1
|
Song W, You O, Sun J, Wu S, Chen C, Huang C, Qiu K, Zhu S, Zhang S, Li T. Fast topological pumps via quantum metric engineering on photonic chips. SCIENCE ADVANCES 2024; 10:eadn5028. [PMID: 39058788 PMCID: PMC11277470 DOI: 10.1126/sciadv.adn5028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 06/21/2024] [Indexed: 07/28/2024]
Abstract
Topological pumps have garnered substantial attention in physics. However, the requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application in on-chip devices. Here, we discover a direct link between adiabaticity and quantum metric, the real part of quantum geometry that has been relatively less explored compared to its imaginary counterpart, the Berry curvature. We demonstrate that the evolution speed of topological pumps between nontrivial edge states can be increased by reducing the quantum metric via introduction of long-range coupling to the celebrated Rice-Mele model. This fast topological pump can occur without affecting the bulk state evolution, which challenges the common understanding. We experimentally confirm our findings by using a platform consisting of bilayer integrated silicon waveguides operating at telecommunication wavelengths. Our work provides possibilities for lifting topological pumps from the constraints of slow evolution and paves the way toward compact photonic integration.
Collapse
Affiliation(s)
- Wange Song
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Oubo You
- New Cornerstone Science Laboratory, Department of Physics, University of Hong Kong, Hong Kong, China
| | - Jiacheng Sun
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Shengjie Wu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Chen Chen
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Chunyu Huang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Kai Qiu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Shining Zhu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Shuang Zhang
- New Cornerstone Science Laboratory, Department of Physics, University of Hong Kong, Hong Kong, China
- Department of Electronic and Electrical Engineering, University of Hong Kong, Hong Kong, China
- Materials Innovation Institute for Life Sciences and Energy (MILES), HKU-SIRI, Shenzhen, P.R. China
| | - Tao Li
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulations, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| |
Collapse
|
2
|
Dai T, Ma A, Mao J, Ao Y, Jia X, Zheng Y, Zhai C, Yang Y, Li Z, Tang B, Luo J, Zhang B, Hu X, Gong Q, Wang J. A programmable topological photonic chip. NATURE MATERIALS 2024; 23:928-936. [PMID: 38777873 PMCID: PMC11230904 DOI: 10.1038/s41563-024-01904-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Controlling topological phases of light allows the observation of abundant topological phenomena and the development of robust photonic devices. The prospect of more sophisticated control with topological photonic devices for practical implementations requires high-level programmability. Here we demonstrate a fully programmable topological photonic chip with large-scale integration of silicon photonic nanocircuits and microresonators. Photonic artificial atoms and their interactions in our compound system can be individually addressed and controlled, allowing the arbitrary adjustment of structural parameters and geometrical configurations for the observation of dynamic topological phase transitions and diverse photonic topological insulators. Individual programming of artificial atoms on the generic chip enables the comprehensive statistical characterization of topological robustness against relatively weak disorders, and counterintuitive topological Anderson phase transitions induced by strong disorders. This generic topological photonic chip can be rapidly reprogrammed to implement multifunctionalities, providing a flexible and versatile platform for applications across fundamental science and topological technologies.
Collapse
Affiliation(s)
- Tianxiang Dai
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China.
| | - Anqi Ma
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
| | - Jun Mao
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
| | - Yutian Ao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
- Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University, Singapore, Singapore
| | - Xinyu Jia
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
| | - Yun Zheng
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
| | - Chonghao Zhai
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
| | - Yan Yang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China.
| | - Zhihua Li
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China
| | - Bo Tang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China
| | - Jun Luo
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
- Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University, Singapore, Singapore
| | - Xiaoyong Hu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China.
- Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China.
- Hefei National Laboratory, Hefei, China.
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China
- Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China
- Hefei National Laboratory, Hefei, China
| | - Jianwei Wang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, China.
- Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China.
- Hefei National Laboratory, Hefei, China.
| |
Collapse
|
3
|
Lyu X, Bai K, Xiao M. Routing light with different wavevectors using synthetic dimensions. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2024; 41:1122-1127. [PMID: 38856426 DOI: 10.1364/josaa.519506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 04/25/2024] [Indexed: 06/11/2024]
Abstract
Synthetic dimensions have drawn intense recent attention in investigating higher-dimensional topological physics and offering additional degrees of freedom for manipulating light. It has been demonstrated that synthetic dimensions can help to concentrate light with different frequencies at different locations. Here, we show that synthetic dimensions can also route light from different incident directions. Our system consists of an interface formed by two different photonic crystals. A synthetic dimension ξ is introduced by shifting the termination position of the photonic crystal on the right-hand side of the interface. We identify a correspondence between ξ and the interface state such that light incident from a specific direction can be collected. Thus, routing incident light from different directions is achieved by designing an interface with a proper distribution of ξ. Traditionally, this goal is achieved with a standard 4f optical system using a convex lens, and our approach offers the possibility for such a capability within a few lattice sites of photonic crystals. Such an approach reduces the size of the system, making it easier for integration. Our work provides, to our knowledge, a new direction for routing light with different momentums and possibly contributes to applications such as lidar.
Collapse
|
4
|
Pellerin F, Houvenaghel R, Coish WA, Carusotto I, St-Jean P. Wave-Function Tomography of Topological Dimer Chains with Long-Range Couplings. PHYSICAL REVIEW LETTERS 2024; 132:183802. [PMID: 38759187 DOI: 10.1103/physrevlett.132.183802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/19/2024]
Abstract
The ability to tailor with a high accuracy the intersite connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the Su-Schrieffer-Heeger model which, in its conventional form, is limited to nearest-neighbor couplings only. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wave functions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class.
Collapse
Affiliation(s)
- F Pellerin
- Département de Physique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
| | - R Houvenaghel
- Département de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, F69007 Lyon, France
| | - W A Coish
- Department of Physics, McGill University, 3600 rue University, Montreal, Québec H3A 2T8, Canada
| | - I Carusotto
- Pitaevskii BEC Center, INO-CNR and Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38123 Trento, Italy
| | - P St-Jean
- Département de Physique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
- Institut Courtois, Université de Montréal, Montréal, Quebec H2V 0B3, Canada
| |
Collapse
|
5
|
Bouhiron JB, Fabre A, Liu Q, Redon Q, Mittal N, Satoor T, Lopes R, Nascimbene S. Realization of an atomic quantum Hall system in four dimensions. Science 2024; 384:223-227. [PMID: 38603489 DOI: 10.1126/science.adf8459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 02/14/2024] [Indexed: 04/13/2024]
Abstract
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.
