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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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Xu J, Carney TE, Zhou R, Shepard C, Kanai Y. Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics. J Am Chem Soc 2024; 146:5011-5029. [PMID: 38362887 DOI: 10.1021/jacs.3c08226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.
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Affiliation(s)
- Jianhang Xu
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Thomas E Carney
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Ruiyi Zhou
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Christopher Shepard
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
- Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
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3
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Ren M, Yu Y, Wu B, Qi X, Wang Y, Yao X, Ren J, Guo Z, Jiang H, Chen H, Liu XJ, Chen Z, Sun Y. Realization of Gapped and Ungapped Photonic Topological Anderson Insulators. PHYSICAL REVIEW LETTERS 2024; 132:066602. [PMID: 38394559 DOI: 10.1103/physrevlett.132.066602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 01/03/2024] [Indexed: 02/25/2024]
Abstract
It is commonly believed that topologically nontrivial one-dimensional systems support edge states rather than bulk states at zero energy. In this work, we find an unanticipated case of topological Anderson insulator (TAI) phase where two bulk modes are degenerate at zero energy, in addition to degenerate edge modes. We term this "ungapped TAI" to distinguish it from the previously known gapped TAIs. Our experimental realization of both gapped and ungapped TAIs relies on coupled photonic resonators, in which the disorder in coupling is judiciously engineered by adjusting the spacing between the resonators. By measuring the local density of states both in the bulk and at the edges, we demonstrate the existence of these two types of TAIs, together forming a TAI plateau in the phase diagram. Our experimental findings are well supported by theoretical analysis. In the ungapped TAI phase, we observe stable coexistence of topological edge states and localized bulk states at zero energy, highlighting the distinction between TAIs and traditional topological insulators.
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Affiliation(s)
- Mina Ren
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Ye Yu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Bintao Wu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xin Qi
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Yiwei Wang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiaogang Yao
- Information Materials and Devices Research Center, Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 201800, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Zhiwei Guo
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Haitao Jiang
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- International Quantum Academy, Shenzhen 518048, China
| | - Zhigang Chen
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Yong Sun
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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4
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Zhou R, Kanai Y. Molecular Control of Floquet Topological Phase in Non-adiabatic Thouless Pumping. J Phys Chem Lett 2023; 14:8205-8212. [PMID: 37672485 DOI: 10.1021/acs.jpclett.3c01746] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/08/2023]
Abstract
Non-adiabatic Thouless pumping of electrons is studied in the framework of topological Floquet engineering, particularly with a focus on how atomistic changes to chemical moieties control the emergence of the Floquet topological phase. We employ real-time time-dependent density functional theory to investigate the extent to which the topological invariant, the winding number, is impacted by molecular-level changes to trans-polyacetylene. In particular, several substitutions to trans-polyacetylene are studied to examine different effects on the electronic structure, including the mesomeric effect, inductive effect, and electron conjugation effect. Maximally localized Wannier functions are employed to relate the winding number to the valence bond description by expressing the topological pumping as the transport dynamics of the localized Wannier functions. By further exploiting the gauge invariance of the quantum dynamics in terms of the minimal particle-hole excitations, the topological pumping of electrons can be also represented as a cyclic transition among the bonding and antibonding orbitals. Having connected the topological invariant to the chemical concepts, we demonstrate molecular-level control of the emergence of the Floquet topological phase, presenting an exciting opportunity for the intuitive engineering of molecular systems with such an exotic topological phase.
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Affiliation(s)
- Ruiyi Zhou
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, United States
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, United States
- Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, United States
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Wang LC, Chen Y, Tian ZN, Wang YD, Ren XF, Chen QD. Observation of delocalization transition in topological waveguide arrays with long-range interactions. OPTICS LETTERS 2023; 48:3283-3286. [PMID: 37319082 DOI: 10.1364/ol.493113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 05/24/2023] [Indexed: 06/17/2023]
Abstract
Topological edge states are a generic feature of topological insulators, and the long-range interactions, which break certain properties of topological edge states, are always non-negligible in real physical systems. In this Letter, we investigate the influence of next-nearest-neighbor (NNN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) model by extracting the survival probabilities at the boundary of the photonic lattices. By introducing a series of integrated photonic waveguide arrays with different strengths of long-range interactions, we experimentally observe delocalization transition of light in SSH lattices with nontrivial phase, which is in good agreement with our theoretical predictions. The results indicate that the NNN interactions can significantly affect the edge states, and that the localization of these states can be absent in topologically nontrivial phase. Our work provides an alternative way to investigate the interplay between long-range interactions and localized states, which may stimulate further interest in topological properties in relevant structures.
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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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7
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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.
