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Wang C, Li N, Xie J, Ding C, Ji Z, Xiao L, Jia S, Yan B, Hu Y, Zhao Y. Exceptional Nexus in Bose-Einstein Condensates with Collective Dissipation. PHYSICAL REVIEW LETTERS 2024; 132:253401. [PMID: 38996274 DOI: 10.1103/physrevlett.132.253401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 04/01/2024] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
In multistate non-Hermitian systems, higher-order exceptional points and exotic phenomena with no analogues in two-level systems arise. A paradigm is the exceptional nexus (EX), a third-order EP as the cusp singularity of exceptional arcs (EAs), that has a hybrid topological nature. Using atomic Bose-Einstein condensates to implement a dissipative three-state system, we experimentally realize an EX within a two-parameter space, despite the absence of symmetry. The engineered dissipation exhibits density dependence due to the collective atomic response to resonant light. Based on extensive analysis of the system's decay dynamics, we demonstrate the formation of an EX from the coalescence of two EAs with distinct geometries. These structures arise from the different roles played by dissipation in the strong coupling limit and quantum Zeno regime. Our Letter paves the way for exploring higher-order exceptional physics in the many-body setting of ultracold atoms.
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Affiliation(s)
- Chenhao Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Nan Li
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Jin Xie
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Cong Ding
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Zhonghua Ji
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Bo Yan
- Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou 310027, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Yanting Zhao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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Ji X, Yang X. Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:243001. [PMID: 38387101 DOI: 10.1088/1361-648x/ad2c73] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Accepted: 02/22/2024] [Indexed: 02/24/2024]
Abstract
We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.
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Affiliation(s)
- Xiang Ji
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Xiaosen Yang
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
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3
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Bai K, Liu TR, Fang L, Li JZ, Lin C, Wan D, Xiao M. Observation of Nonlinear Exceptional Points with a Complete Basis in Dynamics. PHYSICAL REVIEW LETTERS 2024; 132:073802. [PMID: 38427883 DOI: 10.1103/physrevlett.132.073802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 01/12/2024] [Indexed: 03/03/2024]
Abstract
The exotic physics associated with exceptional points (EPs) is always under the scrutiny of theoretical and experimental science. Recently, considerable effort has been invested in the combination of nonlinearity and non-Hermiticity. The concept of nonlinear EPs (NEPs) has been introduced, which can avoid the loss of completeness of the eigenbasis in dynamics while retaining the key features of linear EPs. Here, we present the first direct experimental demonstration of a NEP based on two non-Hermition coupled circuit resonators combined with a nonlinear saturable gain. At the NEP, the response of the eigenfrequency to perturbations demonstrates a third-order root law and the eigenbasis of the Hamiltonian governing the system dynamics is still complete. Our results bring this counterintuitive aspect of the NEP to light and possibly open new avenues for applications.
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Affiliation(s)
- Kai Bai
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Tian-Rui Liu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liang Fang
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jia-Zheng Li
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Chen Lin
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Duanduan Wan
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Meng Xiao
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
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4
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Lee J, Kim J, An K. Frequency pushing enhanced by an exceptional point in an atom-cavity coupled system. Sci Rep 2024; 14:3471. [PMID: 38342945 PMCID: PMC11306339 DOI: 10.1038/s41598-024-54008-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Accepted: 02/07/2024] [Indexed: 02/13/2024] Open
Abstract
We observed the frequency pushing of the cavity resonance as a result of the coupling of the cavity field with the ground state 138Ba in a high-Q cavity. A weak probe laser propagated along the axis of a Fabry-Pérot cavity while ground-state barium atoms traversed the cavity mode perpendicularly. By operating the atom-cavity composite in the vicinity of an exceptional point, we could observe a greatly enhanced frequency shift of the cavity transmission peak, which was pushed away from the atomic resonance, resulting in up to 41 ± 7 kHz frequency shift per atom from the empty cavity resonance. We analyzed our results by using the Maxwell-Schrödinger equation and obtained good agreement with the measurements.
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Affiliation(s)
- Joohye Lee
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea
| | - Jinuk Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea
- Department of Physics, Yale University, New Haven, CT, 06520, USA
| | - Kyungwon An
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.
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Han PR, Wu F, Huang XJ, Wu HZ, Zou CL, Yi W, Zhang M, Li H, Xu K, Zheng D, Fan H, Wen J, Yang ZB, Zheng SB. Exceptional Entanglement Phenomena: Non-Hermiticity Meeting Nonclassicality. PHYSICAL REVIEW LETTERS 2023; 131:260201. [PMID: 38215365 DOI: 10.1103/physrevlett.131.260201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 11/15/2023] [Indexed: 01/14/2024]
Abstract
Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.