Collapse
Affiliation(s)
- Jean-Baptiste Bouhiron
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Aurélien Fabre
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Qi Liu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Quentin Redon
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Nehal Mittal
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Tanish Satoor
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Raphael Lopes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Sylvain Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| |
Collapse
|
6
|
Tian M, Velkovsky I, Chen T, Sun F, He Q, Gadway B. Manipulation of Weyl Points in Reciprocal and Nonreciprocal Mechanical Lattices. PHYSICAL REVIEW LETTERS 2024; 132:126602. [PMID: 38579212 DOI: 10.1103/physrevlett.132.126602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 02/22/2024] [Indexed: 04/07/2024]
Abstract
We introduce feedback-measurement technologies to achieve flexible control of Weyl points and conduct the first experimental demonstration of Weyl type I-II transition in mechanical systems. We demonstrate that non-Hermiticity can expand the Fermi arc surface states from connecting Weyl points to Weyl rings, and lead to a localization transition of edge states influenced by the interplay between band topology and the non-Hermitian skin effect. Our findings offer valuable insights into the design and manipulation of Weyl points in mechanical systems, providing a promising avenue for manipulating topological modes in non-Hermitian systems.
Collapse
Affiliation(s)
- Mingsheng Tian
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Ivan Velkovsky
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Tao Chen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Fengxiao Sun
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
| | - Qiongyi He
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Hefei National Laboratory, Hefei, 230088, China
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| |
Collapse
|
7
|
Wu HC, Xu HS, Xie LC, Jin L. Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:083801. [PMID: 38457698 DOI: 10.1103/physrevlett.132.083801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 01/10/2024] [Indexed: 03/10/2024]
Abstract
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.
Collapse
Affiliation(s)
- H C Wu
- School of Physics, Nankai University, Tianjin 300071, China
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - H S Xu
- School of Physics, Nankai University, Tianjin 300071, China
| | - L C Xie
- School of Physics, Nankai University, Tianjin 300071, China
| | - L Jin
- School of Physics, Nankai University, Tianjin 300071, China
| |
Collapse
|
8
|
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.
Collapse
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
| |
Collapse
|
9
|
Tyner AC, Juričić V. Three-dimensional [Formula: see text] topological insulators without reflection symmetry. Sci Rep 2024; 14:4288. [PMID: 38383545 PMCID: PMC10882006 DOI: 10.1038/s41598-024-54821-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 02/16/2024] [Indexed: 02/23/2024] Open
Abstract
In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the [Formula: see text] paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a "parent" four-dimensional topological insulator exhibits a [Formula: see text] topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a [Formula: see text]-dimensional "parent" Hamiltonian in d dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phononic crystals, topolectric circuits, and designer systems.
Collapse
Affiliation(s)
- Alexander C Tyner
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91, Stockholm, Sweden.
- Department of Physics, University of Connecticut, Storrs, CT, 06269, USA.
| | - Vladimir Juričić
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91, Stockholm, Sweden.
- Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110, Valparaiso, Chile.
| |
Collapse
|
10
|
Chen ZX, Peng YG, Chen ZG, Liu Y, Chen P, Zhu XF, Lu YQ. Robust temporal adiabatic passage with perfect frequency conversion between detuned acoustic cavities. Nat Commun 2024; 15:1478. [PMID: 38368404 PMCID: PMC10874448 DOI: 10.1038/s41467-024-45932-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 02/08/2024] [Indexed: 02/19/2024] Open
Abstract
For classical waves, phase matching is vital for enabling efficient energy transfer in many scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here, we propose a temporal quasi-phase matching method and realize robust and complete acoustical energy transfer between arbitrarily detuned cavities. In a set of three cavities, A, B, and C, the time-varying coupling is established between adjacent elements. Analogy to the concept of stimulated Raman adiabatic passage, amplitudes of the two couplings are modulated as time-delayed Gaussian functions, and the couplings' signs are periodically flipped to eliminate temporal phase mismatching. As a result, robust and complete acoustic energy transfer from A to C is achieved. The non-reciprocal frequency conversion properties of our design are demonstrated. Our research takes a pivotal step towards expanding wave steering through time-dependent modulations and is promising to extend the frequency conversion based on state evolution in various linear Hermitian systems to nonlinear and non-Hermitian regimes.
Collapse
Affiliation(s)
- Zhao-Xian Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China
| | - Yu-Gui Peng
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China
| | - Ze-Guo Chen
- School of Materials Science and Intelligent Engineering, Nanjing University, Suzhou, 215163, China.
| | - Yuan Liu
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China
| | - Peng Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China
| | - Xue-Feng Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China.
| | - Yan-Qing Lu
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, China.
| |
Collapse
|
11
|
Suh J, Kim G, Park H, Fan S, Park N, Yu S. Photonic Topological Spin Pump in Synthetic Frequency Dimensions. PHYSICAL REVIEW LETTERS 2024; 132:033803. [PMID: 38307059 DOI: 10.1103/physrevlett.132.033803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/15/2023] [Indexed: 02/04/2024]
Abstract
Reducing geometrical complexity while preserving desired wave properties is critical for proof-of-concept studies in wave physics, as evidenced by recent efforts to realize photonic synthetic dimensions, isospectrality, and hyperbolic lattices. Laughlin's topological pump, which elucidates quantum Hall states in cylindrical geometry with a radial magnetic field and a time-varying axial magnetic flux, is a prime example of these efforts. Here we propose a two-dimensional dynamical photonic system for the topological pumping of pseudospin modes by exploiting synthetic frequency dimensions. The system provides the independent control of pseudomagnetic fields and electromotive forces achieved by the interplay between mode-dependent and mode-independent gauge fields. To address the axial open boundaries and azimuthal periodicity of the system, we define the adjusted local Chern marker with rotating azimuthal coordinates, proving the nontrivial topology of the system. We demonstrate the adiabatic pumping for crosstalk-free frequency conversion with wave front molding. Our approach allows for reproducing Laughlin's thought experiment at room temperature with a scalable setup.
Collapse
Affiliation(s)
- Joseph Suh
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Gyunghun Kim
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Hyungchul Park
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Shanhui Fan
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Namkyoo Park
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Sunkyu Yu
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| |
Collapse
|
12
|
Oliver C, Mukherjee S, Rechstman MC, Carusotto I, Price HM. Artificial gauge fields in the t- z mapping for optical pulses: Spatiotemporal wave packet control and quantum Hall physics. SCIENCE ADVANCES 2023; 9:eadj0360. [PMID: 37862408 PMCID: PMC10588944 DOI: 10.1126/sciadv.adj0360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 09/18/2023] [Indexed: 10/22/2023]
Abstract
We extend the t-z mapping of time-dependent paraxial optics by engineering a synthetic magnetic vector potential, leading to a nontrivial band topology. We consider an inhomogeneous 1D array of coupled optical waveguides and show that the wave equation describing paraxial propagation of optical pulses can be recast as a Schrödinger equation, including a synthetic magnetic field whose strength can be controlled via the spatial gradient of the waveguide properties across the array. We use an experimentally motivated model of a laser-written array to demonstrate that this synthetic magnetic field can be engineered in realistic setups and can produce interesting physics such as cyclotron motion, a controllable Hall drift of the pulse in space or time, and propagation in chiral edge states. These results substantially extend the physics that can be explored within propagating geometries and pave the way for higher-dimensional topological physics and strongly correlated fluids of light.
