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Pang Z, Wong BTT, Hu J, Yang Y. Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2024; 132:043804. [PMID: 38335358 DOI: 10.1103/physrevlett.132.043804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Accepted: 11/27/2023] [Indexed: 02/12/2024]
Abstract
Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for vector potentials, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences. With SU(2) gauge fields, the braiding degrees that can be achieved are twice the highest hopping order of a lattice model, indicating the utility of spinful freedom to attain high-order nontrivial braiding. At both ends of an open chain, non-Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population can be effectively tuned near the exceptional points. Generalizing to two dimensions, the gauge invariance of Wilson loops can also break down in non-Hermitian lattices dressed with non-Abelian gauge fields. Toward realization, we present a concrete experimental proposal for non-Abelian gauge fields in non-Hermitian systems via the synthetic frequency dimension of a polarization-multiplexed fiber ring resonator.
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Affiliation(s)
- Zehai Pang
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Bengy Tsz Tsun Wong
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Jinbing Hu
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
- College of Optical-Electrical Information and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Yi Yang
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
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2
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Suh J, Kim G, Park H, Fan S, Park N, Yu S. Photonic Topological Spin Pump in Synthetic Frequency Dimensions. PHYSICAL REVIEW LETTERS 2024; 132:033803. [PMID: 38307059 DOI: 10.1103/physrevlett.132.033803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 12/15/2023] [Indexed: 02/04/2024]
Abstract
Reducing geometrical complexity while preserving desired wave properties is critical for proof-of-concept studies in wave physics, as evidenced by recent efforts to realize photonic synthetic dimensions, isospectrality, and hyperbolic lattices. Laughlin's topological pump, which elucidates quantum Hall states in cylindrical geometry with a radial magnetic field and a time-varying axial magnetic flux, is a prime example of these efforts. Here we propose a two-dimensional dynamical photonic system for the topological pumping of pseudospin modes by exploiting synthetic frequency dimensions. The system provides the independent control of pseudomagnetic fields and electromotive forces achieved by the interplay between mode-dependent and mode-independent gauge fields. To address the axial open boundaries and azimuthal periodicity of the system, we define the adjusted local Chern marker with rotating azimuthal coordinates, proving the nontrivial topology of the system. We demonstrate the adiabatic pumping for crosstalk-free frequency conversion with wave front molding. Our approach allows for reproducing Laughlin's thought experiment at room temperature with a scalable setup.
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Affiliation(s)
- Joseph Suh
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Gyunghun Kim
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Hyungchul Park
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Shanhui Fan
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
| | - Namkyoo Park
- Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
| | - Sunkyu Yu
- Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea
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3
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Fan L, Wang K, Wang H, Dutt A, Fan S. Experimental realization of convolution processing in photonic synthetic frequency dimensions. SCIENCE ADVANCES 2023; 9:eadi4956. [PMID: 37566663 PMCID: PMC10421045 DOI: 10.1126/sciadv.adi4956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 07/12/2023] [Indexed: 08/13/2023]
Abstract
Convolution is an essential operation in signal and image processing and consumes most of the computing power in convolutional neural networks. Photonic convolution has the promise of addressing computational bottlenecks and outperforming electronic implementations. Performing photonic convolution in the synthetic frequency dimension, which harnesses the dynamics of light in the spectral degrees of freedom for photons, can lead to highly compact devices. Here, we experimentally realize convolution operations in the synthetic frequency dimension. Using a modulated ring resonator, we synthesize arbitrary convolution kernels using a predetermined modulation waveform with high accuracy. We demonstrate the convolution computation between input frequency combs and synthesized kernels. We also introduce the idea of an additive offset to broaden the kinds of kernels that can be implemented experimentally when the modulation strength is limited. Our work demonstrate the use of synthetic frequency dimension to efficiently encode data and implement computation tasks, leading to a compact and scalable photonic computation architecture.