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Affiliation(s)
- Pei-Rong Han
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Fan Wu
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Xin-Jie Huang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Huai-Zhi Wu
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
| | - Chang-Ling Zou
- 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, Hefei 230088, China
| | - Wei Yi
- 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, Hefei 230088, China
| | - Mengzhen Zhang
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Hefei National Laboratory, Hefei 230088, China
| | - Jianming Wen
- Department of Physics, Kennesaw State University, Marietta, Georgia 30060, USA
| | - Zhen-Biao Yang
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
- Hefei National Laboratory, Hefei 230088, China
| | - Shi-Biao Zheng
- Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
- Hefei National Laboratory, Hefei 230088, China
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Mao X, Qin GQ, Zhang H, Wang BY, Long D, Li GQ, Long GL. Enhanced Sensing Mechanism Based on Shifting an Exceptional Point. RESEARCH (WASHINGTON, D.C.) 2023; 6:0260. [PMID: 37915766 PMCID: PMC10616973 DOI: 10.34133/research.0260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 10/10/2023] [Indexed: 11/03/2023]
Abstract
Non-Hermitian systems associated with exceptional points (EPs) are expected to demonstrate a giant response enhancement for various sensors. The widely investigated enhancement mechanism based on diverging from an EP should destroy the EP and further limits its applications for multiple sensing scenarios in a time sequence. To break the above limit, here, we proposed a new enhanced sensing mechanism based on shifting an EP. Different from the mechanism of diverging from an EP, our scheme is an EP nondemolition and the giant enhancement of response is acquired by a slight shift of the EP along the parameter axis induced by perturbation. The new sensing mechanism can promise the most effective response enhancement for all sensors in the case of multiple sensing in a time sequence. To verify our sensing mechanism, we construct a mass sensor and a gyroscope with concrete physical implementations. Our work will deepen the understanding of EP-based sensing and inspire designing various high-sensitivity sensors in different physical systems.
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Affiliation(s)
- Xuan Mao
- Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics,
Tsinghua University, Beijing 100084, China
| | - Guo-Qing Qin
- Beijing Institute of Radio Measurement, The Second Academy of China Aerospace Science and Industry Corporation (CASIC), Beijing 100854, China
| | - Hao Zhang
- Purple Mountain Laboratories, Nanjing 211111, China
| | - Bo-Yang Wang
- Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics,
Tsinghua University, Beijing 100084, China
| | - Dan Long
- Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics,
Tsinghua University, Beijing 100084, China
| | - Gui-Qin Li
- Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics,
Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
| | - Gui-Lu Long
- Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics,
Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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7
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Bai K, Li JZ, Liu TR, Fang L, Wan D, Xiao M. Nonlinear Exceptional Points with a Complete Basis in Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:266901. [PMID: 37450800 DOI: 10.1103/physrevlett.130.266901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Revised: 04/13/2023] [Accepted: 06/08/2023] [Indexed: 07/18/2023]
Abstract
Exceptional points (EPs) are special spectral singularities at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become identical. In conventional wisdom, the coalescence of eigenvectors inevitably leads to the loss of completeness of the eigenbasis. Here, we show that this scenario breaks down in general at nonlinear EPs (NEPs). As an example, we realize a fifth-order NEP (NEP_{5}) within only three coupled resonators with both a theoretical model and simulations in circuits. One stable and another four auxiliary steady eigenstates of the nonlinear Hamiltonian coalesce at the NEP_{5}, and the response of eigenfrequency to perturbations demonstrates a fifth-order root law. Intriguingly, the biorthogonal eigenbasis of the Hamiltonian governing the system dynamics is still complete, and this fact is corroborated by a finite Petermann factor instead of a divergent one at conventional EPs. Consequently, the amplification of noise, which diverges at other EPs, converges at our NEP_{5}. Our finding transforms the understanding of EPs and shows potential for miniaturizing various key applications operating near EPs.
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Affiliation(s)
- Kai Bai
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jia-Zheng Li
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Tian-Rui Liu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liang Fang
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Duanduan Wan
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Meng Xiao
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
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Li H, Jia Q, Lyu B, Cao F, Yang G, Liu D, Shi J. Parity-time symmetry breaking optical nanocircuit. OPTICS EXPRESS 2023; 31:14986-14996. [PMID: 37157350 DOI: 10.1364/oe.488467] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Gain and loss balanced parity-time (PT) inversion symmetry has been achieved across multiple platforms including acoustics, electronics, and photonics. Tunable subwavelength asymmetric transmission based on PT symmetry breaking has attracted great interest. However, due to the diffraction limit, the geometric size of an optical PT symmetric system is much larger than the resonant wavelength, which limits the device miniaturization. Here, we theoretically studied a subwavelength optical PT symmetry breaking nanocircuit based on the similarity between a plasmonic system and an RLC circuit. Firstly, the asymmetric coupling of an input signal is observed by varying the coupling strength and gain-loss ratio between the nanocircuits. Furthermore, a subwavelength modulator is proposed by modulating the gain of the amplified nanocircuit. Notably, the modulation effect near the exceptional point is remarkable. Finally, we introduce a four-level atomic model modified by the Pauli exclusion principle to simulate the nonlinear dynamics of a PT symmetry broken laser. The asymmetric emission of a coherent laser is realized by full-wave simulation with a contrast of about 50. This subwavelength optical nanocircuit with broken PT symmetry is of great significance for realizing directional guided light, modulator and asymmetric-emission laser at subwavelength scales.