Collapse
Affiliation(s)
- Christopher Oliver
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| | | | - Mikael C. Rechstman
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Iacopo Carusotto
- Pitaevskii BEC Center, INO-CNR and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
| | - Hannah M. Price
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| |
Collapse
|
13
|
Xiang ZC, Huang K, Zhang YR, Liu T, Shi YH, Deng CL, Liu T, Li H, Liang GH, Mei ZY, Yu H, Xue G, Tian Y, Song X, Liu ZB, Xu K, Zheng D, Nori F, Fan H. Simulating Chern insulators on a superconducting quantum processor. Nat Commun 2023; 14:5433. [PMID: 37669968 PMCID: PMC10480218 DOI: 10.1038/s41467-023-41230-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 08/23/2023] [Indexed: 09/07/2023] Open
Abstract
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions on a programable 30-qubit-ladder superconducting processor. We directly measure the band structures of the 2D Chern insulator along synthetic dimensions with various configurations of Aubry-André-Harper chains and observe dynamical localisation of edge excitations. With these two signatures of topology, our experiments implement the bulk-edge correspondence in the synthetic 2D Chern insulator. Moreover, we simulate two different bilayer Chern insulators on the ladder-type superconducting processor. With the same and opposite periodically modulated on-site potentials for two coupled chains, we simulate topologically nontrivial edge states with zero Hall conductivity and a Chern insulator with higher Chern numbers, respectively. Our work shows the potential of using superconducting qubits for investigating different intriguing topological phases of quantum matter.
Collapse
Affiliation(s)
- Zhong-Cheng Xiang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Kaixuan Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Teda Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China
| | - Yu-Ran Zhang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, 510640, China
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama, 351-0198, Japan
- Center for Quantum Computing, RIKEN, Wako-shi, Saitama, 351-0198, Japan
| | - Tao Liu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, 510640, China
| | - Yun-Hao Shi
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Cheng-Lin Deng
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Tong Liu
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Gui-Han Liang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Zheng-Yang Mei
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Haifeng Yu
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
| | - Guangming Xue
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
| | - Ye Tian
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Xiaohui Song
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Zhi-Bo Liu
- Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Teda Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China
| | - Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- CAS Centre for Excellence in Topological Quantum Computation, UCAS, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, China.
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- CAS Centre for Excellence in Topological Quantum Computation, UCAS, Beijing, 100190, China
- Songshan Lake Materials Laboratory, Dongguan, 523808, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama, 351-0198, Japan.
- Center for Quantum Computing, RIKEN, Wako-shi, Saitama, 351-0198, Japan.
- Physics Department, University of Michigan, Ann Arbor, MI, 48109-1040, USA.
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- CAS Centre for Excellence in Topological Quantum Computation, UCAS, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, 523808, China.
| |
Collapse
|
14
|
Chen XD, Shi FL, Liu JW, Shen K, He XT, Chan CT, Chen WJ, Dong JW. Second Chern crystals with inherently non-trivial topology. Natl Sci Rev 2023; 10:nwac289. [PMID: 37389141 PMCID: PMC10306366 DOI: 10.1093/nsr/nwac289] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Revised: 11/02/2022] [Accepted: 11/02/2022] [Indexed: 07/31/2023] Open
Abstract
Chern insulators have been generalized to many classical wave systems and thereby lead to many potential applications such as robust waveguides, quantum computation and high-performance lasers. However, the band structure of a material can be either topologically trivial or non-trivial, depending on how the crystal structure is designed. Here, we propose a second Chern crystal in a four-dimensional parameter space by introducing two extra synthetic translation dimensions. Since the topology of the bulk bands in the synthetic translation space is intrinsically non-trivial, our proposed four-dimensional crystal is guaranteed to be topologically non-trivial regardless of the crystal's detailed configuration. We derive the topologically protected modes on the lower dimensional boundaries of such a crystal via dimension reduction. Remarkably, we observe the one-dimensional gapless dislocation modes and confirm their robustness in experiments. Our findings provide novel perspectives on topologically non-trivial crystals and may inspire designs of classical wave devices.
Collapse
Affiliation(s)
- Xiao-Dong Chen
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
| | - Fu-Long Shi
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
| | - Jian-Wei Liu
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
| | - Ke Shen
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
| | - Xin-Tao He
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, China
| | - C T Chan
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China
| | | | | |
Collapse
|
15
|
Wang S, Hu Z, Wu Q, Chen H, Prodan E, Zhu R, Huang G. Smart patterning for topological pumping of elastic surface waves. SCIENCE ADVANCES 2023; 9:eadh4310. [PMID: 37506214 PMCID: PMC10381920 DOI: 10.1126/sciadv.adh4310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 06/26/2023] [Indexed: 07/30/2023]
Abstract
Topological pumping allows waves to navigate a sample undisturbed by disorders and defects. We demonstrate this phenomenon with elastic surface waves by strategically patterning an elastic surface to create a synthetic dimension. The surface is decorated with arrays of resonating pillars that are connected by spatially slow-varying coupling bridges and support eigenmodes located below the sound cone. We establish a connection between the collective dynamics of the pillars and that of electrons in a magnetic field by developing a tight-binding model and a WKB (Wentzel-Kramers-Brillouin) analysis. This enables us to predict the topological pumping pattern, which we validate through numerical and experimental steering of waves from one edge to the other. Furthermore, we observe the immune nature of the topologically pumped surface waves to disorder and defects. The combination of surface patterning and WKB analysis provides a versatile platform for controlling surface waves and exploring topological matter in higher dimensions.
Collapse
Affiliation(s)
- Shaoyun Wang
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
| | - Zhou Hu
- School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
| | - Qian Wu
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
| | - Hui Chen
- Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics Ningbo University, Ningbo 315211, China
| | - Emil Prodan
- Department of Physics, Yeshiva University, New York, NY 10016, USA
| | - Rui Zhu
- School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
| | - Guoliang Huang
- Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
| |
Collapse
|
16
|
Li Z, Luo XW, Lin D, Gharajeh A, Moon J, Hou J, Zhang C, Gu Q. Topological Microlaser with a Non-Hermitian Topological Bulk. PHYSICAL REVIEW LETTERS 2023; 131:023202. [PMID: 37505939 DOI: 10.1103/physrevlett.131.023202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 05/25/2023] [Indexed: 07/30/2023]
Abstract
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.
