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Du Z, Liao K, Dai T, Wang Y, Gao J, Huang H, Qi H, Li Y, Wang X, Su X, Wang X, Yang Y, Lu C, Hu X, Gong Q. Ultracompact and multifunctional integrated photonic platform. SCIENCE ADVANCES 2024; 10:eadm7569. [PMID: 38896615 PMCID: PMC11186496 DOI: 10.1126/sciadv.adm7569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 05/13/2024] [Indexed: 06/21/2024]
Abstract
Realizing a multifunctional integrated photonic platform is one of the goals for future optical information processing, which usually requires large size to realize due to multiple integration challenges. Here, we realize a multifunctional integrated photonic platform with ultracompact footprint based on inverse design. The photonic platform is compact with 86 inverse designed-fixed couplers and 91 phase shifters. The footprint of each coupler is 4 μm by 2 μm, while the whole photonic platform is 3 mm by 0.2 mm-one order of magnitude smaller than previous designs. One-dimensional Floquet Su-Schrieffer-Heeger model and Aubry-André-Harper model are performed with measured fidelities of 97.90 (±0.52) % and 99.34 (±0.44) %, respectively. We also demonstrate a handwritten digits classification task with the test accuracy of 87% using on-chip training. Moreover, the scalability of this platform has been proved by demonstrating more complex computing tasks. This work provides an effective method to realize an ultrasmall integrated photonic platform.
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Affiliation(s)
- Zhuochen Du
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Kun Liao
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Tianxiang Dai
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Yufei Wang
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Jinze Gao
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Haiqi Huang
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Huixin Qi
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Yandong Li
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Xiaoxiao Wang
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
| | - Xinran Su
- School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
| | - Xingyuan Wang
- College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
| | - Yan Yang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
| | - Cuicui Lu
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Xiaoyong Hu
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Hefei National Laboratory, Hefei 230088, China
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter, Beijing Academy of Quantum Information Sciences, Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Hefei National Laboratory, Hefei 230088, China
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Jiang T, Zhang J, Xin G, Dang Y, Xiang A, Qi X, Zhang W, Yang Z. Topological oscillated edge states in trimer lattices. OPTICS EXPRESS 2024; 32:18605-18617. [PMID: 38859013 DOI: 10.1364/oe.522432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 04/16/2024] [Indexed: 06/12/2024]
Abstract
We investigate a 1D trimer optical lattice model. Two kinds of topological oscillating optical transmission phenomena at edges are shown. The exact and the approximate solutions of the system's edge states are obtained with and without the inversion symmetry for this system respectively. Based on the solutions, the existence and the periods of the oscillations can be controlled arbitrarily. Moreover, in a system without inversion symmetry, controlling the incident beam can eliminate both types of oscillations, resulting in a more stable edge state compared to the one with inversion symmetry. This prompts us to reconsider topological systems under symmetry protection.
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Roberts N, Baardink G, Nunn J, Mosley PJ, Souslov A. Topological supermodes in photonic crystal fiber. SCIENCE ADVANCES 2022; 8:eadd3522. [PMID: 36542705 PMCID: PMC9770996 DOI: 10.1126/sciadv.add3522] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a length-scalable platform such as optical fiber. We demonstrate, through both modeling and experiment, optical fiber that hosts topological supermodes across multiple light-guiding cores. We directly measure the photonic winding number invariant characterizing the bulk and observe topological guidance of visible light over meter length scales. Furthermore, the mechanical flexibility of fiber allows us to reversibly reconfigure the topological state. As the fiber is bent, we find that the edge states first lose their localization and then become relocalized because of disorder. We envision fiber as a scalable platform to explore and exploit topological effects in photonic networks.