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Cayao J. Exceptional degeneracies in non-Hermitian Rashba semiconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:254002. [PMID: 37021876 DOI: 10.1088/1361-648x/acc7e9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 03/27/2023] [Indexed: 06/19/2023]
Abstract
Exceptional points (EPs) are spectral degeneracies of non-Hermitian (NH) systems where eigenvalues and eigenvectors coalesce, inducing unique topological phases that have no counterpart in the Hermitian realm. Here we consider an NH system by coupling a two-dimensional semiconductor with Rashba spin-orbit coupling (SOC) to a ferromagnet lead and show the emergence of highly tunable EPs along rings in momentum space. Interestingly, these exceptional degeneracies are the endpoints of lines formed by the eigenvalue coalescence at finite real energy, resembling the bulk Fermi arcs commonly defined at zero real energy. We then show that an in-plane Zeeman field provides a way to control these exceptional degeneracies although higher values of non-Hermiticity are required in contrast to the zero Zeeman field regime. Furthermore, we find that the spin projections also coalescence at the exceptional degeneracies and can acquire larger values than in the Hermitian regime. Finally, we demonstrate that the exceptional degeneracies induce large spectral weights, which can be used as a signature for their detection. Our results thus reveal the potential of systems with Rashba SOC for realizing NH bulk phenomena.
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Affiliation(s)
- Jorge Cayao
- Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
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10
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Li Y, Cao Y, Chen Y, Yang X. Universal characteristics of one-dimensional non-Hermitian superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:055401. [PMID: 36410037 DOI: 10.1088/1361-648x/aca4b4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 11/21/2022] [Indexed: 06/16/2023]
Abstract
We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone. The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points. If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be theZ2skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitianp- ands-wave topological superconductors. In terms of Majorana Pfaffian, aZ2non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence for the non-Hermitian topological superconductors.
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Affiliation(s)
- Yang Li
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Yang Cao
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Yuanping Chen
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
| | - Xiaosen Yang
- Department of Physics, Jiangsu University, Zhenjiang 212013, People's Republic of China
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11
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Lu Y, Zhao Y, Li R, Liu J. Anomalous spontaneous emission dynamics at chiral exceptional points. OPTICS EXPRESS 2022; 30:41784-41803. [PMID: 36366646 DOI: 10.1364/oe.473824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.
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12
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Bachelard N, Schumer A, Kumar B, Garay C, Arlandis J, Touzani R, Sebbah P. Coalescence of Anderson-localized modes at an exceptional point in 2D random media. OPTICS EXPRESS 2022; 30:18098-18107. [PMID: 36221617 DOI: 10.1364/oe.454493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/09/2022] [Indexed: 06/16/2023]
Abstract
In non-Hermitian settings, the particular position at which two eigenstates coalesce in the complex plane under a variation of a physical parameter is called an exceptional point. An open disordered system is a special class of non-Hermitian system, where the degree of scattering directly controls the confinement of the modes. Herein a non-perturbative theory is proposed which describes the evolution of modes when the permittivity distribution of a 2D open dielectric system is modified, thereby facilitating to steer individual eigenstates to such a non-Hermitian degeneracy. The method is used to predict the position of such an exceptional point between two Anderson-localized states in a disordered scattering medium. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems.
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Hosseini MV, Askari M. Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal. Sci Rep 2021; 11:22206. [PMID: 34772988 PMCID: PMC8589957 DOI: 10.1038/s41598-021-01591-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2021] [Accepted: 10/25/2021] [Indexed: 12/05/2022] Open
Abstract
We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green's function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.
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Affiliation(s)
- Mir Vahid Hosseini
- Department of Physics, Faculty of Science, University of Zanjan, Zanjan, 45371-38791, Iran.
| | - Mehdi Askari
- grid.510469.fDepartment of Physics, Faculty of Science, Salman Farsi University of Kazerun, Kazerun, Iran
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14
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Kim J, Kim K, Lee D, Shin Y, Kang S, Kim JR, Choi Y, An K, Lee M. Locking Multi-Laser Frequencies to a Precision Wavelength Meter: Application to Cold Atoms. SENSORS (BASEL, SWITZERLAND) 2021; 21:6255. [PMID: 34577462 PMCID: PMC8473145 DOI: 10.3390/s21186255] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Revised: 09/13/2021] [Accepted: 09/14/2021] [Indexed: 11/17/2022]
Abstract
We herein report a simultaneous frequency stabilization of two 780-nm external cavity diode lasers using a precision wavelength meter (WLM). The laser lock performance is characterized by the Allan deviation measurement in which we find σy=10-12 at an averaging time of 1000 s. We also obtain spectral profiles through a heterodyne spectroscopy, identifying the contribution of white and flicker noises to the laser linewidth. The frequency drift of the WLM is measured to be about 2.0(4) MHz over 36 h. Utilizing the two lasers as a cooling and repumping field, we demonstrate a magneto-optical trap of 87Rb atoms near a high-finesse optical cavity. Our laser stabilization technique operates at broad wavelength range without a radio frequency element.