Collapse
Affiliation(s)
- Zhitong Li
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Dayang Lin
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Abouzar Gharajeh
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Jiyoung Moon
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chuanwei Zhang
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Qing Gu
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| |
Collapse
|
17
|
Cheng D, Lustig E, Wang K, Fan S. Multi-dimensional band structure spectroscopy in the synthetic frequency dimension. LIGHT, SCIENCE & APPLICATIONS 2023; 12:158. [PMID: 37369684 DOI: 10.1038/s41377-023-01196-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 05/23/2023] [Accepted: 05/26/2023] [Indexed: 06/29/2023]
Abstract
The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.
Collapse
Affiliation(s)
- Dali Cheng
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Eran Lustig
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
- Department of Physics, McGill University, Montreal, QC, H3A 2T8, Canada
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
| |
Collapse
|
18
|
Elshahat S, Zhang H, Lu C. Topological rainbow based on coupling of topological waveguide and cavity. OPTICS EXPRESS 2023; 31:20187-20199. [PMID: 37381418 DOI: 10.1364/oe.493182] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 05/18/2023] [Indexed: 06/30/2023]
Abstract
Topological photonics and topological photonic states have opened up a new frontier for optical manipulation and robust light trapping. The topological rainbow can separate different frequencies of topological states into different positions. This work combines a topological photonic crystal waveguide (topological PCW) with the optical cavity. The dipole and quadrupole topological rainbows are realized through increasing cavity size along the coupling interface. The flatted band can be obtained by increasing cavity length due to interaction strength between the optical field and defected region material which is extensively promoted. The light propagation through the coupling interface is built on the evanescent overlapping mode tails of the localized fields between bordering cavities. Thus, the ultra-low group velocity is realized at a cavity length more than the lattice constant, which is appropriate for realizing an accurate and precise topological rainbow. Hence, this is a novel release for strong localization with robust transmission and owns the possibility to realize high-performance optical storage devices.
Collapse
|
19
|
Pan Y, Chen Z, Wang B, Poem E. Floquet Gauge Anomaly Inflow and Arbitrary Fractional Charge in Periodically Driven Topological-Normal Insulator Heterostructures. PHYSICAL REVIEW LETTERS 2023; 130:223403. [PMID: 37327446 DOI: 10.1103/physrevlett.130.223403] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Revised: 11/14/2022] [Accepted: 02/27/2023] [Indexed: 06/18/2023]
Abstract
Usually, when coupling in a background gauge field, topological zero modes would yield an anomalous current at the interface, culminating in the zero-mode anomaly inflow, which is ultimately conserved by extra contributions from the topological bulk. However, the anomaly inflow mechanism for guiding Floquet steady states is rarely explored in periodically driven systems. Here we synthesize a driven topological-normal insulator heterostructure and propose a Floquet gauge anomaly inflow, associated with the occurrence of arbitrary fractional charge. Through our photonic modeling, we experimentally observed a Floquet gauge anomaly as the system was driven into anomalous topological phases. Prospectively, we believe our findings could pave a novel avenue on exploring Floquet gauge anomalies in driven systems of condensed matter, photonics, and ultracold atoms.
Collapse
Affiliation(s)
- Yiming Pan
- School of Physical Science and Technology and Center for Transformative Science, ShanghaiTech University, Shanghai 200031, China
- Physics Department and Solid-State Institute, Technion, Haifa 32000, Israel
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Zhaopin Chen
- Physics Department and Solid-State Institute, Technion, Haifa 32000, Israel
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
- Department of Electrical Engineering Physical Electronics, Tel Aviv University, Ramat Aviv 69978, Israel
| | - Bing Wang
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China
| | - Eilon Poem
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| |
Collapse
|
20
|
Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
Collapse
Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
| |
Collapse
|
21
|
Del Pino J, Zilberberg O. Dynamical Gauge Fields with Bosonic Codes. PHYSICAL REVIEW LETTERS 2023; 130:171901. [PMID: 37172225 DOI: 10.1103/physrevlett.130.171901] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Revised: 03/31/2023] [Accepted: 04/04/2023] [Indexed: 05/14/2023]
Abstract
The quantum simulation of dynamical gauge field theories offers the opportunity to study complex high-energy physics with controllable low-energy devices. For quantum computation, bosonic codes promise robust error correction that exploits multiparticle redundancy in bosons. Here, we demonstrate how bosonic codes can be used to simulate dynamical gauge fields. We encode both matter and dynamical gauge fields in a network of resonators that are coupled via three-wave mixing. The mapping to a Z_{2} dynamical lattice gauge theory is established when the gauge resonators operate as Schrödinger cat states. We explore the optimal conditions under which the system preserves the required gauge symmetries. Our findings promote realizing high-energy models using bosonic codes.
Collapse
Affiliation(s)
- Javier Del Pino
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Oded Zilberberg
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany
| |
Collapse
|
22
|
Chen K, Komissarenko F, Smirnova D, Vakulenko A, Kiriushechkina S, Volkovskaya I, Guddala S, Menon V, Alù A, Khanikaev AB. Photonic Dirac cavities with spatially varying mass term. SCIENCE ADVANCES 2023; 9:eabq4243. [PMID: 36947629 PMCID: PMC10032596 DOI: 10.1126/sciadv.abq4243] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 02/17/2023] [Indexed: 06/18/2023]
Abstract
In recent years, photonics has proven itself as an excellent platform for emulation of relativistic phenomena. Here, we show an example of relativistic-like trapping in photonic system that realizes Dirac-like dispersion with spatially inhomogeneous mass term. The modes trapped by such cavities, their energy levels, and corresponding orbitals are then characterized through optical imaging in real and momentum space. The fabricated cavities host a hierarchy of photonic modes with distinct radiation profiles directly analogous to various atomic orbitals endowed with unique characteristics, such as pseudo-particle-hall symmetry and spin degeneracy, and they carry topological charge which gives rise to radiative profiles with angular momentum. We demonstrate that these modes can be directionally excited by pseudo-spin-polarized boundary states. In addition to the fundamental interest in the structure of these pseudo-relativistic orbitals, the proposed system offers a route for designing new types of nanophotonic devices, spin-full resonators and topological light sources compatible with integrated photonics platforms.