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8
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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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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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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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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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12
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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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13
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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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14
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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
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15
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Yu F, Tian ZN, Piacentini S, Li XY, Chen QD, Osellame R, Sun HB. Resetting directional couplers for high-fidelity quantum photonic integrated chips. OPTICS LETTERS 2021; 46:5181-5184. [PMID: 34653146 DOI: 10.1364/ol.439178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
In this Letter, we propose a fabrication technique based on femtosecond laser secondary direct writing (FsLSDW) that allows us to statically reset the beam-splitting ratio of directional couplers. By modifying the interaction region with a second inscription, the coupling coefficient of the reconstructed devices can be indeed changed continuously within the range of 0.49-2.1 rad/mm, thus enabling a complete tunability of the reconstructed splitting ratio from zero to full power transfer between the waveguides. This powerful reconstruction capability facilitates the arbitrary reset of an imperfect device, from any initial splitting ratio to the correct one. In the future, such static control method could potentially solve the fabrication error problem in the manufacturing of high-fidelity large-scale integrated photonic quantum chips.
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16
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Jürgensen M, Mukherjee S, Rechtsman MC. Quantized nonlinear Thouless pumping. Nature 2021; 596:63-67. [PMID: 34349291 DOI: 10.1038/s41586-021-03688-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 06/01/2021] [Indexed: 02/06/2023]
Abstract
The topological protection of wave transport, originally observed in the context of the quantum Hall effect in two-dimensional electron gases1, has been shown to apply broadly to a range of physical platforms, including photonics2-5, ultracold atoms in optical lattices6-8 and others9-12. That said, the behaviour of such systems can be very different from the electronic case, particularly when interparticle interactions or nonlinearity play a major role13-22. A Thouless pump23 is a one-dimensional model that captures the topological quantization of transport in the quantum Hall effect using the notion of dimensional reduction: an adiabatically, time-varying potential mathematically maps onto a momentum coordinate in a conceptual second dimension24-34. Importantly, quantization assumes uniformly filled electron bands below a Fermi energy, or an equivalent occupation for non-equilibrium bosonic systems. Here we theoretically propose and experimentally demonstrate quantized nonlinear Thouless pumping of photons with a band that is decidedly not uniformly occupied. In our system, nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry-breaking bifurcations. Quantization follows from the fact that the instantaneous soliton solutions centred upon a given unit cell are identical after each pump cycle, up to translation invariance; this is an entirely different mechanism from traditional Thouless pumping. This result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behaviour without a linear counterpart.
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Affiliation(s)
- Marius Jürgensen
- Department of Physics, The Pennsylvania State University, University Park, PA, USA.
| | - Sebabrata Mukherjee
- Department of Physics, The Pennsylvania State University, University Park, PA, USA
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, PA, USA.
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17
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Zhou R, Yost DC, Kanai Y. First-Principles Demonstration of Nonadiabatic Thouless Pumping of Electrons in a Molecular System. J Phys Chem Lett 2021; 12:4496-4503. [PMID: 33956458 DOI: 10.1021/acs.jpclett.1c01037] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We demonstrate nonadiabatic Thouless pumping of electrons in trans-polyacetylene in the framework of Floquet engineering using first-principles theory. We identify the regimes in which the quantized pump is operative with respect to the driving electric field for a time-dependent Hamiltonian. By employing the time-dependent maximally localized Wannier functions in real-time time-dependent density functional theory simulation, we connect the winding number, a topological invariant, to a molecular-level understanding of the quantized pumping. While the pumping dynamics constitutes the opposing movement of the Wannier functions that represent both double and single bonds, the resulting current is unidirectional due to the greater number of double-bond electrons. Using a gauge-invariant formulation called dynamical transition orbitals, an alternative viewpoint on the nonequilibrium dynamics is obtained in terms of the particle-hole excitation. A single time-dependent transition orbital is found to be largely responsible for the observed quantized pumping. In this representation, the pumping dynamics manifests itself in the dynamics of this single orbital as it undergoes changes from its π bonding orbital character at equilibrium to acquiring resonance and antibonding character in the driving cycle. The work demonstrates the Floquet engineering of the nonadiabatic topological state in an extended molecular system, paving the way for experimental realization of the new quantum material phase.
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Affiliation(s)
- Ruiyi Zhou
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Dillon C Yost
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
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18
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Chen Z, Buljan H, Leykam D. Special Issue on "Topological photonics and beyond: novel concepts and recent advances". LIGHT, SCIENCE & APPLICATIONS 2020; 9:203. [PMID: 33353948 PMCID: PMC7755899 DOI: 10.1038/s41377-020-00437-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Accepted: 11/17/2020] [Indexed: 06/12/2023]
Affiliation(s)
- Zhigang Chen
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China.
- Department of Physics and Astronomy, San Francisco State University, San Francisco, CA, 94132, USA.
| | - Hrvoje Buljan
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China
- Department of Physics, Faculty of Science, University of Zagreb, Bijenicka cesta 32, 10000, Zagreb, Croatia
| | - Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, 117543, Singapore
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