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Affiliation(s)
- Lingling Fan
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Kai Wang
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- Department of Physics, McGill University, 3600 Rue University, Montreal, Quebec H3A 2T8, Canada
| | - Heming Wang
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Avik Dutt
- Department of Mechanical Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | - Shanhui Fan
- Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
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4
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Cheng D, Lustig E, Wang K, Fan S. Multi-dimensional band structure spectroscopy in the synthetic frequency dimension. LIGHT, SCIENCE & APPLICATIONS 2023; 12:158. [PMID: 37369684 DOI: 10.1038/s41377-023-01196-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 05/23/2023] [Accepted: 05/26/2023] [Indexed: 06/29/2023]
Abstract
The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.
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Affiliation(s)
- Dali Cheng
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Eran Lustig
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA
- Department of Physics, McGill University, Montreal, QC, H3A 2T8, Canada
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
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5
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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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6
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Li G, Wang L, Ye R, Zheng Y, Wang DW, Liu XJ, Dutt A, Yuan L, Chen X. Direct extraction of topological Zak phase with the synthetic dimension. LIGHT, SCIENCE & APPLICATIONS 2023; 12:81. [PMID: 36977678 PMCID: PMC10050404 DOI: 10.1038/s41377-023-01126-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Revised: 02/25/2023] [Accepted: 03/06/2023] [Indexed: 06/18/2023]
Abstract
Measuring topological invariants is an essential task in characterizing topological phases of matter. They are usually obtained from the number of edge states due to the bulk-edge correspondence or from interference since they are integrals of the geometric phases in the energy band. It is commonly believed that the bulk band structures could not be directly used to obtain the topological invariants. Here, we implement the experimental extraction of Zak phase from the bulk band structures of a Su-Schrieffer-Heeger (SSH) model in the synthetic frequency dimension. Such synthetic SSH lattices are constructed in the frequency axis of light, by controlling the coupling strengths between the symmetric and antisymmetric supermodes of two bichromatically driven rings. We measure the transmission spectra and obtain the projection of the time-resolved band structure on lattice sites, where a strong contrast between the non-trivial and trivial topological phases is observed. The topological Zak phase is naturally encoded in the bulk band structures of the synthetic SSH lattices, which can hence be experimentally extracted from the transmission spectra in a fiber-based modulated ring platform using a laser with telecom wavelength. Our method of extracting topological phases from the bulk band structure can be further extended to characterize topological invariants in higher dimensions, while the exhibited trivial and non-trivial transmission spectra from the topological transition may find future applications in optical communications.
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Affiliation(s)
- Guangzhen Li
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Luojia Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Rui Ye
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yuanlin Zheng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China
| | - Da-Wei Wang
- Interdisciplinary Center for Quantum Information and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials and School of Physics, Peking University, Beijing, 100871, China
- International Quantum Academy, Shenzhen, 518048, China
| | - Avik Dutt
- Department of Mechanical Engineering, Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China.
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China.
- Collaborative Innovation Center of Light Manipulation and Applications, Shandong Normal University, Jinan, 250358, China.
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7
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Cheng D, Wang K, Fan S. Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension. PHYSICAL REVIEW LETTERS 2023; 130:083601. [PMID: 36898123 DOI: 10.1103/physrevlett.130.083601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non-Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.
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Affiliation(s)
- Dali Cheng
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
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8
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Yang M, Zhang HQ, Liao YW, Liu ZH, Zhou ZW, Zhou XX, Xu JS, Han YJ, Li CF, Guo GC. Realization of exceptional points along a synthetic orbital angular momentum dimension. SCIENCE ADVANCES 2023; 9:eabp8943. [PMID: 36696496 PMCID: PMC9876542 DOI: 10.1126/sciadv.abp8943] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/06/2022] [Accepted: 12/20/2022] [Indexed: 06/17/2023]
Abstract
Exceptional points (EPs), at which more than one eigenvalue and eigenvector coalesce, are unique spectral features of non-Hermiticity (NH) systems. They exist widely in open systems with complex energy spectra. We experimentally demonstrate the appearance of paired EPs in a periodical-driven degenerate optical cavity along the synthetic orbital angular momentum dimension with a tunable parameter. The complex-energy band structures and the key features of EPs, i.e., their bulk Fermi arcs, parity-time symmetry breaking transition, energy swapping, and half-integer band windings, are directly observed by detecting the wavefront angle-resolved transmission spectrum. Our results demonstrate the flexibility of using the photonic synthetic dimensions to implement NH systems beyond their geometric dimension and EP-based sensing.