Collapse
Affiliation(s)
- Kai Chen
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
- Department of Physics, City College of New York, New York, NY 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY 10016, USA
| | - Filipp Komissarenko
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
| | - Daria Smirnova
- Research School of Physics, Australian National University, Canberra ACT 2601, Australia
| | - Anton Vakulenko
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
| | - Svetlana Kiriushechkina
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
| | - Irina Volkovskaya
- Research School of Physics, Australian National University, Canberra ACT 2601, Australia
| | - Sriram Guddala
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
| | - Vinod Menon
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
| | - Andrea Alù
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY 10016, USA
| | - Alexander B. Khanikaev
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY 10031, USA
- Department of Physics, City College of New York, New York, NY 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY 10016, USA
| |
Collapse
|
23
|
Liu Q, Liu W, Ziegler K, Chen F. Engineering of Zeno Dynamics in Integrated Photonics. PHYSICAL REVIEW LETTERS 2023; 130:103801. [PMID: 36962047 DOI: 10.1103/physrevlett.130.103801] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 11/06/2022] [Accepted: 02/15/2023] [Indexed: 06/18/2023]
Abstract
Frequent observations to a quantum system modify its coherent evolution through the Zeno effect and Zeno dynamics. Generally, the measurement process destroys the evolution environment of the monitored system, making repeated observations remain a challenge. Here, using the quantum analogy experiments, we realize and engineer the Zeno effect and Zeno dynamics in optical waveguide arrays, where the optical modes correspond to distinct quantum states, and the temporal evolution is mapped into the spatial propagation. We propose a new, extensible experimental strategy for realizing an optical analog of stroboscopic measurements, which are performed by the build-in, on-demand segmented waveguide portions. The weak-to-strong stroboscopic measurements are realized, where the monitored system undergoes a transition from free evolution to optical Zeno freezing. Setting the measurements in the strong regime, the optical Zeno effect and optical Zeno dynamics are successfully generated, and their relationship is demonstrated in optics. We then propose a novel quantum Zeno slicing approach, which allows us to dynamically engineer the Hilbert space of the monitored system. This generic approach is verified by generating a series of Zeno subspaces with different measurement projectors, based on the quantum-optical analogy. The complexity of light dynamics is largely increased, providing full control of the propagation via steering Zeno dynamics. Our results pave the way for manipulation of quantum states by harnessing Zeno dynamics in integrated photonics.
Collapse
Affiliation(s)
- Quancheng Liu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Weijie Liu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| | - Klaus Ziegler
- Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany
| | - Feng Chen
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| |
Collapse
|
24
|
Hyperbolic band topology with non-trivial second Chern numbers. Nat Commun 2023; 14:1083. [PMID: 36841813 PMCID: PMC9968300 DOI: 10.1038/s41467-023-36767-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 02/08/2023] [Indexed: 02/27/2023] Open
Abstract
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic Bloch theorem. This theory promotes the investigation of hyperbolic band topology, where hyperbolic topological band insulators protected by first Chern numbers have been proposed. Here, we report a new finding on the construction of hyperbolic topological band insulators with a vanished first Chern number but a non-trivial second Chern number. Our model possesses the non-abelian translational symmetry of {8,8} hyperbolic tiling. By engineering intercell couplings and onsite potentials of sublattices in each unit cell, the non-trivial bandgaps with quantized second Chern numbers can appear. In experiments, we fabricate two types of finite hyperbolic circuit networks with periodic boundary conditions and partially open boundary conditions to detect hyperbolic topological band insulators. Our work suggests a new way to engineer hyperbolic topological states with higher-order topological invariants.
Collapse
|
25
|
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: 5] [Impact Index Per Article: 5.0] [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.
Collapse
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
| |
Collapse
|
26
|
Adiyatullin AF, Upreti LK, Lechevalier C, Evain C, Copie F, Suret P, Randoux S, Delplace P, Amo A. Topological Properties of Floquet Winding Bands in a Photonic Lattice. PHYSICAL REVIEW LETTERS 2023; 130:056901. [PMID: 36800474 DOI: 10.1103/physrevlett.130.056901] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
The engineering of synthetic materials characterized by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterized by a winding number. The winding emerges from the breakup of inversion symmetry, and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enriches the variety of topological phases available in lattices subject to Floquet driving and suggests the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.
Collapse
Affiliation(s)
- Albert F Adiyatullin
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Lavi K Upreti
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Corentin Lechevalier
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Clement Evain
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Francois Copie
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Pierre Suret
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Stephane Randoux
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Pierre Delplace
- ENS de Lyon, CNRS, Laboratoire de physique (UMR CNRS 5672), F-69342 Lyon, France
| | - Alberto Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| |
Collapse
|
27
|
Roberts N, Baardink G, Nunn J, Mosley PJ, Souslov A. Topological supermodes in photonic crystal fiber. SCIENCE ADVANCES 2022; 8:eadd3522. [PMID: 36542705 PMCID: PMC9770996 DOI: 10.1126/sciadv.add3522] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a length-scalable platform such as optical fiber. We demonstrate, through both modeling and experiment, optical fiber that hosts topological supermodes across multiple light-guiding cores. We directly measure the photonic winding number invariant characterizing the bulk and observe topological guidance of visible light over meter length scales. Furthermore, the mechanical flexibility of fiber allows us to reversibly reconfigure the topological state. As the fiber is bent, we find that the edge states first lose their localization and then become relocalized because of disorder. We envision fiber as a scalable platform to explore and exploit topological effects in photonic networks.
Collapse
Affiliation(s)
- Nathan Roberts
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
| | - Guido Baardink
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
| | - Josh Nunn
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
- ORCA Computing Ltd., 30 Eastbourne Terrace, London W2 6LA, UK
| | - Peter J. Mosley
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
| | - Anton Souslov
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
| |
Collapse
|
28
|
Lee KY, Yoon S, Song SH, Yoon JW. Topological beaming of light. SCIENCE ADVANCES 2022; 8:eadd8349. [PMID: 36490348 PMCID: PMC9733916 DOI: 10.1126/sciadv.add8349] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Nanophotonic light emitters are key components in numerous application areas because of their compactness and versatility. Here, we propose a topological beam emitter structure that takes advantage of submicrometer footprint size, small divergence angle, high efficiency, and adaptable beam shaping capability. The proposed structure consists of a topological junction of two guided-mode resonance gratings inducing a leaky Jackiw-Rebbi state resonance. The leaky Jackiw-Rebbi state leads to in-plane optical confinement with funnel-like energy flow and enhanced emission probability, resulting in highly efficient optical beam emission. In addition, the structure allows adaptable beam shaping for any desired positive definite profiles by means of Dirac mass distribution control, which can be directly encoded in lattice geometry parameters. Therefore, the proposed approach provides highly desirable properties for efficient micro-light emitters and detectors in various applications including display, solid-state light detection and ranging, laser machining, label-free sensors, optical interconnects, and telecommunications.