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Affiliation(s)
- Nathan Roberts
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
| | - Guido Baardink
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
| | - Josh Nunn
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
- ORCA Computing Ltd., 30 Eastbourne Terrace, London W2 6LA, UK
| | - Peter J. Mosley
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
- Centre for Photonics and Photonic Materials, University of Bath, Bath BA2 7AY, UK
| | - Anton Souslov
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK
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Yang Y, Cao D. Observation of the topological phase transition from the spatial correlation of a biphoton in a one-dimensional topological photonic waveguide array. OPTICS EXPRESS 2022; 30:37899-37909. [PMID: 36258369 DOI: 10.1364/oe.471703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
We propose a simple method, using the first singular value (FSV) of the spatial correlation of biphotons, to characterize topological phase transitions (TPTs) in one-dimensional (1D) topological photonic waveguide arrays (PWAs). After analyzing the spatial correlation of biphotons using the singular value decomposition, we found that the FSV of the spatial correlation of biphotons in real space can characterize TPTs and distinguish between the topological trivial and nontrivial phases in PWAs based on the Su-Schrieffer-Heeger model. The analytical simulation results were demonstrated by applying the coupled-mode theory to biphotons and were found to be in good agreement with those of the numerical simulation. Moreover, the numerical simulation of the FSV (of the spatial correlation of biphotons) successfully characterized the TPT in a PWA based on the Aubry-André-Harper and Rice-Mele models, demonstrating the universality of this method for 1D topological PWAs. Our method provides biphotons with the possibility of acquiring information regarding TPTs directly from the spatial correlation in real space, and their potential applications in quantum topological photonics and topological quantum computing as quantum simulators and information carriers.
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Zhou WH, Vijayan MK, Wang XW, Lu YH, Gao J, Jiao ZQ, Ren RJ, Chang YJ, Shen ZS, Rohde PP, Jin XM. Reducing circuit complexity in optical quantum computation using 3D architectures. OPTICS EXPRESS 2022; 30:32887-32894. [PMID: 36242341 DOI: 10.1364/oe.464108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 07/06/2022] [Indexed: 06/16/2023]
Abstract
Integrated photonic architectures based on optical waveguides are one of the leading candidates for the future realisation of large-scale quantum computation. One of the central challenges in realising this goal is simultaneously minimising loss whilst maximising interferometric visibility within waveguide circuits. One approach is to reduce circuit complexity and depth. A major constraint in most planar waveguide systems is that beamsplitter transformations between distant optical modes require numerous intermediate SWAP operations to couple them into nearest neighbour proximity, each of which introduces loss and scattering. Here, we propose a 3D architecture which can significantly mitigate this problem by geometrically bypassing trivial intermediate operations. We demonstrate the viability of this concept by considering a worst-case 2D scenario, where we interfere the two most distant optical modes in a planar structure. Using femtosecond laser direct-writing technology we experimentally construct a 2D architecture to implement Hong-Ou-Mandel interference between its most distant modes, and a 3D one with corresponding physical dimensions, demonstrating significant improvement in both fidelity and efficiency in the latter case. In addition to improving fidelity and efficiency of individual non-adjacent beamsplitter operations, this approach provides an avenue for reducing the optical depth of circuits comprising complex arrays of beamsplitter operations.
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Hu H, Han S, Yang Y, Liu D, Xue H, Liu GG, Cheng Z, Wang QJ, Zhang S, Zhang B, Luo Y. Observation of Topological Edge States in Thermal Diffusion. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2202257. [PMID: 35674403 DOI: 10.1002/adma.202202257] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 06/01/2022] [Indexed: 06/15/2023]
Abstract
Topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and is widely observed for electromagnetic and acoustic waves. Here, the notion of band topology is extended from wave to diffusion dynamics. Unlike wave systems that are usually Hermitian, diffusion systems are anti-Hermitian with purely imaginary eigenvalues corresponding to decay rates. By direct probe of the temperature diffusion, the Hamiltonian of a thermal lattice is experimentally retrieved, and the emergence of topological edge decays is observed within the gap of bulk decays. The results of this work show that such edge states exhibit robust decay rates, which are topologically protected against disorder. This work constitutes a thermal analogue of topological insulators and paves the way to exploring defect-immune heat dissipation.
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Affiliation(s)
- Hao Hu
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Song Han
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, Key Lab. of Advanced Micro/Nano Electronic Devices and Smart Systems of Zhejiang, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
| | - Dongjue Liu
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Qi Jie Wang
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Shuang Zhang
- Department of Physics, University of Hong Kong, Hong Kong, 999077, China
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, 999077, China
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Yu Luo
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
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Chang YJ, Lu YH, Yang YY, Wang Y, Zhou WH, Wang XW, Jin XM. Inhibition and Reconstruction of Zener Tunneling in Photonic Honeycomb Lattices. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2110044. [PMID: 35306698 DOI: 10.1002/adma.202110044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 03/06/2022] [Indexed: 06/14/2023]
Abstract
Quantum coherence is the central element of particle states, and it characterizes the overall performance of various quantum materials. Bloch oscillation is a fundamental coherent behavior of particles under a static potential, which can be easily destroyed by Zener tunneling in multiband 2D lattice materials. The control of Zener tunneling therefore plays the key role in quantum engineering for complicated physical systems. Here, the inhibition and reconstruction of Zener tunneling in photonic honeycomb lattices are experimentally demonstrated. Deformed honeycomb lattices are integrated and an effective static potential is realized on the 2D lattice materials. Zener tunneling disappears in stretch-type lattices and wave packets stay in the dispersionless upper energy band. On the contrary, Zener tunneling is greatly enhanced in compression-type lattices and wave packets exhibit directional oscillations without branches, which manifest the preserved coherence of the wave packets. The results demonstrate the protection of photonic coherence by structurally controlling the Zener tunneling, representing a step toward flexible quantum engineering for large-scale artificial quantum materials.