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Affiliation(s)
- Mu Yang
- 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
| | - Hao-Qing Zhang
- 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
| | - Yu-Wei Liao
- 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
| | - Zheng-Hao Liu
- 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
| | - Zheng-Wei Zhou
- 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
| | - Xing-Xiang Zhou
- 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
| | - Jin-Shi Xu
- 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
| | - Yong-Jian Han
- 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
| | - Chuan-Feng Li
- 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
| | - Guang-Can Guo
- 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
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9
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High-order dynamic localization and tunable temporal cloaking in ac-electric-field driven synthetic lattices. Nat Commun 2022; 13:7653. [PMID: 36496493 PMCID: PMC9741653 DOI: 10.1038/s41467-022-35398-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 11/30/2022] [Indexed: 12/13/2022] Open
Abstract
Dynamic localization (DL) of photons, i.e., the light-motion cancellation effect arising from lattice's quasi-energy band collapse under a synthetic ac-electric-field, provides a powerful and alternative mechanism to Anderson localization for coherent light confinement. So far only low-order DLs, corresponding to weak ac-fields, have been demonstrated using curved-waveguide lattices where the waveguide's bending curvature plays the role of ac-field as required in original Dunlap-Kenkre model of DL. However, the inevitable bending losses pose a severe limitation for the observation of high-order DL. Here, we break the weak-field limitation by transferring lattice concepts from spatial to synthetic time dimensions using fiber-loop circuits and observe up to fifth-order DL. We find that high-order DLs possess superior localization and robustness against random noise over lower-order ones. As an exciting application, by judiciously combining low- and high-order DLs, we demonstrate a temporal cloaking scheme with flexible tunability both for cloak's window size and opening time. Our work pushes DL towards high-order regimes using synthetic-lattice schemes, which may find potential applications in robust signal transmission, protection, processing, and cloaking.
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10
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Abstract
Mirrors are ubiquitous in optics and are used to control the propagation of optical signals in space. Here we propose and demonstrate frequency domain mirrors that provide reflections of the optical energy in a frequency synthetic dimension, using electro-optic modulation. First, we theoretically explore the concept of frequency mirrors with the investigation of propagation loss, and reflectivity in the frequency domain. Next, we explore the mirror formed through polarization mode-splitting in a thin-film lithium niobate micro-resonator. By exciting the Bloch waves of the synthetic frequency crystal with different wave vectors, we show various states formed by the interference between forward propagating and reflected waves. Finally, we expand on this idea, and generate tunable frequency mirrors as well as demonstrate trapped states formed by these mirrors using coupled lithium niobate micro-resonators. The ability to control the flow of light in the frequency domain could enable a wide range of applications, including the study of random walks, boson sampling, frequency comb sources, optical computation, and topological photonics. Furthermore, demonstration of optical elements such as cavities, lasers, and photonic crystals in the frequency domain, may be possible.