Collapse
Affiliation(s)
- Ki Young Lee
- Department of Physics, Hanyang University, Seoul, 133-791, Republic of Korea
| | - Seungjin Yoon
- James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK
| | - Seok Ho Song
- Department of Physics, Hanyang University, Seoul, 133-791, Republic of Korea
| | - Jae Woong Yoon
- Department of Physics, Hanyang University, Seoul, 133-791, Republic of Korea
| |
Collapse
|
29
|
Two-dimensional Thouless pumping of light in photonic moiré lattices. Nat Commun 2022; 13:6738. [PMID: 36347871 PMCID: PMC9643509 DOI: 10.1038/s41467-022-34394-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 10/21/2022] [Indexed: 11/09/2022] Open
Abstract
Continuous and quantized transports are profoundly different. The latter is determined by the global rather than local properties of a system, it exhibits unique topological features, and its ubiquitous nature causes its occurrence in many areas of science. Here we report the first observation of fully-two-dimensional Thouless pumping of light by bulk modes in a purpose-designed tilted moiré lattices imprinted in a photorefractive crystal. Pumping in such unconfined system occurs due to the longitudinal adiabatic and periodic modulation of the refractive index. The topological nature of this phenomenon manifests itself in the magnitude and direction of shift of the beam center-of-mass averaged over one pumping cycle. Our experimental results are supported by systematic numerical simulations in the frames of the continuous Schrödinger equation governing propagation of probe light beam in optically-induced photorefractive moiré lattice. Our system affords a powerful platform for the exploration of topological pumping in tunable commensurate and incommensurate geometries. Extending the control over topological system will open the doors to both fundamental studies and applications. Here the authors demonstrate thouless topological transport of light in a bulk tunable moiré lattice.
Collapse
|
30
|
Fu Q, Wang P, Kartashov YV, Konotop VV, Ye F. Two-Dimensional Nonlinear Thouless Pumping of Matter Waves. PHYSICAL REVIEW LETTERS 2022; 129:183901. [PMID: 36374696 DOI: 10.1103/physrevlett.129.183901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
Collapse
Affiliation(s)
- Qidong Fu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| |
Collapse
|
31
|
Abstract
Mirrors are ubiquitous in optics and are used to control the propagation of optical signals in space. Here we propose and demonstrate frequency domain mirrors that provide reflections of the optical energy in a frequency synthetic dimension, using electro-optic modulation. First, we theoretically explore the concept of frequency mirrors with the investigation of propagation loss, and reflectivity in the frequency domain. Next, we explore the mirror formed through polarization mode-splitting in a thin-film lithium niobate micro-resonator. By exciting the Bloch waves of the synthetic frequency crystal with different wave vectors, we show various states formed by the interference between forward propagating and reflected waves. Finally, we expand on this idea, and generate tunable frequency mirrors as well as demonstrate trapped states formed by these mirrors using coupled lithium niobate micro-resonators. The ability to control the flow of light in the frequency domain could enable a wide range of applications, including the study of random walks, boson sampling, frequency comb sources, optical computation, and topological photonics. Furthermore, demonstration of optical elements such as cavities, lasers, and photonic crystals in the frequency domain, may be possible.
Collapse
|
32
|
Topological boundary states transport in synthetic four-dimensional acoustic system. Sci Bull (Beijing) 2022; 67:1950-1953. [PMID: 36546202 DOI: 10.1016/j.scib.2022.09.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Revised: 07/25/2022] [Accepted: 08/29/2022] [Indexed: 01/07/2023]
|
33
|
Mostaan N, Grusdt F, Goldman N. Quantized topological pumping of solitons in nonlinear photonics and ultracold atomic mixtures. Nat Commun 2022; 13:5997. [PMID: 36220824 PMCID: PMC9554178 DOI: 10.1038/s41467-022-33478-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Accepted: 09/20/2022] [Indexed: 12/02/2022] Open
Abstract
Exploring the interplay between topological band structures and tunable nonlinearities has become possible with the development of synthetic lattice systems. In this emerging field of nonlinear topological physics, an experiment revealed the quantized motion of solitons in Thouless pumps and suggested that this phenomenon was dictated by the Chern number of the band from which solitons emanate. Here, we elucidate the origin of this nonlinear topological effect, by showing that the motion of solitons is established by the quantized displacement of the underlying Wannier functions. Our general theoretical approach, which fully clarifies the central role of the Chern number in solitonic pumps, provides a framework for describing the topological transport of nonlinear excitations in a broad class of physical systems. Exploiting this interdisciplinarity, we introduce an interaction-induced topological pump for ultracold atomic mixtures, where solitons of impurity atoms experience a quantized drift resulting from genuine interaction processes with their environment. Synthetic lattice systems are powerful platforms for studying the influence of intrinsic nonlinearities on topological phenomena. Here the authors elucidate the topological transport of solitons in terms of Wannier functions displacement and they introduce a nonlinearity-induced topological transport effect that could be observed in ultracold quantum mixtures.
Collapse
Affiliation(s)
- Nader Mostaan
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333, München, Germany. .,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany. .,CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050, Brussels, Belgium.
| | - Fabian Grusdt
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, D-80333, München, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050, Brussels, Belgium.
| |
Collapse
|
34
|
Photonic topological insulator induced by a dislocation in three dimensions. Nature 2022; 609:931-935. [PMID: 36171384 DOI: 10.1038/s41586-022-05129-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 07/20/2022] [Indexed: 02/01/2023]
Abstract
The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2-4 and are emerging as a promising tool for robust lasers5, quantum devices6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and acoustic waves10-13, where the topological protection in the latter is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14-17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.
Collapse
|
35
|
Zheng S, Man X, Kong ZL, Lin ZK, Duan G, Chen N, Yu D, Jiang JH, Xia B. Observation of fractal higher-order topological states in acoustic metamaterials. Sci Bull (Beijing) 2022; 67:2069-2075. [DOI: 10.1016/j.scib.2022.09.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Revised: 08/20/2022] [Accepted: 09/16/2022] [Indexed: 10/14/2022]
|
36
|
Sheng C, Wang Y, Chang Y, Wang H, Lu Y, Yang Y, Zhu S, Jin X, Liu H. Bound vortex light in an emulated topological defect in photonic lattices. LIGHT, SCIENCE & APPLICATIONS 2022; 11:243. [PMID: 35915073 PMCID: PMC9343378 DOI: 10.1038/s41377-022-00931-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 07/10/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.
Collapse
Affiliation(s)
- Chong Sheng
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yijun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Huiming Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yongheng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yingyue Yang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Shining Zhu
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Xianmin Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China.
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Hui Liu
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China.
| |
Collapse
|
37
|
Wu X, Wang L, Li G, Cheng D, Yu D, Zheng Y, Yakovlev VV, Yuan L, Chen X. Technologically feasible quasi-edge states and topological Bloch oscillation in the synthetic space. OPTICS EXPRESS 2022; 30:24924-24935. [PMID: 36237035 PMCID: PMC9363031 DOI: 10.1364/oe.462156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 06/15/2022] [Accepted: 06/15/2022] [Indexed: 06/03/2023]
Abstract
The dimensionality of a physical system is one of the major parameters defining its physical properties. The recently introduced concept of synthetic dimension has made it possible to arbitrarily manipulate the system of interest and harness light propagation in different ways. It also facilitates the transformative architecture of system-on-a-chip devices enabling far reaching applications such as optical isolation. In this report, a novel architecture based on dynamically-modulated waveguide arrays with the Su-Schrieffer-Heeger configuration in the spatial dimension is proposed and investigated with an eye on a practical implementation. The propagation of light through the one-dimensional waveguide arrays mimics time evolution of the field in a synthetic two-dimensional lattice. The addition of the effective gauge potential leads to an exotic topologically protected one-way transmission along adjacent boundary. A cosine-shape isolated band, which supports the topological Bloch oscillation in the frequency dimension under the effective constant force, appears and is localized at the spatial boundary being robust against small perturbations. This work paves the way to improved light transmission capabilities under topological protections in both spatial and spectral regimes and provides a novel platform based on a technologically feasible lithium niobate platform for optical computing and communication.