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Affiliation(s)
- Yi-Jun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Yong-Heng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Ying-Yue Yang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- TuringQ Co., Ltd., Shanghai, 200240, China
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Nie W, Antezza M, Liu YX, Nori F. Dissipative Topological Phase Transition with Strong System-Environment Coupling. PHYSICAL REVIEW LETTERS 2021; 127:250402. [PMID: 35029435 DOI: 10.1103/physrevlett.127.250402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Revised: 07/20/2021] [Accepted: 11/01/2021] [Indexed: 06/14/2023]
Abstract
A primary motivation for studying topological matter regards the protection of topological order from its environment. In this work, we study a topological emitter array coupled to an electromagnetic environment. The photon-emitter coupling produces nonlocal interactions between emitters. Using periodic boundary conditions for all ranges of environment-induced interactions, the chiral symmetry inherent to the emitter array is preserved. This chiral symmetry protects the Hamiltonian and induces parity in the Lindblad operator. A topological phase transition occurs at a critical photon-emitter coupling related to the energy spectrum width of the emitter array. Interestingly, the critical point nontrivially changes the dissipation rates of edge states, yielding a dissipative topological phase transition. In the protected topological phase, edge states suffer from environment-induced dissipation for weak photon-emitter coupling. However, strong coupling leads to robust dissipationless edge states with a window at the emitter spacing. Our work shows the potential to manipulate topological quantum matter with electromagnetic environments.
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Affiliation(s)
- Wei Nie
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Mauro Antezza
- Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, F- 34095 Montpellier, France
- Institut Universitaire de France, 1 rue Descartes, F-75231 Paris Cedex 05, France
| | - Yu-Xi Liu
- School of Integrated Circuits, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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Jiao ZQ, Longhi S, Wang XW, Gao J, Zhou WH, Wang Y, Fu YX, Wang L, Ren RJ, Qiao LF, Jin XM. Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices. PHYSICAL REVIEW LETTERS 2021; 127:147401. [PMID: 34652196 DOI: 10.1103/physrevlett.127.147401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 08/27/2021] [Indexed: 06/13/2023]
Abstract
Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.
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Affiliation(s)
- Zhi-Qiang Jiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
| | - Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jun Gao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yu-Xuan Fu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Li Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruo-Jing Ren
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu-Feng Qiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- TuringQ Co., Ltd., Shanghai 200240, China
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Wang Y, Xie BY, Lu YH, Chang YJ, Wang HF, Gao J, Jiao ZQ, Feng Z, Xu XY, Mei F, Jia S, Lu MH, Jin XM. Quantum superposition demonstrated higher-order topological bound states in the continuum. LIGHT, SCIENCE & APPLICATIONS 2021; 10:173. [PMID: 34462419 PMCID: PMC8405621 DOI: 10.1038/s41377-021-00612-8] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Revised: 07/26/2021] [Accepted: 08/09/2021] [Indexed: 06/13/2023]
Abstract
Higher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.
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Affiliation(s)
- Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Bi-Ye Xie
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China
- Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
| | - Yong-Heng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yi-Jun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Hong-Fei Wang
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China
- Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Jun Gao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Zhi-Qiang Jiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Zhen Feng
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Xiao-Yun Xu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi, 030006, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi, 030006, China.
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi, 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi, 030006, China
| | - Ming-Hui Lu
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China.
- Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China.
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing, 210093, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China.
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11
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Liu YG, Xu L, Li Z. Quantum phase transition in a non-Hermitian XYspin chain with global complex transverse field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:295401. [PMID: 33984851 DOI: 10.1088/1361-648x/ac00dd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 05/13/2021] [Indexed: 06/12/2023]
Abstract
In this work, we investigate the quantum phase transition in a non-HermitianXYspin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditionalXYmodel. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.