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Affiliation(s)
- Junwoo Kim
- Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea; (J.K.); (K.K.); (D.L.); (Y.S.)
| | - Keumhyun Kim
- Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea; (J.K.); (K.K.); (D.L.); (Y.S.)
| | - Dowon Lee
- Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea; (J.K.); (K.K.); (D.L.); (Y.S.)
| | - Yongha Shin
- Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea; (J.K.); (K.K.); (D.L.); (Y.S.)
| | - Sungsam Kang
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea;
- Department of Physics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea
| | - Jung-Ryul Kim
- Kyungbock High School, 28 Jahamun-ro 9-gil, Jongno-gu, Seoul 03049, Korea;
| | - Youngwoon Choi
- Department of Bioengineering, Korea University, Seoul 02841, Korea;
- Interdisciplinary Program in Precision Public Health, Korea University, Seoul 02841, Korea
| | - Kyungwon An
- Department of Physics & Institute of Applied Physics, Seoul National University, Seoul 08826, Korea;
| | - Moonjoo Lee
- Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea; (J.K.); (K.K.); (D.L.); (Y.S.)
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15
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Bao XX, Guo GF, Tan L. Exploration of the topological properties in a non-Hermitian long-range system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:465403. [PMID: 34425563 DOI: 10.1088/1361-648x/ac2040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 08/23/2021] [Indexed: 06/13/2023]
Abstract
The asymmetrical long-range hopping amplitudes have a rich influence on the topological properties. Here, a non-Hermitian model including the long-range hopping amplitudes is constructed to explore those properties. It can be found that an extra topological invariantW= 2 emerges as a consequence of the long-range hopping amplitudes. Furthermore, we find that the phaseW= 2 can be directly characterized by the generalized Brillouin zone (GBZ) itself through the concept of the argument principle. Meanwhile, a gapless phase dubbed as topological semimetal phase can be induced by the asymmetrical long-range hopping. Moreover, the physical origin of the topological semimetal phase can be explained by the solutions of eigen-equation. It is also shown that the skin modes exist as long as the GBZ and the Brillouin zone differ from each other. These interesting phases may be realized in an electrical-circuit simulator.
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Affiliation(s)
- Xi-Xi Bao
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
| | - Gang-Feng Guo
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
| | - Lei Tan
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
- Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, People's Republic of China
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16
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Sun XQ, Zhu P, Hughes TL. Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2021; 127:066401. [PMID: 34420349 DOI: 10.1103/physrevlett.127.066401] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 06/29/2021] [Indexed: 06/13/2023]
Abstract
We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle, which is an integer multiple of 2π, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the effective surface Dirac fermion(s) in the presence of a pseudomagnetic flux induced by disclinations. Furthermore, we find that our results have a field theoretic description, and the corresponding geometric response actions (e.g., the Euclidean Wen-Zee action) enrich the topological field theory of non-Hermitian systems.
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Affiliation(s)
- Xiao-Qi Sun
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Penghao Zhu
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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17
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Zhang K, Yang Z, Fang C. Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2020; 125:126402. [PMID: 33016766 DOI: 10.1103/physrevlett.125.126402] [Citation(s) in RCA: 101] [Impact Index Per Article: 25.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 08/24/2020] [Indexed: 05/05/2023]
Abstract
We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary conditions in non-Hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the nonvanishing current through the system.
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Affiliation(s)
- Kai Zhang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhesen Yang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Chen Fang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- CAS Center for Excellence in Topological Quantum Computation, Beijing 100190, China
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18
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Ann BM, Song Y, Kim J, Yang D, An K. Observation of scalable sub-Poissonian-field lasing in a microlaser. Sci Rep 2019; 9:17110. [PMID: 31745233 PMCID: PMC6863906 DOI: 10.1038/s41598-019-53525-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Accepted: 11/01/2019] [Indexed: 11/19/2022] Open
Abstract
Sub-Poisson field with much reduced fluctuations in a cavity can boost quantum precision measurements via cavity-enhanced light-matter interactions. Strong coupling between an atom and a cavity mode has been utilized to generate highly sub-Poisson fields. However, a macroscopic number of optical intracavity photons with more than 3 dB variance reduction has not been possible. Here, we report sub-Poisson field lasing in a microlaser operating with hundreds of atoms with well-regulated atom-cavity coupling and interaction time. Its photon-number variance was 4 dB below the standard quantum limit while the intracavity mean photon number scalable up to 600. The highly sub-Poisson photon statistics were not deteriorated by simultaneous interaction of a large number of atoms. Our finding suggests an effective pathway to widely scalable near-Fock-state lasing at the macroscopic scale.
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Affiliation(s)
- Byoung-Moo Ann
- Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ, Delft, The Netherlands
| | - Younghoon Song
- Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Department of Field Application, ASML Korea, Hwaseong, 18449, Korea
| | - Junki Kim
- Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, 27708, USA
| | - Daeho Yang
- Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Samsung Advanced Institute of Technology, Suwon, 16678, Korea
| | - Kyungwon An
- Department of Physics and Astronomy & Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.
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19
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Song F, Yao S, Wang Z. Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 123:170401. [PMID: 31702238 DOI: 10.1103/physrevlett.123.170401] [Citation(s) in RCA: 73] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Indexed: 06/10/2023]
Abstract
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.