Collapse
Affiliation(s)
- Xiaoxiong Wu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Luojia Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Guangzhen Li
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Dali Cheng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yuanlin Zheng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | | | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Jinan Institute of Quantum Technology, Jinan 250101, China
- Collaborative Innovation Center of Light Manipulation and Applications, Shandong Normal University, Jinan 250358, China
| |
Collapse
|
38
|
You O, Liang S, Xie B, Gao W, Ye W, Zhu J, Zhang S. Observation of Non-Abelian Thouless Pump. PHYSICAL REVIEW LETTERS 2022; 128:244302. [PMID: 35776444 DOI: 10.1103/physrevlett.128.244302] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Revised: 01/17/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
Thouless pump provides robust ways to realize quantized transport of waves and particles, and it casts the static 2D quantum Hall effect onto 1D dynamic systems where one of the momentum dimensions is replaced by the evolution time or path parameter. In the past few decades, various types of Abelian Thouless pump have been achieved theoretically and experimentally. However, the study of non-Abelian Thouless pump is scarce, which tells us that the order of two evolution loops with the same base point cannot be changed, and there has been no experimental observation of non-Abelian Thouless pump. Here we report the observation of a non-Abelian Thouless pump in coupled acoustic waveguide array. The non-Abelian property originates from the noncommutative combination of two different ℤ_{3} pump cycles that traverse across multiple band degeneracies in the parameter space in a three-band system. Moreover, we can pump a specific initial state to any state on any lattice site by applying these two ℤ_{3} pump cycles multiple times in a well-designed sequence. Our study paves the way for exploring and utilizing non-Abelian dynamical effects in classical wave systems and may offer different recipes for quantum walking, quantum optics, and quantum computation.
Collapse
Affiliation(s)
- Oubo You
- Department of Physics, University of Hong Kong, Hong Kong, China
| | - Shanjun Liang
- Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, Hong Kong Polytechnic University, Hong Kong, China
| | - Biye Xie
- Department of Physics, University of Hong Kong, Hong Kong, China
| | - Wenlong Gao
- Department of Physics, Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
| | - Weimin Ye
- College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, 410073, China
| | - Jie Zhu
- Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong, China
| | - Shuang Zhang
- Department of Physics, University of Hong Kong, Hong Kong, China
- Department of Electronic and Electrical Engineering, University of Hong Kong, Hong Kong, China
| |
Collapse
|
39
|
Khanikaev AB. More nodes bring more Floquet modes. NATURE MATERIALS 2022; 21:618-619. [PMID: 35641562 DOI: 10.1038/s41563-022-01268-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Affiliation(s)
- Alexander B Khanikaev
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY, USA.
| |
Collapse
|
40
|
Fan X, Xia T, Qiu H, Zhang Q, Qiu C. Tracking Valley Topology with Synthetic Weyl Paths. PHYSICAL REVIEW LETTERS 2022; 128:216403. [PMID: 35687437 DOI: 10.1103/physrevlett.128.216403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.
Collapse
Affiliation(s)
- Xiying Fan
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Tianzhi Xia
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Huahui Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qicheng Zhang
- 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
| |
Collapse
|
41
|
Observation of novel topological states in hyperbolic lattices. Nat Commun 2022; 13:2937. [PMID: 35618723 PMCID: PMC9135738 DOI: 10.1038/s41467-022-30631-x] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 05/08/2022] [Indexed: 11/30/2022] Open
Abstract
The discovery of novel topological states has served as a major branch in physics and material sciences. To date, most of the established topological states have been employed in Euclidean systems. Recently, the experimental realization of the hyperbolic lattice, which is the regular tessellation in non-Euclidean space with a constant negative curvature, has attracted much attention. Here, we demonstrate both in theory and experiment that exotic topological states can exist in engineered hyperbolic lattices with unique properties compared to their Euclidean counterparts. Based on the extended Haldane model, the boundary-dominated first-order Chern edge state with a nontrivial real-space Chern number is achieved. Furthermore, we show that the fractal-like midgap higher-order zero modes appear in deformed hyperbolic lattices, and the number of zero modes increases exponentially with the lattice size. These novel topological states are observed in designed hyperbolic circuit networks by measuring site-resolved impedance responses and dynamics of voltage packets. Our findings suggest a useful platform to study topological phases beyond Euclidean space, and may have potential applications in the field of high-efficient topological devices, such as topological lasers, with enhanced edge responses. Recent evidence of hyperbolic lattice calls for whether topological states can exist in such non-Euclidean system. Here, the authors evidence firstorder Chern edge states with a nontrivial real-space Chern number and fractal-like midgap higher-order zero modes in hyperbolic circuit networks.
Collapse
|
42
|
Fu Q, Wang P, Kartashov YV, Konotop VV, Ye F. Nonlinear Thouless Pumping: Solitons and Transport Breakdown. PHYSICAL REVIEW LETTERS 2022; 128:154101. [PMID: 35499898 DOI: 10.1103/physrevlett.128.154101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.
Collapse
Affiliation(s)
- Qidong Fu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| |
Collapse
|
43
|
Jürgensen M, Rechtsman MC. Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps. PHYSICAL REVIEW LETTERS 2022; 128:113901. [PMID: 35363022 DOI: 10.1103/physrevlett.128.113901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that, for low-power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that a soliton's position is dictated by that of the Wannier state throughout the pump cycle. Furthermore, we describe soliton pumping in two dimensions.
Collapse
Affiliation(s)
- Marius Jürgensen
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| |
Collapse
|
44
|
Abstract
Topological mechanics is rapidly emerging as an attractive field of research where mechanical waveguides can be designed and controlled via topological methods. With the development of topological phases of matter, recent advances have shown that topological states have been realized in the elastic media exploiting analogue quantum Hall effect, analogue quantum spin Hall effect, analogue quantum valley Hall effect, higher-order topological physics, topological pump, topological lattice defects and so on. This review aims to introduce the experimental and theoretical achievements with defect-immune protected elastic waves in mechanical systems based on the abovementioned methods, respectively. From these discussions, we predict the possible perspective of topological mechanics.