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11
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Abstract
Synthetic dimensions have garnered widespread interest for implementing high dimensional classical and quantum dynamics on low-dimensional geometries. Synthetic frequency dimensions, in particular, have been used to experimentally realize a plethora of bulk physics effects. However, in synthetic frequency dimension there has not been a demonstration of a boundary which is of paramount importance in topological physics due to the bulk-edge correspondence. Here we construct boundaries in the frequency dimension of dynamically modulated ring resonators by strongly coupling an auxiliary ring. We explore various effects associated with such boundaries, including confinement of the spectrum of light, discretization of the band structure, and the interaction of boundaries with one-way chiral modes in a quantum Hall ladder, which exhibits topologically robust spectral transport. Our demonstration of sharp boundaries fundamentally expands the capability of exploring topological physics, and has applications in classical and quantum information processing in synthetic frequency dimensions.
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12
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Abstract
The era of Big Data requires nanophotonic chips to have large information processing capacity. Multiple frequency on-chip nanophotonic devices are highly desirable for density integration, but such devices are more susceptible to structural imperfection because of their nano-scale. Topological photonics provides a robust platform for next-generation nanophotonic chips. Here we give an experimental report of an on-chip nanophotonic topological rainbow realized by employing a translational deformation freedom as a synthetic dimension. The topological rainbow can separate, slow, and trap topological photonic states of different frequencies into different positions. A homemade scattering scanning near-field optical microscope with high resolution is introduced to directly measure the topological rainbow effect of the silicon-based photonic chip. The topological rainbow based on synthetic dimension have no restrictions for optical lattice types, symmetries, materials, wavelength band, and is easy for on-chip integration. This work builds a bridge between silicon chip technologies and topological photonics. Here the authors provide the experimental observation of a topological rainbow in a silicon-based nanophotonic chip. The system is robust against disorders allows to separate and trap topological photonic states of different wavelength into different positions.
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13
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Topological band structure via twisted photons in a degenerate cavity. Nat Commun 2022; 13:2040. [PMID: 35440661 PMCID: PMC9018724 DOI: 10.1038/s41467-022-29779-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 03/28/2022] [Indexed: 11/09/2022] Open
Abstract
Synthetic dimensions based on particles’ internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological phenomena. Exploring more synthetic dimensions is one of the paths toward higher dimensional physics. In this work, we design and experimentally control the coupling among synthetic dimensions consisting of the intrinsic photonic orbital angular momentum and spin angular momentum degrees of freedom in a degenerate optical resonant cavity, which generates a periodically driven spin-orbital coupling system. We directly characterize the system’s properties, including the density of states, energy band structures and topological windings, through the transmission intensity measurements. Our work demonstrates a mechanism for exploring the spatial modes of twisted photons as the synthetic dimension, which paves the way to design rich topological physics in a highly compact platform. Tailoring topological physics in optical cavity is a challenge that would allow new possibilities for the design optical components. In this paper, the authors, harnessing the potential of synthetic dimensions, experimentally demonstrate a degenerate cavity containing many optical angular momenta.
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14
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Balčytis A, Ozawa T, Ota Y, Iwamoto S, Maeda J, Baba T. Synthetic dimension band structures on a Si CMOS photonic platform. SCIENCE ADVANCES 2022; 8:eabk0468. [PMID: 35089790 PMCID: PMC8797776 DOI: 10.1126/sciadv.abk0468] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Synthetic dimensions, which simulate spatial coordinates using nonspatial degrees of freedom, are drawing interest in topological science and other fields for modeling higher-dimensional phenomena on simple structures. We present the first realization of a synthetic frequency dimension on a silicon ring resonator integrated photonic device fabricated using a CMOS process. We confirm that its coupled modes correspond to a one-dimensional tight-binding model through acquisition of up to 280-GHz bandwidth optical frequency comb-like spectra and by measuring synthetic band structures. Furthermore, we realized two types of gauge potentials along the frequency dimension and probed their effects through the associated band structures. An electric field analog was produced via modulation detuning, whereas effective magnetic fields were induced using synchronized nearest- and second nearest-neighbor couplings. Creation of coupled mode lattices and two effective forces on a monolithic Si CMOS device represents a key step toward wider adoption of topological principles.