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Affiliation(s)
- Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Shunyu Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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20
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Qian C, Xie X, Yang J, Peng K, Wu S, Song F, Sun S, Dang J, Yu Y, Steer MJ, Thayne IG, Jin K, Gu C, Xu X. Enhanced Strong Interaction between Nanocavities and p-shell Excitons Beyond the Dipole Approximation. PHYSICAL REVIEW LETTERS 2019; 122:087401. [PMID: 30932617 DOI: 10.1103/physrevlett.122.087401] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Indexed: 06/09/2023]
Abstract
Large coupling strengths in exciton-photon interactions are important for the quantum photonic network, while strong cavity-quantum dot interactions have been focused on s-shell excitons with small coupling strengths. Here we demonstrate strong interactions between cavities and p-shell excitons with a great enhancement by the in situ wave-function control. The p-shell excitons are demonstrated with much larger wave-function extents and nonlocal interactions beyond the dipole approximation. Then the interaction is tuned from the nonlocal to the local regime by the wave function shrinking, during which the enhancement is obtained. A large coupling strength of 210 μeV has been achieved, indicating the great potential of p-shell excitons for coherent information exchange. Furthermore, we propose a distributed delay model to quantitatively explain the coupling strength variation, revealing the intertwining of excitons and photons beyond the dipole approximation.
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Affiliation(s)
- Chenjiang Qian
- 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
| | - 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
| | - Jingnan Yang
- 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
| | - Kai Peng
- 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
| | - Shiyao Wu
- 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
| | - Feilong Song
- 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
| | - Sibai Sun
- 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
| | - 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
| | - Yang Yu
- 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
| | - Matthew J Steer
- School of Engineering, University of Glasgow, Glasgow G12 8LT, United Kingdom
| | - Iain G Thayne
- School of Engineering, University of Glasgow, Glasgow G12 8LT, United Kingdom
| | - 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
| | - Changzhi Gu
- 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
| | - 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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21
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Wang J, Yin Y, Hao Q, Yang YD, Valligatla S, Saei Ghareh Naz E, Li Y, Saggau CN, Ma L, Schmidt OG. Curved Nanomembrane-Based Concentric Ring Cavities for Supermode Hybridization. NANO LETTERS 2018; 18:7261-7267. [PMID: 30339757 DOI: 10.1021/acs.nanolett.8b03453] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report the mode interactions and resonant hybridization in nanomembrane-formed concentric dual ring cavities supporting whispering gallery mode resonances. Utilizing a rolled-up nanomembrane with subwavelength thickness as an interlayer, dual concentric microring cavities are formed by coating high-index nanomembranes on the inner and outer surfaces of the rolled-up dielectric nanomembrane. In such a hybrid cavity system, the conventional fundamental mode resonating along a single ring orbit splits into symmetric and antisymmetric modes confined by concentric dual ring orbits. Detuning of the coupled supermodes is realized by spatially resolved measurements along the cavity axial direction. A spectral anticrossing feature is observed as a clear evidence of strong coupling. Upon strong coupling, the resonant orbits of symmetric and antisymmetric modes cross over each other in the form of superwaves oscillating between the concentric rings with opposite phase. Notably, the present system provides high flexibilities in controlling the coupling strength by varying the thickness of the spacer layer and thus enables switching between strong and weak coupling regimes. Our work offers a compact and robust scheme using curved nanomembranes to realize novel cavity mode interactions for both fundamental and applied studies.
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Affiliation(s)
- Jiawei Wang
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
- Material Systems for Nanoelectronics , Technische Universität Chemnitz , 09111 Chemnitz , Germany
| | - Yin Yin
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
- Department of Physics , Xiamen University , Xiamen , 361005 , China
| | - Qi Hao
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Yue-De Yang
- State Key Laboratory of Integrated Optoelectronics, Institute of Semiconductors , Chinese Academy of Sciences , Beijing , 100083 , China
| | - Sreeramulu Valligatla
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Ehsan Saei Ghareh Naz
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Yuan Li
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Christian Niclaas Saggau
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Libo Ma
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
| | - Oliver G Schmidt
- Institute for Integrative Nanosciences , IFW Dresden , Helmholtzstraße 20 , 01069 Dresden , Germany
- Material Systems for Nanoelectronics , Technische Universität Chemnitz , 09111 Chemnitz , Germany
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22
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Yao S, Song F, Wang Z. Non-Hermitian Chern Bands. PHYSICAL REVIEW LETTERS 2018; 121:136802. [PMID: 30312068 DOI: 10.1103/physrevlett.121.136802] [Citation(s) in RCA: 112] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2018] [Revised: 06/14/2018] [Indexed: 06/08/2023]
Abstract
The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.
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Affiliation(s)
- Shunyu Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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23
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Yao S, Wang Z. Edge States and Topological Invariants of Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2018; 121:086803. [PMID: 30192628 DOI: 10.1103/physrevlett.121.086803] [Citation(s) in RCA: 264] [Impact Index Per Article: 44.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Indexed: 05/05/2023]
Abstract
The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.
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Affiliation(s)
- Shunyu Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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24
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Samlan CT, Viswanathan NK. Chiral dynamics of exceptional points in weakly absorbing biaxial crystal. OPTICS LETTERS 2018; 43:3538-3541. [PMID: 30067704 DOI: 10.1364/ol.43.003538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2018] [Accepted: 06/26/2018] [Indexed: 06/08/2023]
Abstract
In this Letter, we report the chiral dynamics of optical exceptional points (EPs), the singular axes in weakly absorbing biaxial crystal, arising due to a fine balance between the birefringence and dichroism. Taking advantage of the coincidence of the singular axes and C-point singularity, the EPs are characterized using conoscopic Stokes polarimetry. We observe that the two optic axes of the biaxial crystal split into two pairs of singular axes upon introducing weak dichroism which, upon application of a transverse electric field, follows a helical trajectory to coalesce and disappear. Our results show a fine control on the chiral behavior of EPs due to an electrogyration effect, which controls the retardance gradient and the fast-axis orientation in the crystal.
