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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.
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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
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2
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Ehrhardt M, Dittel C, Heinrich M, Szameit A. Topological Hong-Ou-Mandel interference. Science 2024; 384:1340-1344. [PMID: 38900876 DOI: 10.1126/science.ado8192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2024] [Accepted: 05/03/2024] [Indexed: 06/22/2024]
Abstract
The interplay of topology and optics provides a route to pursue robust photonic devices, with the application to photonic quantum computation in its infancy. However, the possibilities of harnessing topological structures to process quantum information with linear optics, through the quantum interference of photons, remain largely uncharted. Here, we present a Hong-Ou-Mandel interference effect of topological origin. We show that this interference of photon pairs-ranging from constructive to destructive-is solely determined by a synthetic magnetic flux, rendering it resilient to errors on a fundamental level. Our implementation establishes a quantized flux that facilitates exclusively destructive quantum interference. Our findings pave the way toward the development of next-generation photonic quantum circuitry and scalable quantum computing protected by virtue of topologically robust quantum gates.
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Affiliation(s)
- Max Ehrhardt
- University of Rostock, Institute of Physics, Albert-Einstein-Str. 23, 18059 Rostock, Germany
| | - Christoph Dittel
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - Matthias Heinrich
- University of Rostock, Institute of Physics, Albert-Einstein-Str. 23, 18059 Rostock, Germany
| | - Alexander Szameit
- University of Rostock, Institute of Physics, Albert-Einstein-Str. 23, 18059 Rostock, Germany
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3
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Flower CJ, Jalali Mehrabad M, Xu L, Moille G, Suarez-Forero DG, Örsel O, Bahl G, Chembo Y, Srinivasan K, Mittal S, Hafezi M. Observation of topological frequency combs. Science 2024; 384:1356-1361. [PMID: 38900874 DOI: 10.1126/science.ado0053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Accepted: 05/09/2024] [Indexed: 06/22/2024]
Abstract
On-chip generation of optical frequency combs using nonlinear ring resonators has enabled numerous applications of combs that were otherwise limited to mode-locked lasers. Nevertheless, on-chip frequency combs have relied predominantly on single-ring resonators. In this study, we experimentally demonstrate the generation of a novel class of frequency combs, the topological frequency combs, in a two-dimensional lattice of hundreds of ring resonators that hosts fabrication-robust topological edge states with linear dispersion. By pumping these edge states, we demonstrate the generation of a nested frequency comb that shows oscillation of multiple edge state resonances across ≈40 longitudinal modes and is spatially confined at the lattice edge. Our results provide an opportunity to explore the interplay between topological physics and nonlinear frequency comb generation in a commercially available nanophotonic platform.
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Affiliation(s)
- Christopher J Flower
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Mahmoud Jalali Mehrabad
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Lida Xu
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Gregory Moille
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Daniel G Suarez-Forero
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Oğulcan Örsel
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Gaurav Bahl
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Yanne Chembo
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
| | - Kartik Srinivasan
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
| | - Sunil Mittal
- Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA
| | - Mohammad Hafezi
- Joint Quantum Institute, National Institute of Standards and Technology, University of Maryland, College Park, MD, USA
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4
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Coen S, Garbin B, Xu G, Quinn L, Goldman N, Oppo GL, Erkintalo M, Murdoch SG, Fatome J. Nonlinear topological symmetry protection in a dissipative system. Nat Commun 2024; 15:1398. [PMID: 38360729 PMCID: PMC10869785 DOI: 10.1038/s41467-023-44640-x] [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: 04/19/2023] [Accepted: 12/21/2023] [Indexed: 02/17/2024] Open
Abstract
We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters. Rigorous statistical tests confirm the robustness of the underlying symmetry protection, which manifests itself by a periodic alternation of the modes reminiscent of period-doubling. This dynamic also confers long term stability to various localized structures including domain walls, solitons, and breathers. Our findings are supported by an effective Hamiltonian model and have relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. They could also be beneficial to the implementation of coherent Ising machines.
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Affiliation(s)
- Stéphane Coen
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand.
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand.
| | - Bruno Garbin
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- NcodiN SAS, 10 Boulevard Thomas Gobert, F-91120, Palaiseau, France
| | - Gang Xu
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- School of Optical and Electronic Information, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, China
| | - Liam Quinn
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, B-1050, Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005, Paris, France
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow, G4 0NG, Scotland
| | - Miro Erkintalo
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Stuart G Murdoch
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - Julien Fatome
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 9 Avenue Alain Savary, BP 47870, F-21078, Dijon, France
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5
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Arkhipova AA, Zhang Y, Kartashov YV, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Zadkov VN. Observation of π solitons in oscillating waveguide arrays. Sci Bull (Beijing) 2023; 68:2017-2024. [PMID: 37573247 DOI: 10.1016/j.scib.2023.07.048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Revised: 06/23/2023] [Accepted: 07/18/2023] [Indexed: 08/14/2023]
Abstract
Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.