Collapse
|
45
|
Lee KY, Yoo KW, Cheon S, Joo WJ, Yoon JW, Song SH. Synthetic Topological Nodal Phase in Bilayer Resonant Gratings. PHYSICAL REVIEW LETTERS 2022; 128:053002. [PMID: 35179923 DOI: 10.1103/physrevlett.128.053002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 01/03/2022] [Indexed: 06/14/2023]
Abstract
The notion of synthetic dimensions in artificial photonic systems has received considerable attention as it provides novel methods for exploring hypothetical topological phenomena as well as potential device applications. Here, we present nanophotonic manifestation of a two-dimensional topological nodal phase in bilayer resonant grating structures. Using the mathematical analogy between a topological semimetal and vertically asymmetric photonic lattices, we show that the interlayer shift simulates an extra momentum dimension for creating a two-dimensional topological nodal phase. We present a theoretical model and rigorous numerical analyses showing the two nodal points that produce a complex gapless band structure and localized edge states in the topologically nontrivial region. Therefore, our results provide a practical scheme for producing high-dimensional topological effects in simple low-dimensional photonic structures.
Collapse
Affiliation(s)
- Ki Young Lee
- Department of Physics, Hanyang University, Seoul 133-791, Korea
| | - Kwang Wook Yoo
- Department of Physics, Hanyang University, Seoul 133-791, Korea
| | - Sangmo Cheon
- Department of Physics, Hanyang University, Seoul 133-791, Korea
| | - Won-Jae Joo
- Samsung Advanced Institute of Technology, Samsung Electronics, Suwon 16678, Korea
| | - Jae Woong Yoon
- Department of Physics, Hanyang University, Seoul 133-791, Korea
| | - Seok Ho Song
- Department of Physics, Hanyang University, Seoul 133-791, Korea
| |
Collapse
|
46
|
Abstract
Topological photonics was initially inspired by the quantum-optical analogy between the Schrödinger equation for an electron wavefunction and the paraxial equation for a light beam. Here, we reveal an unexpected phenomenon in topological pumping observed in arrays of nonparaxial optical waveguides where the quantum-optical analogy becomes invalid. We predict theoretically and demonstrate experimentally an asymmetric topological pumping when the injected field transfers from one side of the waveguide array to the other side whereas the reverse process is unexpectedly forbidden. Our finding could open an avenue for exploring topological photonics that enables nontrivial topological phenomena and designs in photonics driven by nonparaxiality. The understanding of the topological properties of light is at the base of the future optical devices development. In this work the authors aim to suggesting a different paradigm for topological transport and manipulation of nonparaxial light, paving the way toward the new developments in the field of topological photonics
Collapse
|
47
|
Wang W, Chen ZG, Ma G. Synthetic Three-Dimensional Z×Z_{2} Topological Insulator in an Elastic Metacrystal. PHYSICAL REVIEW LETTERS 2021; 127:214302. [PMID: 34860114 DOI: 10.1103/physrevlett.127.214302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Revised: 07/21/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
We report a three-dimensional (3D) topological insulator (TI) formed by stacking identical layers of Chern insulators in a hybrid real-synthetic space. By introducing staggered interlayer hopping that respects mirror symmetry, the bulk bands possess an additional Z_{2} topological invariant along the stacking dimension, which, together with the nontrivial Chern numbers, endows the system with a Z×Z_{2} topology. A 4-tuple topological index characterizes the system's bulk bands. Consequently, two distinct types of topological surface modes (TSMs) are found localized on different surfaces. Type-I TSMs are gapless and are protected by Chern numbers, whereas type-II gapped TSMs are protected by Z_{2} bulk polarization in the stacking direction. Remarkably, each type-II TSM band is also topologically nontrivial, giving rise to second-order topological hinge modes (THMs). Both types of TSMs and the THMs are experimentally observed in an elastic metacrystal.
Collapse
Affiliation(s)
- Wei Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Ze-Guo Chen
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| |
Collapse
|
48
|
Guo J, Sun J, Zhu X, Li CA, Guo H, Feng S. Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:035603. [PMID: 34663768 DOI: 10.1088/1361-648x/ac30b4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 10/18/2021] [Indexed: 06/13/2023]
Abstract
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
Collapse
Affiliation(s)
- Jiaojiao Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Junsong Sun
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Xingchuan Zhu
- Center for Basic Teaching and Experiment, Nanjing University of Science and Technology, Jiangyin 214443, People's Republic of China
| | - Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
| | - Huaiming Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing, 100875, People's Republic of China
| |
Collapse
|
49
|
Jiao ZQ, Longhi S, Wang XW, Gao J, Zhou WH, Wang Y, Fu YX, Wang L, Ren RJ, Qiao LF, Jin XM. Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices. PHYSICAL REVIEW LETTERS 2021; 127:147401. [PMID: 34652196 DOI: 10.1103/physrevlett.127.147401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 08/27/2021] [Indexed: 06/13/2023]
Abstract
Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.
Collapse
Affiliation(s)
- Zhi-Qiang Jiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
| | - Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jun Gao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yu-Xuan Fu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Li Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruo-Jing Ren
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu-Feng Qiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- TuringQ Co., Ltd., Shanghai 200240, China
| |
Collapse
|
50
|
Xian L, Fischer A, Claassen M, Zhang J, Rubio A, Kennes DM. Engineering Three-Dimensional Moiré Flat Bands. NANO LETTERS 2021; 21:7519-7526. [PMID: 34516114 PMCID: PMC8461648 DOI: 10.1021/acs.nanolett.1c01684] [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: 04/28/2021] [Revised: 08/25/2021] [Indexed: 06/13/2023]
Abstract
Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena. Here, we generalize this concept of so-called moiré flat bands to engineer flat bands in all three spatial dimensions controlled by the twist angle. The basic concept is to stack the material such that the large spatial moiré interference patterns are spatially shifted from one twisted layer to the next. We exemplify the general concept by considering graphitic systems, boron nitride, and WSe2, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride, we develop an ab initio fitted tight binding model that captures the corresponding three-dimensional low-energy electronic structure. We outline that interesting three-dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.
Collapse
Affiliation(s)
- Lede Xian
- Songshan
Lake Materials Laboratory, 523808 Dongguan, Guangdong China
- Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Ammon Fischer
- Institut
für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information
Technology, 52056 Aachen, Germany
| | - Martin Claassen
- Department
of Physics and Astronomy, University of
Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Jin Zhang
- Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
| | - Angel Rubio
- Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Simons
Foundation Flatiron Institute, New York, New York 10010 United States
- Nano-Bio
Spectroscopy Group, Departamento de Fisica de Materiales, Universidad del País Vasco, UPV/EHU- 20018 San Sebastián, Spain
| | - Dante M. Kennes
- Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
- Institut
für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information
Technology, 52056 Aachen, Germany
| |
Collapse
|