveguide circuits with tailored birefringence. This testbed for the experimental exploration of multiparticle quantum walks on complex, highly connected graphs paves the way toward exploiting the applicative potential of fermionic dynamics in integrated quantum photonics.
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Affiliation(s)
- Max Ehrhardt
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23 18059 Rostock, Germany
| | - Robert Keil
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria
| | - Lukas J Maczewsky
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23 18059 Rostock, Germany
| | - Christoph Dittel
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Matthias Heinrich
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23 18059 Rostock, Germany
| | - Alexander Szameit
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23 18059 Rostock, Germany.
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7
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Qi Y, Qiu C, Xiao M, He H, Ke M, Liu Z. Acoustic Realization of Quadrupole Topological Insulators. PHYSICAL REVIEW LETTERS 2020; 124:206601. [PMID: 32501055 DOI: 10.1103/physrevlett.124.206601] [Citation(s) in RCA: 50] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 04/29/2020] [Indexed: 06/11/2023]
Abstract
A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here, we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge, and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.
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Affiliation(s)
- Yajuan Qi
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Meng Xiao
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Hailong He
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
| | - Manzhu Ke
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
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8
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Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10103425] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.
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9
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Observation of an acoustic octupole topological insulator. Nat Commun 2020; 11:2442. [PMID: 32415220 PMCID: PMC7229046 DOI: 10.1038/s41467-020-16350-1] [Citation(s) in RCA: 67] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 04/21/2020] [Indexed: 12/30/2022] Open
Abstract
Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.
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10
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A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages. Nat Commun 2020; 11:907. [PMID: 32060268 PMCID: PMC7021779 DOI: 10.1038/s41467-020-14692-4] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Accepted: 01/23/2020] [Indexed: 11/08/2022] Open
Abstract
Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized nonlocal property commonly manifests through exotic bulk phenomena and corresponding robust boundary effects. In our work we study a system where the spectral bands are associated with non-quantized indices, but nevertheless possess robust boundary states. We present a theoretical analysis, where we show that the square of the Hamiltonian exhibits quantized indices. The findings are experimentally demonstrated by using photonic Aharonov-Bohm cages.
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11
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Banerjee R, Mandal S, Liew TCH. Coupling between Exciton-Polariton Corner Modes through Edge States. PHYSICAL REVIEW LETTERS 2020; 124:063901. [PMID: 32109115 DOI: 10.1103/physrevlett.124.063901] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Revised: 11/28/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional localized corner modes that reside within the band gap of the system along with edge modes that inhabit a band edge next to bulk modes. Thanks to the topological nature, information can be trapped at the corners of these systems, which will be unhampered even in the presence of disorder. Being localized at the corners, the exchange of information among the corner states is an issue. Here we show that the nonlinearity in an exciton polariton system can allow the coupling between the different corners through the edge states based on optical parametric scattering, realizing a system of multiple connectible topological modes.
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Affiliation(s)
- R Banerjee
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - S Mandal
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - T C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
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12
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Röntgen M, Morfonios CV, Brouzos I, Diakonos FK, Schmelcher P. Quantum Network Transfer and Storage with Compact Localized States Induced by Local Symmetries. PHYSICAL REVIEW LETTERS 2019; 123:080504. [PMID: 31491209 DOI: 10.1103/physrevlett.123.080504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Indexed: 06/10/2023]
Abstract
We propose modulation protocols designed to generate, store, and transfer compact localized states in a quantum network. Induced by parameter tuning or local reflection symmetries, such states vanish outside selected domains of the complete system and are therefore ideal for information storage. Their creation and transfer is here achieved either via amplitude phase flips or via optimal temporal control of intersite couplings. We apply the concept to a decorated, locally symmetric Lieb lattice where one sublattice is dimerized, and also demonstrate it for more complex setups. The approach allows for a flexible storage and transfer of states along independent paths in lattices supporting flat energetic bands. We further demonstrate a method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks. We show that these compact localized states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications. The generic network and protocols proposed can be utilized in various physical setups such as atomic or molecular spin lattices, photonic waveguide arrays, and acoustic setups.
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Affiliation(s)
- M Röntgen
- Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - C V Morfonios
- Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - I Brouzos
- Department of Physics, University of Athens, 15771 Athens, Greece
| | - F K Diakonos
- Department of Physics, University of Athens, 15771 Athens, Greece
| | - P Schmelcher
- Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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13
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Ke S, Zhao D, Liu J, Liu Q, Liao Q, Wang B, Lu P. Topological bound modes in anti-PT-symmetric optical waveguide arrays. OPTICS EXPRESS 2019; 27:13858-13870. [PMID: 31163844 DOI: 10.1364/oe.27.013858] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Accepted: 04/21/2019] [Indexed: 06/09/2023]
Abstract
We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.
