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Yang YB, Wang JH, Li K, Xu Y. Higher-order topological phases in crystalline and non-crystalline systems: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:283002. [PMID: 38574683 DOI: 10.1088/1361-648x/ad3abd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 04/04/2024] [Indexed: 04/06/2024]
Abstract
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.
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Affiliation(s)
- Yan-Bin Yang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region of China, People's Republic of China
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Kai Li
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yong Xu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
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Zhang H, Wang WW, Qiao C, Zhang L, Liang MC, Wu R, Wang XJ, Liu XJ, Zhang X. Topological spin-orbit-coupled fermions beyond rotating wave approximation. Sci Bull (Beijing) 2024; 69:747-755. [PMID: 38331706 DOI: 10.1016/j.scib.2024.01.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Revised: 12/24/2023] [Accepted: 01/15/2024] [Indexed: 02/10/2024]
Abstract
The realization of spin-orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation (RWA). By neglecting the counter-rotating terms, RWA characterizes a single near-resonant spin-orbit (SO) coupling in a two-level system. Here, we propose and experimentally realize a new scheme for achieving a pair of two-dimensional (2D) SO couplings for ultracold fermions beyond RWA. This work not only realizes the first anomalous Floquet topological Fermi gas beyond RWA, but also significantly improves the lifetime of the 2D-SO-coupled Fermi gas. Based on pump-probe quench measurements, we observe a deterministic phase relation between two sets of SO couplings, which is characteristic of our beyond-RWA scheme and enables the two SO couplings to be simultaneously tuned to the optimum 2D configurations. We observe intriguing band topology by measuring two-ring band-inversion surfaces, quantitatively consistent with a Floquet topological Fermi gas in the regime of high Chern numbers. Our study can open an avenue to explore exotic SO physics and anomalous topological states based on long-lived SO-coupled ultracold fermions.
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Affiliation(s)
- Han Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Wen-Wei Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Chang Qiao
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
| | - Long Zhang
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; Hefei National Laboratory, Hefei 230088, China
| | - Ming-Cheng Liang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Rui Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xu-Jie Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Hefei National Laboratory, Hefei 230088, China; International Quantum Academy, Shenzhen 518048, China.
| | - Xibo Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Hefei National Laboratory, Hefei 230088, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
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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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Li L, Gong J. Probing higher-order band topology via spin texture measurements: quantum simulation. Sci Bull (Beijing) 2021; 66:1817-1818. [PMID: 36654388 DOI: 10.1016/j.scib.2021.05.025] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Affiliation(s)
- Linhu Li
- Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, School of Physics and Astronomy, Sun Yat-sen University Zhuhai Campus, Zhuhai 519082, China.
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117551, Singapore.
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