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Affiliation(s)
- Armandas Balčytis
- Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
- Corresponding author:
| | - Tomoki Ozawa
- Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - Yasutomo Ota
- Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
- Institute for Nano Quantum Information Electronics, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - Satoshi Iwamoto
- Institute for Nano Quantum Information Electronics, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
- Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
- Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - Jun Maeda
- Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
| | - Toshihiko Baba
- Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
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15
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Liu Z, Qin C, Liu W, Zheng L, Ren S, Wang B, Lu P. Frequency manipulation of topological surface states by Weyl phase transitions. OPTICS LETTERS 2021; 46:5719-5722. [PMID: 34780445 DOI: 10.1364/ol.442890] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.
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16
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Hwang Y, Rhim JW, Yang BJ. Geometric characterization of anomalous Landau levels of isolated flat bands. Nat Commun 2021; 12:6433. [PMID: 34741062 PMCID: PMC8571270 DOI: 10.1038/s41467-021-26765-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 10/14/2021] [Indexed: 12/03/2022] Open
Abstract
According to the Onsager’s semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids. Landau levels are normally bounded by upper and lower band edges at zero magnetic field. Here, the authors predict a system with isolated flat bands, where anomalous Landau level spreading appears outside the zero-field energy bounds.
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Affiliation(s)
- Yoonseok Hwang
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul, 08826, Korea.,Department of Physics and Astronomy, Seoul National University, Seoul, 08826, Korea.,Center for Theoretical Physics (CTP), Seoul National University, Seoul, 08826, Korea
| | - Jun-Won Rhim
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul, 08826, Korea. .,Department of Physics and Astronomy, Seoul National University, Seoul, 08826, Korea. .,Department of Physics, Ajou University, Suwon, 16499, Korea.
| | - Bohm-Jung Yang
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul, 08826, Korea. .,Department of Physics and Astronomy, Seoul National University, Seoul, 08826, Korea. .,Center for Theoretical Physics (CTP), Seoul National University, Seoul, 08826, Korea.
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17
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Topological complex-energy braiding of non-Hermitian bands. Nature 2021; 598:59-64. [PMID: 34616054 DOI: 10.1038/s41586-021-03848-x] [Citation(s) in RCA: 53] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 07/21/2021] [Indexed: 11/08/2022]
Abstract
Effects connected with the mathematical theory of knots1 emerge in many areas of science, from physics2,3 to biology4. Recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems5, where the complex band energies can braid in momentum space. However, such braids of complex-energy bands have not been realized or controlled experimentally. Here, we introduce a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands 𝔹2. We experimentally demonstrate such topological complex-energy braiding of non-Hermitian bands in a synthetic dimension6,7. Our experiments utilize frequency modes in two coupled ring resonators, one of which undergoes simultaneous phase and amplitude modulation. We observe a wide variety of two-band braiding structures that constitute representative instances of links and knots, including the unlink, the unknot, the Hopf link and the trefoil. We also show that the handedness of braids can be changed. Our results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.
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18
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Yu D, Peng B, Chen X, Liu XJ, Yuan L. Topological holographic quench dynamics in a synthetic frequency dimension. LIGHT, SCIENCE & APPLICATIONS 2021; 10:209. [PMID: 34620837 PMCID: PMC8497532 DOI: 10.1038/s41377-021-00646-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2021] [Revised: 09/10/2021] [Accepted: 09/14/2021] [Indexed: 05/06/2023]
Abstract
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.
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Affiliation(s)
- Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
| | - Bo Peng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
- Shanghai Research Center for Quantum Sciences, 201315, Shanghai, China
- Jinan Institute of Quantum Technology, 250101, Jinan, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, 250358, Jinan, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials and School of Physics, Peking University, 100871, Beijing, China.
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China.
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China.
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19
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Arbitrary linear transformations for photons in the frequency synthetic dimension. Nat Commun 2021; 12:2401. [PMID: 33893284 PMCID: PMC8065043 DOI: 10.1038/s41467-021-22670-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 03/25/2021] [Indexed: 02/02/2023] Open
Abstract
Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.