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14
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Smirnova DA, Padmanabhan P, Leykam D. Parity anomaly laser. OPTICS LETTERS 2019; 44:1120-1123. [PMID: 30821785 DOI: 10.1364/ol.44.001120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Accepted: 01/22/2019] [Indexed: 06/09/2023]
Abstract
We propose a novel supersymmetry-inspired scheme for achieving robust single-mode lasing in arrays of coupled microcavities, based on factorizing a given array Hamiltonian into its "supercharge" partner array. Pumping a single sublattice of the partner array preferentially induces lasing of an unpaired zero mode. A chiral symmetry protects the zero mode similar to 1D topological arrays, but it need not be localized to domain walls or edges. We demonstrate single-mode lasing over a wider parameter regime by designing the zero mode to have a uniform intensity profile.
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15
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Gao Z, Wu L, Gao F, Luo Y, Zhang B. Spoof Plasmonics: From Metamaterial Concept to Topological Description. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2018; 30:e1706683. [PMID: 29782662 DOI: 10.1002/adma.201706683] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Revised: 01/24/2018] [Indexed: 06/08/2023]
Abstract
Advances in metamaterials have offered the opportunity of engineering electromagnetic properties beyond the limits of natural materials. A typical example is "spoof" surface plasmon polaritons (SPPs), which mimic features of SPPs without penetrating into metal, but only with periodic corrugations on metal surfaces. They hold considerable promise in device applications from microwaves to the far infrared, where real SPP modes do not exist. The original spoof SPP concept is derived from the description of corrugated surfaces by a metamaterial that hosts an effective plasma frequency. Later, studies have attempted to describe spoof SPP modes with the band structure by strictly solving Maxwell's equations, which can possess band gaps from polaritonic anticrossing principle or Bragg interference. More recently, as inspired by the development of topological framework in condensed matter physics, the topological description of spoof SPPs is used to propose topologically protected waveguiding phenomena. Here, the developments of spoof SPPs from both practical and fundamental perspectives are reviewed.
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Affiliation(s)
- Zhen Gao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Lin Wu
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore
| | - Fei Gao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
- State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China
| | - Yu Luo
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, 637371, Singapore
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16
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Benalcazar WA, Bernevig BA, Hughes TL. Quantized electric multipole insulators. Science 2017; 357:61-66. [DOI: 10.1126/science.aah6442] [Citation(s) in RCA: 912] [Impact Index Per Article: 130.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Accepted: 06/02/2017] [Indexed: 11/02/2022]
Abstract
The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.
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17
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Gao Z, Gao F, Zhang Y, Xu H, Luo Y, Zhang B. Forward/Backward Switching of Plasmonic Wave Propagation Using Sign-Reversal Coupling. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2017; 29:1700018. [PMID: 28464456 DOI: 10.1002/adma.201700018] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2017] [Revised: 02/24/2017] [Indexed: 06/07/2023]
Abstract
Backward waves with wave-front propagation opposite in direction to that of energy flow have attracted considerable interest in the context of photonic metamaterials. However, switching between forward and backward waves in the same frequency range has remained a challenge. Here, on a platform of coupled designer surface plasmon resonators in the microwave regime, multiband forward/backward switching of plasmonic wave propagation is demonstrated. This approach makes use of sign-reversal coupling that occurs when switching the coupling configuration between tightly confined photonic modes. Direct experimental measurements of plasmon dispersion curves confirm the forward/backward propagation of plasmonic waves in the same frequency range. This study provides a solution to forward/backward switching of subwavelength plasmonic wave propagation, and may find potential applications in photonic integrated systems.
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Affiliation(s)
- Zhen Gao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Fei Gao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Youming Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Hongyi Xu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Yu Luo
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore
| | - Baile Zhang
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, 637371, Singapore
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18
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Cantillano C, Morales-Inostroza L, Real B, Rojas-Rojas S, Delgado A, Szameit A, Vicencio RA. Observation of dipolar transport in one-dimensional photonic lattices. Sci Bull (Beijing) 2017; 62:339-344. [PMID: 36659418 DOI: 10.1016/j.scib.2017.01.035] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2016] [Revised: 01/19/2017] [Accepted: 01/20/2017] [Indexed: 01/21/2023]
Abstract
We experimentally study the transport properties of dipolar and fundamental modes on one dimensional (1D) coupled waveguide arrays. By carefully modulating a wide optical beam, we are able to effectively excite dipolar or fundamental modes to study discrete diffraction (single-site excitation) and gaussian beam propagation (multi-site excitation plus a phase gradient). We observe that dipolar modes experience a larger spreading area due to an effective larger coupling constant, which is found to be more than two times larger than the one for fundamental modes. Additionally, we study the effect of non-diagonal disorder and find that while fundamental modes are already trapped on a weakly disorder array, dipoles are still able to propagate across the system.
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Affiliation(s)
- Camilo Cantillano
- Departamento de Física, MSI-Nucleus on Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago, Chile
| | - Luis Morales-Inostroza
- Departamento de Física, MSI-Nucleus on Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago, Chile
| | - Bastián Real
- Departamento de Física, MSI-Nucleus on Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago, Chile
| | - Santiago Rojas-Rojas
- Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile
| | - Aldo Delgado
- Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile
| | - Alexander Szameit
- Institute for Physics, University of Rostock, D-18059 Rostock, Germany
| | - Rodrigo A Vicencio
- Departamento de Física, MSI-Nucleus on Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
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