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25
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Shen H, Zhen B, Fu L. Topological Band Theory for Non-Hermitian Hamiltonians. PHYSICAL REVIEW LETTERS 2018; 120:146402. [PMID: 29694133 DOI: 10.1103/physrevlett.120.146402] [Citation(s) in RCA: 192] [Impact Index Per Article: 32.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2017] [Indexed: 06/08/2023]
Abstract
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.
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Affiliation(s)
- Huitao Shen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bo Zhen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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26
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Wu N, Zhang C, Jin XR, Zhang YQ, Lee Y. Unidirectional reflectionless phenomena in a non-Hermitian quantum system of quantum dots coupled to a plasmonic waveguide. OPTICS EXPRESS 2018; 26:3839-3849. [PMID: 29475362 DOI: 10.1364/oe.26.003839] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Accepted: 01/25/2018] [Indexed: 06/08/2023]
Abstract
Unidirectional reflectionless phenomena are investigated theoretically in a non-Hermitian quantum system composed of several quantum dots and a plasmonic waveguide. By adjusting the phase shifts between quantum dots, single- and dual-band unidirectional reflectionlessnesses are realized at exceptional points based on two and three quantum dots coupled to a plasmonic waveguide, respectively. In addition, single- and dual-band unidirectional perfect absorptions with high quality factors are obtained at the vicinity of exceptional points.
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27
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Exceptional points enhance sensing in an optical microcavity. Nature 2017; 548:192-196. [PMID: 28796206 DOI: 10.1038/nature23281] [Citation(s) in RCA: 347] [Impact Index Per Article: 49.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2017] [Accepted: 06/07/2017] [Indexed: 01/30/2023]
Abstract
Sensors play an important part in many aspects of daily life such as infrared sensors in home security systems, particle sensors for environmental monitoring and motion sensors in mobile phones. High-quality optical microcavities are prime candidates for sensing applications because of their ability to enhance light-matter interactions in a very confined volume. Examples of such devices include mechanical transducers, magnetometers, single-particle absorption spectrometers, and microcavity sensors for sizing single particles and detecting nanometre-scale objects such as single nanoparticles and atomic ions. Traditionally, a very small perturbation near an optical microcavity introduces either a change in the linewidth or a frequency shift or splitting of a resonance that is proportional to the strength of the perturbation. Here we demonstrate an alternative sensing scheme, by which the sensitivity of microcavities can be enhanced when operated at non-Hermitian spectral degeneracies known as exceptional points. In our experiments, we use two nanoscale scatterers to tune a whispering-gallery-mode micro-toroid cavity, in which light propagates along a concave surface by continuous total internal reflection, in a precise and controlled manner to exceptional points. A target nanoscale object that subsequently enters the evanescent field of the cavity perturbs the system from its exceptional point, leading to frequency splitting. Owing to the complex-square-root topology near an exceptional point, this frequency splitting scales as the square root of the perturbation strength and is therefore larger (for sufficiently small perturbations) than the splitting observed in traditional non-exceptional-point sensing schemes. Our demonstration of exceptional-point-enhanced sensitivity paves the way for sensors with unprecedented sensitivity.
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28
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Universal Critical Behaviours in Non-Hermitian Phase Transitions. Sci Rep 2017; 7:7165. [PMID: 28769064 PMCID: PMC5540997 DOI: 10.1038/s41598-017-07344-z] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Accepted: 06/26/2017] [Indexed: 11/08/2022] Open
Abstract
Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 - 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 - 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.
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Xu J, Du YX, Huang W, Zhang DW. Detecting topological exceptional points in a parity-time symmetric system with cold atoms. OPTICS EXPRESS 2017; 25:15786-15795. [PMID: 28789091 DOI: 10.1364/oe.25.015786] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Accepted: 05/25/2017] [Indexed: 06/07/2023]
Abstract
We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to sweep the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the atomic interferometry. Since the proposed operations and detection are experimentally feasible, our scheme may pave a promising way to explore the novel properties of non-Hermitian systems.
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Gu X, Bai R, Zhang C, Jin XR, Zhang YQ, Zhang S, Lee YP. Unidirectional reflectionless propagation in a non-ideal parity-time metasurface based on far field coupling. OPTICS EXPRESS 2017; 25:11778-11787. [PMID: 28788737 DOI: 10.1364/oe.25.011778] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose a scheme to achieve a controllable unidirectional reflectionless propagation at exceptional point (EP) in a non-ideal parity-time metasurface consisting of two silver ring resonators. The unidirectional reflectionless propagation can be manipulated by simply adjusting the angle of incident wave and the distance s between two silver rings based on the far field coupling. In addition, the angle of incident wave in a wide range of ∼25° is available to achieve the unidirectional reflectionless propagation. Moreover, the unidirectional reflectionless propagation at EP is insensitive to the polarization of incident wave due to the two-ring structure.