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20
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Chen Y, Zhang YL, Shen Z, Zou CL, Guo GC, Dong CH. Synthetic Gauge Fields in a Single Optomechanical Resonator. PHYSICAL REVIEW LETTERS 2021; 126:123603. [PMID: 33834826 DOI: 10.1103/physrevlett.126.123603] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 02/26/2021] [Indexed: 06/12/2023]
Abstract
Synthetic gauge fields have recently emerged, arising in the context of quantum simulations, topological matter, and the protected transportation of excitations against defects. For example, an ultracold atom experiences a light-induced effective magnetic field when tunneling in an optical lattice, and offering a platform to simulate the quantum Hall effect and topological insulators. Similarly, the magnetic field associated with photon transport between sites has been demonstrated in a coupled resonator array. Here, we report the first experimental demonstration of a synthetic gauge field in the virtual lattices of bosonic modes in a single optomechanical resonator. By employing degenerate clockwise and counterclockwise optical modes and a mechanical mode, a controllable synthetic gauge field is realized by tuning the phase of the driving lasers. The nonreciprocal conversion between the three modes is realized for different synthetic magnetic fluxes. As a proof-of-principle demonstration, we also show the dynamics of the system under a fast-varying synthetic gauge field, and demonstrate synthetic electric field. Our demonstration not only provides a versatile and controllable platform for studying synthetic gauge fields in high dimensions but also enables an exploration of ultrafast gauge field tuning with a large dynamic range, which is restricted for a magnetic field.
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Affiliation(s)
- Yuan Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Yan-Lei Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Zhen Shen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chang-Ling Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chun-Hua Dong
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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21
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Wang K, Dutt A, Yang KY, Wojcik CC, Vučković J, Fan S. Generating arbitrary topological windings of a non-Hermitian band. Science 2021; 371:1240-1245. [PMID: 33737483 DOI: 10.1126/science.abf6568] [Citation(s) in RCA: 54] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 02/09/2021] [Indexed: 01/19/2023]
Abstract
The nontrivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature of non-Hermitian systems is the nontrivial winding of the energy band in the complex energy plane. We provide experimental demonstrations of such nontrivial winding by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations, and by directly characterizing the complex band structures. Moreover, we show that the topological winding can be controlled by changing the modulation waveform. Our results allow for the synthesis and characterization of topologically nontrivial phases in nonconservative systems.
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Affiliation(s)
- Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Avik Dutt
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Ki Youl Yang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Casey C Wojcik
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Jelena Vučković
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA.
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22
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Chen H, Yang N, Qin C, Li W, Wang B, Han T, Zhang C, Liu W, Wang K, Long H, Zhang X, Lu P. Real-time observation of frequency Bloch oscillations with fibre loop modulation. LIGHT, SCIENCE & APPLICATIONS 2021; 10:48. [PMID: 33674556 PMCID: PMC7935930 DOI: 10.1038/s41377-021-00494-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Revised: 02/09/2021] [Accepted: 02/15/2021] [Indexed: 05/06/2023]
Abstract
Bloch oscillations (BOs) were initially predicted for electrons in a solid lattice to which a static electric field is applied. The observation of BOs in solids remains challenging due to the collision scattering and barrier tunnelling of electrons. Nevertheless, analogies of electron BOs for photons, acoustic phonons and cold atoms have been experimentally demonstrated in various lattice systems. Recently, BOs in the frequency dimension have been proposed and studied by using an optical micro-resonator, which provides a unique approach to controlling the light frequency. However, the finite resonator lifetime and intrinsic loss hinder the effect from being observed practically. Here, we experimentally demonstrate BOs in a synthetic frequency lattice by employing a fibre-loop circuit with detuned phase modulation. We show that a detuning between the modulation period and the fibre-loop roundtrip time acts as an effective vector potential and hence a constant effective force that can yield BOs in the modulation-induced frequency lattices. With a dispersive Fourier transformation, the pulse spectrum can be mapped into the time dimension, and its transient evolution can be precisely measured. This study offers a promising approach to realising BOs in synthetic dimensions and may find applications in frequency manipulations in optical fibre communication systems.