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Affiliation(s)
- Yu-Guo Liu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Lu Xu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Zhi Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, People's Republic of China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, People's Republic of China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, People's Republic of China
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12
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Mittal V, Raj A, Dey S, Goyal SK. Persistence of topological phases in non-Hermitian quantum walks. Sci Rep 2021; 11:10262. [PMID: 33986329 PMCID: PMC8119463 DOI: 10.1038/s41598-021-89441-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Accepted: 04/22/2021] [Indexed: 12/05/2022] Open
Abstract
Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact [Formula: see text]-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the [Formula: see text]-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.
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Affiliation(s)
- Vikash Mittal
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India
| | - Aswathy Raj
- Okinawa Institute of Science and Technology Graduate University, Okinawa, 904-0495, Japan
| | - Sanjib Dey
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India
| | - Sandeep K Goyal
- Department of Physical Sciences, Indian Institute of Science Education & Research (IISER) Mohali, Sector 81 SAS Nagar, PO 140306, Manauli, Punjab, India.
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13
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St-Jean P, Dauphin A, Massignan P, Real B, Jamadi O, Milicevic M, Lemaître A, Harouri A, Le Gratiet L, Sagnes I, Ravets S, Bloch J, Amo A. Measuring Topological Invariants in a Polaritonic Analog of Graphene. PHYSICAL REVIEW LETTERS 2021; 126:127403. [PMID: 33834841 DOI: 10.1103/physrevlett.126.127403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 09/08/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g., graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D subspaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene where Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems and opens the door to the exploration of more complex topological effects, e.g., involving disorder and interactions.
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Affiliation(s)
- P St-Jean
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Dauphin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - P Massignan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, 08034 Barcelona, Spain
| | - B Real
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - O Jamadi
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M Milicevic
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Harouri
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - L Le Gratiet
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - I Sagnes
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - S Ravets
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - J Bloch
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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14
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Lin S, Zhang L, Tian T, Duan CK, Du J. Dynamic Observation of Topological Soliton States in a Programmable Nanomechanical Lattice. NANO LETTERS 2021; 21:1025-1031. [PMID: 33438395 DOI: 10.1021/acs.nanolett.0c04121] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Topological soliton states, existing in the topological structures with edge defect or interface defect, are usually studied under steady state. Here, we experimentally observe the dynamic processes of the generation and the extinction of such soliton states in the Su-Schrieffer-Heeger model. The different topological structures are implemented on a programmable nanomechanical lattice, consisting of eight adjacent string resonators which are parametrically coupled by manipulation voltages. Moreover, the beating and localization behaviors at different topological interfaces are also observed in the same device. These results explicitly exhibit the dynamic processes of topological soliton states, which reveal real potential toward integrated multifunctional topological materials.
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Affiliation(s)
- Shaochun Lin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Liang Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Tian Tian
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chang-Kui Duan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jiangfeng Du
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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15
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Qian Z, Li Z, Hao H, Shan L, Zhang Q, Dong J, Gong Q, Gu Y. Absorption Reduction of Large Purcell Enhancement Enabled by Topological State-Led Mode Coupling. PHYSICAL REVIEW LETTERS 2021; 126:023901. [PMID: 33512207 DOI: 10.1103/physrevlett.126.023901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
We propose the mechanism of edge state-led mode coupling under topological protection; i.e., localized surface plasmons almost do not have any influence on the edge state, while the edge state greatly changes the local field distribution of surface plasmons. Based on this mechanism, in the well-designed topological photonic structure containing a resonant plasmon nanoantenna, an obvious absorption reduction in the spontaneous emission spectra appears due to the near-field deformation around the antenna induced by the edge state. Because a plasmon antenna with ultrasmall mode volume provides large Purcell enhancement and simultaneously the photonic crystal guides almost all scattering light into its edge state, the rate of nonscattering single photons reaches more than 10^{4}γ_{0}. This topological state-led mode coupling mechanism and induced absorption reduction, which are based on topological protection, will have a profound effect on the study of composite topological photonic structures and related micro- and nanoscale cavity quantum electrodynamics. Also, nonscattering large Purcell enhancement will provide practical use for on-chip quantum light sources, such as single-photon sources and nanolasers.