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Observation of an exceptional point in a two-dimensional ultrasonic cavity of concentric circular shells. Sci Rep 2016; 6:38826. [PMID: 27958315 PMCID: PMC5153842 DOI: 10.1038/srep38826] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Accepted: 11/15/2016] [Indexed: 12/05/2022] Open
Abstract
We report observation of an exceptional point in circular shell ultrasonic cavities in both theory and experiment. In our theoretical analysis we first observe two interacting mode groups, fluid- and solid-based modes, in the acoustic cavities and then show the existence of an EP of these mode groups exhibiting a branch-point topological structure of eigenfrequencies around the EP. We then confirm the mode patterns as well as eigenfrequency structure around the EP in experiments employing the schlieren method, thereby demonstrating utility of ultrasound cavities as experimental platform for investigating non-Hermitian physics.
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Xu H, Mason D, Jiang L, Harris JGE. Topological energy transfer in an optomechanical system with exceptional points. Nature 2016; 537:80-83. [DOI: 10.1038/nature18604] [Citation(s) in RCA: 511] [Impact Index Per Article: 63.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2016] [Accepted: 05/11/2016] [Indexed: 01/11/2023]
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Parity-Time Symmetry Breaking in Coupled Nanobeam Cavities. Sci Rep 2016; 6:24487. [PMID: 27075817 PMCID: PMC4830925 DOI: 10.1038/srep24487] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2015] [Accepted: 03/29/2016] [Indexed: 11/09/2022] Open
Abstract
The concept of parity-time symmetry (PT symmetry) originates from the canonical quantum mechanics and has become a hot topic recently. As a versatile platform to investigate the intriguing concept, both theoretical and experimental works in optics have been implemented. In this paper, the PT symmetry breaking phenomenon is investigated in a coupled nanobeam cavity system. An exceptional point is observed during the tuning of the gain/loss level and the coupling strength of the closely placed nanobeam pair. Unidirectional light propagation is investigated, as well as enhanced sensitivity of single particle detection in the vicinity of the exceptional point. The proposed system is easy to be integrated with photonic integrated circuits and can be strongly coupled to optical waveguides.
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Huang Y, Veronis G, Min C. Unidirectional reflectionless propagation in plasmonic waveguide-cavity systems at exceptional points. OPTICS EXPRESS 2015; 23:29882-29895. [PMID: 26698471 DOI: 10.1364/oe.23.029882] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We design a non-parity-time-symmetric plasmonic waveguide-cavity system, consisting of two metal-dielectric-metal stub resonators side coupled to a metal-dielectric-metal waveguide, to form an exceptional point, and realize unidirectional reflectionless propagation at the optical communication wavelength. The contrast ratio between the forward and backward reflection almost reaches unity. We show that the presence of material loss in the metal is critical for the realization of the unidirectional reflectionlessness in this plasmonic system. We investigate the realized exceptional point, as well as the associated physical effects of level repulsion, crossing and phase transition. We also show that, by periodically cascading the unidirectional reflectionless plasmonic waveguide-cavity system, we can design a wavelength-scale unidirectional plasmonic waveguide perfect absorber. Our results could be potentially important for developing a new generation of highly compact unidirectional integrated nanoplasmonic devices.
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Gao T, Estrecho E, Bliokh KY, Liew TCH, Fraser MD, Brodbeck S, Kamp M, Schneider C, Höfling S, Yamamoto Y, Nori F, Kivshar YS, Truscott AG, Dall RG, Ostrovskaya EA. Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard. Nature 2015; 526:554-8. [PMID: 26458102 DOI: 10.1038/nature15522] [Citation(s) in RCA: 138] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2015] [Accepted: 08/18/2015] [Indexed: 11/09/2022]
Abstract
Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard--a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.
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Affiliation(s)
- T Gao
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - E Estrecho
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - K Y Bliokh
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia.,Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - T C H Liew
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - M D Fraser
- Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan
| | - S Brodbeck
- Technische Physik and Wilhelm-Conrad-Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - M Kamp
- Technische Physik and Wilhelm-Conrad-Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - C Schneider
- Technische Physik and Wilhelm-Conrad-Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - S Höfling
- Technische Physik and Wilhelm-Conrad-Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.,SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK
| | - Y Yamamoto
- ImPACT Project, Japan Science and Technology Agency, Chiyoda-ku, Tokyo 102-0076, Japan.,Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305-4085, USA
| | - F Nori
- Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198, Japan.,Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Y S Kivshar
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - A G Truscott
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - R G Dall
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - E A Ostrovskaya
- Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
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36
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Lee TE, Reiter F, Moiseyev N. Entanglement and spin squeezing in non-Hermitian phase transitions. PHYSICAL REVIEW LETTERS 2014; 113:250401. [PMID: 25554863 DOI: 10.1103/physrevlett.113.250401] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Indexed: 06/04/2023]
Abstract
We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: There is full N-particle entanglement at the transition, in contrast to the Hermitian case. The non-Hermitian model also exhibits more spin squeezing than the Hermitian model, showing that non-Hermitian dynamics are useful for quantum metrology. Experimental implementations with trapped ions and cavity QED are discussed.