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Affiliation(s)
- Hao Chen
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - NingNing Yang
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Chengzhi Qin
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wenwan Li
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Bing Wang
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China.
| | - Tianwen Han
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Chi Zhang
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China.
| | - Weiwei Liu
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Kai Wang
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Hua Long
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Xinliang Zhang
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Peixiang Lu
- School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, 430074, China.
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23
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Li G, Zheng Y, Dutt A, Yu D, Shan Q, Liu S, Yuan L, Fan S, Chen X. Dynamic band structure measurement in the synthetic space. SCIENCE ADVANCES 2021; 7:eabe4335. [PMID: 33524000 PMCID: PMC7793575 DOI: 10.1126/sciadv.abe4335] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Accepted: 11/18/2020] [Indexed: 05/06/2023]
Abstract
Band structure theory plays an essential role in exploring physics in both solid-state systems and photonics. Here, we demonstrate a direct experimental measurement of the dynamic band structure in a synthetic space including the frequency axis of light, realized in a ring resonator under near-resonant dynamic modulation. This synthetic lattice exhibits the physical picture of the evolution of the wave vector reciprocal to the frequency axis in the band structure, analogous to a one-dimensional lattice under an external force. We experimentally measure the trajectories of the dynamic band structure by selectively exciting the band with a continuous wave source with its frequency scanning across the entire energy regime of the band. Our results not only provide a new perspective for exploring the dynamics in fundamental physics of solid-state and photonic systems with the concept of the synthetic dimension but also enable great capability in band structure engineering in photonics.
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Affiliation(s)
- Guangzhen Li
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yuanlin Zheng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Avik Dutt
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
| | - Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Qingrou Shan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Shijie Liu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
- Jinan Institute of Quantum Technology, Jinan 250101, China
- Collaborative Innovation Center of Light Manipulation and Applications, Shandong Normal University, Jinan 250358, China
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24
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Dutt A, Minkov M, Williamson IAD, Fan S. Higher-order topological insulators in synthetic dimensions. LIGHT, SCIENCE & APPLICATIONS 2020; 9:131. [PMID: 32704364 PMCID: PMC7371732 DOI: 10.1038/s41377-020-0334-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2019] [Revised: 04/07/2020] [Accepted: 05/11/2020] [Indexed: 05/22/2023]
Abstract
Conventional topological insulators support boundary states with dimension one lower than that of the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states with dimensions two or more lower than that of the bulk due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here, we construct photonic higher-order topological insulators (PHOTIs) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacent coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.
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Affiliation(s)
- Avik Dutt
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
| | - Momchil Minkov
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
| | - Ian A. D. Williamson
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA
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25
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Wang K, Bell BA, Solntsev AS, Neshev DN, Eggleton BJ, Sukhorukov AA. Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion. LIGHT, SCIENCE & APPLICATIONS 2020; 9:132. [PMID: 32704365 PMCID: PMC7371864 DOI: 10.1038/s41377-020-0299-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Revised: 03/15/2020] [Accepted: 03/22/2020] [Indexed: 05/22/2023]
Abstract
Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. Although direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions implemented by the frequency degree of freedom in photonics is rapidly advancing. The manipulation of light in these artificial lattices is typically realized through electro-optic modulation; yet, their operating bandwidth imposes practical constraints on the range of interactions between different frequency components. Here we propose and experimentally realize all-optical synthetic dimensions involving specially tailored simultaneous short- and long-range interactions between discrete spectral lines mediated by frequency conversion in a nonlinear waveguide. We realize triangular chiral-tube lattices in three-dimensional space and explore their four-dimensional generalization. We implement a synthetic gauge field with nonzero magnetic flux and observe the associated multidimensional dynamics of frequency combs, all within one physical spatial port. We anticipate that our method will provide a new means for the fundamental study of high-dimensional physics and act as an important step towards using topological effects in optical devices operating in the time and frequency domains.