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Affiliation(s)
- Antonina A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Faculty of Physics, Higher School of Economics, Moscow 105066, Russia
| | - Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices (Ministry of Education), School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | | | - Sergei A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Nikolay N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Ivan V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Alexander A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Sergei P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Victor O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia
| | - Sergey V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia
| | - Victor N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Faculty of Physics, Higher School of Economics, Moscow 105066, Russia
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6
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Ren B, Arkhipova AA, Zhang Y, Kartashov YV, Wang H, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Zadkov VN. Observation of nonlinear disclination states. LIGHT, SCIENCE & APPLICATIONS 2023; 12:194. [PMID: 37558694 PMCID: PMC10412544 DOI: 10.1038/s41377-023-01235-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 07/10/2023] [Accepted: 07/14/2023] [Indexed: 08/11/2023]
Abstract
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.
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Affiliation(s)
- Boquan Ren
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Antonina A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
| | - Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
| | - Hongguang Wang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Sergei A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Nikolay N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Ivan V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Alexander A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Sergei P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Victor O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Sergey V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Victor N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
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7
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Parker R, Aceves A, Cuevas-Maraver J, Kevrekidis PG. Standing and traveling waves in a model of periodically modulated one-dimensional waveguide arrays. Phys Rev E 2023; 108:024214. [PMID: 37723691 DOI: 10.1103/physreve.108.024214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
In the present work we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high-power initial conditions yield stationary solutions. We explain these two behaviors, as well as the nature of the transition between the two regimes, by analyzing a simpler model where the couplings between waveguides are given by step functions. For the original model, we numerically construct both stationary and moving coherent structures, which are solutions reproducing themselves exactly after an integer multiple of the coupling period. For the stationary solutions, which are true periodic orbits, we use Floquet analysis to determine the parameter regime for which they are spectrally stable. Typically, the traveling solutions are characterized by having small-amplitude oscillatory tails, although we identify a set of parameters for which these tails disappear. These parameters turn out to be independent of the lattice size, and our simulations suggest that for these parameters, numerically exact traveling solutions are stable.
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Affiliation(s)
- Ross Parker
- Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
| | - Alejandro Aceves
- Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA
| | - Jesús Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/ Virgen de Africa 7, 41011 Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla, Edificio Celestino Mutis, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
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8
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Walter AS, Zhu Z, Gächter M, Minguzzi J, Roschinski S, Sandholzer K, Viebahn K, Esslinger T. Quantization and its breakdown in a Hubbard-Thouless pump. NATURE PHYSICS 2023; 19:1471-1475. [PMID: 37841998 PMCID: PMC10567560 DOI: 10.1038/s41567-023-02145-w] [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: 03/03/2023] [Accepted: 06/23/2023] [Indexed: 10/17/2023]
Abstract
Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems1. For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue-the Thouless pump2-4. However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms5-9, the study of topological matter under variations in interparticle interactions has proven challenging10. Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump's robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter10, including edge effects11 and interaction-induced topological phases12-15.
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Affiliation(s)
- Anne-Sophie Walter
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Zijie Zhu
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Marius Gächter
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Joaquín Minguzzi
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Stephan Roschinski
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Kilian Sandholzer
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Konrad Viebahn
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics & Quantum Center, ETH Zurich, Zurich, Switzerland
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9
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Tian Y, Wang Y, Belić MR, Zhang Y, Li Y, Ye F. Vector valley Hall edge solitons in distorted type-II Dirac photonic lattices. OPTICS EXPRESS 2023; 31:20812-20824. [PMID: 37381196 DOI: 10.1364/oe.491719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 05/25/2023] [Indexed: 06/30/2023]
Abstract
Topological edge states have recently garnered a lot of attention across various fields of physics. The topological edge soliton is a hybrid edge state that is both topologically protected and immune to defects or disorders, and a localized bound state that is diffraction-free, owing to the self-balance of diffraction by nonlinearity. Topological edge solitons hold great potential for on-chip optical functional device fabrication. In this report, we present the discovery of vector valley Hall edge (VHE) solitons in type-II Dirac photonic lattices, formed by breaking lattice inversion symmetry with distortion operations. The distorted lattice features a two-layer domain wall that supports both in-phase and out-of-phase VHE states, appearing in two different band gaps. Superposing soliton envelopes onto VHE states generates bright-bright and bright-dipole vector VHE solitons. The propagation dynamics of such vector solitons reveal a periodic change in their profiles, accompanied by the energy periodically transferring between the layers of the domain wall. The reported vector VHE solitons are found to be metastable.