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Affiliation(s)
- Zhiyuan Qian
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
| | - Zhichao Li
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
| | - He Hao
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
| | - Lingxiao Shan
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
| | - Qi Zhang
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
| | - Jianwen Dong
- State Key Laboratory of Optoelectronic Materials and Technologies and School of Physics, Sun Yat-sen University, Guangzhou 510275, China
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Collaborative Innovation Center of Quantum Matter, and Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Ying Gu
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Collaborative Innovation Center of Quantum Matter, and Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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16
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Lu YH, Wang Y, Mei F, Chang YJ, Gao J, Zheng H, Jia S, Jin XM. Real-space observation of topological invariants in 2D photonic systems. OPTICS EXPRESS 2020; 28:39492-39500. [PMID: 33379497 DOI: 10.1364/oe.399893] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 10/23/2020] [Indexed: 06/12/2023]
Abstract
Topological materials are capable of inherently robust transport and propagation of physical fields against disorder and perturbations, holding the promise of revolutionary technologies in a wide spectrum. Higher-order topological insulators are recently predicted as topological phases beyond the standard bulk-edge correspondence principle, however, their topological invariants have been proven very challenging to observe, even not possible yet by indirect ways. Here, we demonstrate theoretically and experimentally that the topological invariants in two-dimensional systems can be directly revealed in real space by measuring single-photon bulk dynamics. By freely writing photonic lattices with femtosecond laser, we construct and identify the predicted second-order topological insulators, as well as first-order topological insulators with fractional topological winding number. Furthermore, we show that the accumulation and statistics on individual single-particle registrations can eventually lead to the same results of light waves, despite the fact that the development of topological physics was originally based on wave theories, sharing the same spirit of wave-particle nature in quantum mechanics. Our results offer a direct fashion of observing topological phases in two-dimensional systems and may inspire topologically protected artificial devices in high-order topology, high-dimension and quantum regime.
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17
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Li M, Zhang Q, Chen Y, Ren X, Gong Q, Li Y. Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States. MICROMACHINES 2020; 11:mi11121111. [PMID: 33334077 PMCID: PMC7765531 DOI: 10.3390/mi11121111] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Revised: 12/12/2020] [Accepted: 12/13/2020] [Indexed: 11/16/2022]
Abstract
Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 ± 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.
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Affiliation(s)
- Meng Li
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China; (M.L.); (Q.Z.); (Q.G.)
| | - Qian Zhang
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China; (M.L.); (Q.Z.); (Q.G.)
| | - Yang Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; (Y.C.); (X.R.)
| | - Xifeng Ren
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; (Y.C.); (X.R.)
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China; (M.L.); (Q.Z.); (Q.G.)
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, China
| | - Yan Li
- State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing 100871, China; (M.L.); (Q.Z.); (Q.G.)
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, China
- Correspondence:
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18
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Mei F, Guo Q, Yu YF, Xiao L, Zhu SL, Jia S. Digital Simulation of Topological Matter on Programmable Quantum Processors. PHYSICAL REVIEW LETTERS 2020; 125:160503. [PMID: 33124873 DOI: 10.1103/physrevlett.125.160503] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Accepted: 09/23/2020] [Indexed: 06/11/2023]
Abstract
Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize the digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupling and related topological matter can be digitally simulated. In particular, a low-depth topological quantum circuit is performed on both the IBM and Rigetti quantum processors. In the experiments, we not only observe but also distinguish the 0 and π energy topological edge states by measuring the qubit excitation distribution at the output of the circuits.
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Affiliation(s)
- Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Qihao Guo
- School of Science, Xian Jiaotong University, Xian 710049, Shaanxi, China
| | - Ya-Fei Yu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, Frontier Research Institute for Physics and SPTE, South China Normal University, Guangzhou 510006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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19
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Zhang W, Xie X, Hao H, Dang J, Xiao S, Shi S, Ni H, Niu Z, Wang C, Jin K, Zhang X, Xu X. Low-threshold topological nanolasers based on the second-order corner state. LIGHT, SCIENCE & APPLICATIONS 2020; 9:109. [PMID: 32637076 PMCID: PMC7324580 DOI: 10.1038/s41377-020-00352-1] [Citation(s) in RCA: 59] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Revised: 06/10/2020] [Accepted: 06/12/2020] [Indexed: 05/15/2023]
Abstract
Topological lasers are immune to imperfections and disorder. They have been recently demonstrated based on many kinds of robust edge states, which are mostly at the microscale. The realization of 2D on-chip topological nanolasers with a small footprint, a low threshold and high energy efficiency has yet to be explored. Here, we report the first experimental demonstration of a topological nanolaser with high performance in a 2D photonic crystal slab. A topological nanocavity is formed utilizing the Wannier-type 0D corner state. Lasing behaviour with a low threshold of approximately 1 µW and a high spontaneous emission coupling factor of 0.25 is observed with quantum dots as the active material. Such performance is much better than that of topological edge lasers and comparable to that of conventional photonic crystal nanolasers. Our experimental demonstration of a low-threshold topological nanolaser will be of great significance to the development of topological nanophotonic circuitry for the manipulation of photons in classical and quantum regimes.