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Affiliation(s)
- Kai Wang
- Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601 Australia
- Present Address: Ginzton Laboratory, Stanford University, Stanford, CA 94305 USA
| | - Bryn A. Bell
- Institute of Photonics and Optical Science (IPOS), School of Physics, University of Sydney, Sydney, NSW 2006 Australia
- Department of Physics, QOLS, Imperial College London, London, SW7 2AZ UK
| | - Alexander S. Solntsev
- Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601 Australia
- School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, NSW 2007 Australia
| | - Dragomir N. Neshev
- Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601 Australia
| | - Benjamin J. Eggleton
- Institute of Photonics and Optical Science (IPOS), School of Physics, University of Sydney, Sydney, NSW 2006 Australia
| | - Andrey A. Sukhorukov
- Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601 Australia
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26
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Mercier de Lépinay L, Ockeloen-Korppi CF, Malz D, Sillanpää MA. Nonreciprocal Transport Based on Cavity Floquet Modes in Optomechanics. PHYSICAL REVIEW LETTERS 2020; 125:023603. [PMID: 32701306 DOI: 10.1103/physrevlett.125.023603] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2019] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
Directional transport is obtained in various multimode systems by driving multiple, nonreciprocally interfering interactions between individual bosonic modes. However, systems sustaining the required number of modes become physically complex. In our microwave-optomechanical experiment, we show how to configure nonreciprocal transport between frequency components of a single superconducting cavity coupled to two drumhead oscillators. The frequency components are promoted to Floquet modes and generate the missing dimension to realize an isolator and a directional amplifier. A second cavity left free by this arrangement is used to cool the mechanical oscillators and bring the transduction noise close to the quantum limit. We furthermore uncover a new type of instability specific to nonreciprocal coupling. Our approach is generic and can greatly simplify quantum signal processing and the design of topological lattices from low-dimensional systems.
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Affiliation(s)
- Laure Mercier de Lépinay
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Caspar F Ockeloen-Korppi
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Daniel Malz
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
| | - Mika A Sillanpää
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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27
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Muniz ALM, Alberucci A, Jisha CP, Monika M, Nolte S, Morandotti R, Peschel U. Kapitza light guiding in photonic mesh lattice. OPTICS LETTERS 2019; 44:6013-6016. [PMID: 32628207 DOI: 10.1364/ol.44.006013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 11/01/2019] [Indexed: 06/11/2023]
Abstract
We experimentally demonstrate the transverse confinement of light in the presence of a longitudinally periodic photonic potential with vanishing average. In agreement with Kapitza's original findings in classical mechanics, we confirm that light undergoes a transverse localization due to the action of an effective potential proportional to the square of the first derivative of the potential. Experiments are performed based on (1+1) D synthetic dimensions realized in a fiber loop system, allowing for complete control of the transverse and longitudinal distributions of the potential.
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28
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Dutt A, Lin Q, Yuan L, Minkov M, Xiao M, Fan S. A single photonic cavity with two independent physical synthetic dimensions. Science 2019; 367:59-64. [DOI: 10.1126/science.aaz3071] [Citation(s) in RCA: 115] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Accepted: 11/13/2019] [Indexed: 02/05/2023]
Abstract
The concept of synthetic dimensions has generated interest in many branches of science, ranging from ultracold atomic physics to photonics, as it provides a versatile platform for realizing effective gauge potentials and topological physics. Previous experiments have augmented the real-space dimensionality by one additional physical synthetic dimension. In this study, we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We observe a wide variety of physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and signatures of topological chiral one-way edge currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.
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