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10
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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11
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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.
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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
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12
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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.
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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
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13
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Wang LC, Chen Y, Gong M, Yu F, Chen QD, Tian ZN, Ren XF, Sun HB. Edge State, Localization Length, and Critical Exponent from Survival Probability in Topological Waveguides. PHYSICAL REVIEW LETTERS 2022; 129:173601. [PMID: 36332264 DOI: 10.1103/physrevlett.129.173601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Revised: 08/05/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P=(1-e^{-2/ξ_{loc}})^{2}, where ξ_{loc} is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of ν=0.94±0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.
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Affiliation(s)
- Li-Cheng Wang
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Yang Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Ming Gong
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Feng Yu
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Qi-Dai Chen
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Zhen-Nan Tian
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
| | - Xi-Feng Ren
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Hong-Bo Sun
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Haidian, Beijing 100084, China
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14
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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.
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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.
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15
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Frank A, Leykam D, Smirnova DA, Angelakis DG, Ling A. Boosting topological zero modes using elastomer waveguide arrays. OPTICS LETTERS 2022; 47:4620-4623. [PMID: 36107047 DOI: 10.1364/ol.469657] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 08/12/2022] [Indexed: 06/15/2023]
Abstract
We employ the Su-Schrieffer-Heeger model in elastic polymer waveguide arrays to design and realize traveling topologically protected modes. The observed delocalization of the optical field for superluminal defect velocities agrees well with theoretical descriptions. We apply mechanical strain to modulate the lattices' coupling coefficient. This work demonstrates a novel, to the best of our knowledge, platform for rapid prototyping of topological photonic devices and establishes strain-tuning as a viable design parameter for topological waveguide arrays.
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16
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Minguzzi J, Zhu Z, Sandholzer K, Walter AS, Viebahn K, Esslinger T. Topological Pumping in a Floquet-Bloch Band. PHYSICAL REVIEW LETTERS 2022; 129:053201. [PMID: 35960575 DOI: 10.1103/physrevlett.129.053201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
Constructing new topological materials is of vital interest for the development of robust quantum applications. However, engineering such materials often causes technological overhead, such as large magnetic fields, spin-orbit coupling, or dynamical superlattice potentials. Simplifying the experimental requirements has been addressed on a conceptual level-by proposing to combine simple lattice structures with Floquet engineering-but there has been no experimental implementation. Here, we demonstrate topological pumping in a Floquet-Bloch band using a plain sinusoidal lattice potential and two-tone driving with frequencies ω and 2ω. We adiabatically prepare a near-insulating Floquet band of ultracold fermions via a frequency chirp, which avoids gap closings en route from trivial to topological bands. Subsequently, we induce topological pumping by slowly cycling the amplitude and the phase of the 2ω drive. Our system is well described by an effective Shockley model, establishing a novel paradigm to engineer topological matter from simple underlying lattice geometries. This approach could enable the application of quantized pumping in metrology, following recent experimental advances on two-frequency driving in real materials.
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Affiliation(s)
- Joaquín Minguzzi
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Zijie Zhu
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Kilian Sandholzer
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | | | - Konrad Viebahn
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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17
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Jung PS, Pyrialakos GG, Wu FO, Parto M, Khajavikhan M, Krolikowski W, Christodoulides DN. Thermal control of the topological edge flow in nonlinear photonic lattices. Nat Commun 2022; 13:4393. [PMID: 35906224 PMCID: PMC9338248 DOI: 10.1038/s41467-022-32069-7] [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: 03/25/2022] [Accepted: 07/18/2022] [Indexed: 11/29/2022] Open
Abstract
The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics. The nonlinear evolution dynamics in topological photonic lattices is systematically investigated within the framework of optical thermodynamics. This approach allows for the precise prediction of topological currents even under the extreme complexity introduced by nonlinearity.
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Affiliation(s)
- Pawel S Jung
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
| | - Georgios G Pyrialakos
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Fan O Wu
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Midya Parto
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Mercedeh Khajavikhan
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
| | - Wieslaw Krolikowski
- Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT, 0200, Australia.,Science Program, Texas A&M University at Qatar, Doha, Qatar
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18
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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: 11] [Impact Index Per Article: 5.5] [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.
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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
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19
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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.
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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
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20
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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.
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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
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