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Affiliation(s)
- Weixuan Zhang
- Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, 100081 Beijing, China
- Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, Micro-nano Center, School of Physics, Beijing Institute of Technology, 100081 Beijing, China
| | - Xin Xie
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Huiming Hao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors Chinese Academy of Sciences, Beijing, 100083 China
| | - Jianchen Dang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Shan Xiao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Shushu Shi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
| | - Haiqiao Ni
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors Chinese Academy of Sciences, Beijing, 100083 China
| | - Zhichuan Niu
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors Chinese Academy of Sciences, Beijing, 100083 China
| | - Can Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808 China
| | - Kuijuan Jin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808 China
| | - Xiangdong Zhang
- Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, School of Physics, Beijing Institute of Technology, 100081 Beijing, China
- Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, Micro-nano Center, School of Physics, Beijing Institute of Technology, 100081 Beijing, China
| | - Xiulai Xu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049 China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808 China
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20
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Xu XY, Wang QQ, Heyl M, Budich JC, Pan WW, Chen Z, Jan M, Sun K, Xu JS, Han YJ, Li CF, Guo GC. Measuring a dynamical topological order parameter in quantum walks. LIGHT, SCIENCE & APPLICATIONS 2020; 9:7. [PMID: 31993125 PMCID: PMC6971032 DOI: 10.1038/s41377-019-0237-8] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 12/18/2019] [Accepted: 12/18/2019] [Indexed: 05/14/2023]
Abstract
Quantum processes of inherent dynamical nature, such as quantum walks, defy a description in terms of an equilibrium statistical physics ensemble. Until now, identifying the general principles behind the underlying unitary quantum dynamics has remained a key challenge. Here, we show and experimentally observe that split-step quantum walks admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures, at a given time, the winding of the geometric phase accumulated by the wavefunction during a quantum walk. We observe distinct dynamical regimes in our experimentally realized quantum walks, and each regime can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent many-body problem, we reveal an intriguing connection between the nonanalytic changes of the DTOP in quantum walks and the occurrence of dynamical quantum phase transitions.
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Affiliation(s)
- Xiao-Ye 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
| | - Qin-Qin Wang
- 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
| | - Markus Heyl
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
| | - Jan Carl Budich
- Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
| | - Wei-Wei Pan
- 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
| | - Zhe 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
| | - Munsif Jan
- 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
| | - Kai Sun
- 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
| | - 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
| | - 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
| | - 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
| | - 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
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Wang Y, Lu YH, Gao J, Sun K, Jiao ZQ, Tang H, Jin XM. Quantum Topological Boundary States in Quasi-Crystals. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2019; 31:e1905624. [PMID: 31613398 DOI: 10.1002/adma.201905624] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Revised: 09/25/2019] [Indexed: 06/10/2023]
Abstract
Topological phases play a novel and fundamental role in matter and display extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological material and quantum information may lead to inherent fault-tolerant quantum simulations and quantum computing. Quantum features may be preserved by being encoded among topological structures of physical evolution systems. This requires stimulation, manipulation, and observation of topological phenomena at the single quantum particle level, which has not, however, yet been realized. It is asked whether the quantum features of single photons can be preserved in topological structures. The boundary states are experimentally observed at the genuine single-photon level and the performance of the topological phase is demonstrated to protect the quantum features against diffusion-induced decoherence in coupled waveguides and noise decoherence from the ambient environment. Compatibility between macroscopic topological states and microscopic single photons in the ambient environment is thus confirmed, leading to a new avenue to "quantum topological photonics" and providing more new possibilities for quantum materials and quantum technologies.
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Affiliation(s)
- Yao Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Yong-Heng Lu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Jun Gao
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Ke Sun
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Zhi-Qiang Jiao
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Hao Tang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
| | - Xian-Min Jin
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China
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