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Affiliation(s)
- Tony E Lee
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Florentin Reiter
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry and Faculty of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
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37
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Wu JH, Artoni M, La Rocca GC. Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices. PHYSICAL REVIEW LETTERS 2014; 113:123004. [PMID: 25279626 DOI: 10.1103/physrevlett.113.123004] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2014] [Indexed: 06/03/2023]
Abstract
Light propagation in optical lattices of driven cold atoms exhibits non-Hermitian degeneracies when the first-order modulation amplitudes of real and imaginary parts of the probe susceptibility are manipulated to be balanced. At these degeneracies, one may observe complete unidirectional reflectionless light propagation. This strictly occurs with no gain and can be easily tuned and fully reversed as supported by the transfer-matrix calculations and explained via a coupled-mode analysis.
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Affiliation(s)
- Jin-Hui Wu
- Center for Quantum Sciences, Northeast Normal University, Changchun 130117, China
| | - M Artoni
- European Laboratory for Nonlinear Spectroscopy, 50019 Firenze, Italy and Department of Engineering and Information Technology and INO-CNR Sensor Lab, Brescia University, 25133 Brescia, Italy
| | - G C La Rocca
- Scuola Normale Superiore and CNISM, 56126 Pisa, Italy
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38
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Reversing the pump dependence of a laser at an exceptional point. Nat Commun 2014; 5:4034. [PMID: 24925314 PMCID: PMC4082637 DOI: 10.1038/ncomms5034] [Citation(s) in RCA: 117] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2013] [Accepted: 05/05/2014] [Indexed: 11/23/2022] Open
Abstract
When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called exceptional point occurs, which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such non-Hermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power. Exceptional points are singularities that occur when two resonant modes coalesce both in their frequency and width, giving rise to counterintuitive behaviour. Brandstetter et al. demonstrate how to induce such an exceptional point in a coupled pair of lasers, causing a reversal in their pump characteristics.
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39
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Lee M, Kim J, Seo W, Hong HG, Song Y, Dasari RR, An K. Three-dimensional imaging of cavity vacuum with single atoms localized by a nanohole array. Nat Commun 2014; 5:3441. [PMID: 24603683 DOI: 10.1038/ncomms4441] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2013] [Accepted: 02/12/2014] [Indexed: 11/09/2022] Open
Abstract
Zero-point electromagnetic fields were first introduced to explain the origin of atomic spontaneous emission. Vacuum fluctuations associated with the zero-point energy in cavities are now utilized in quantum devices such as single-photon sources, quantum memories, switches and network nodes. Here we present three-dimensional (3D) imaging of vacuum fluctuations in a high-Q cavity based on the measurement of position-dependent emission of single atoms. Atomic position localization is achieved by using a nanoscale atomic beam aperture scannable in front of the cavity mode. The 3D structure of the cavity vacuum is reconstructed from the cavity output. The root mean squared amplitude of the vacuum field at the antinode is also measured to be 0.92±0.07 V cm(-1). The present work utilizing a single atom as a probe for sub-wavelength imaging demonstrates the utility of nanometre-scale technology in cavity quantum electrodynamics.
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Affiliation(s)
- Moonjoo Lee
- 1] Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea [2]
| | - Junki Kim
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
| | - Wontaek Seo
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
| | - Hyun-Gue Hong
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
| | - Younghoon Song
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
| | - Ramachandra R Dasari
- G. R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Kyungwon An
- Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea
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40
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Bittner S, Dietz B, Harney HL, Miski-Oglu M, Richter A, Schäfer F. Scattering experiments with microwave billiards at an exceptional point under broken time-reversal invariance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032909. [PMID: 24730915 DOI: 10.1103/physreve.89.032909] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Indexed: 06/03/2023]
Abstract
Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
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Affiliation(s)
- S Bittner
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany and Laboratoire de Photonique Quantique et Moléculaire, CNRS UMR 8537, Institut d'Alembert FR 3242, Ecole Normale Supérieure de Cachan, F-94235 Cachan, France
| | - B Dietz
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - H L Harney
- Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany
| | - M Miski-Oglu
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - A Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - F Schäfer
- Division of Physics and Astronomy, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
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41
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Feng L, Zhu X, Yang S, Zhu H, Zhang P, Yin X, Wang Y, Zhang X. Demonstration of a large-scale optical exceptional point structure. OPTICS EXPRESS 2014; 22:1760-1767. [PMID: 24515183 DOI: 10.1364/oe.22.001760] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We report a large-size (4-inch) optical exceptional point structure at visible frequencies by designing a multilayer structure of absorbing and non-absorbing dielectrics. The optical exceptional point was implemented as indicated by the realized unidirectional reflectionless light transport at a wafer scale. The associated abrupt phase transition is theoretically and experimentally confirmed when crossing over the exceptional point in wavelengths. The large scale demonstration of phase transition around exceptional points will open new possibilities in important applications in free space optical devices.
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42
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Kim J, Lee M, Kim D, Seo W, Hong HG, Song Y, An K. Prescribed nondegenerate high-order modes in an axial-asymmetric high-finesse Fabry-Perot microcavity. OPTICS LETTERS 2012; 37:1457-1459. [PMID: 22555703 DOI: 10.1364/ol.37.001457] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We report an axial-asymmetric high-Q Fabry-Perot cavity supporting nondegenerate Hermite-Gaussian modes of the same mode order. Axial asymmetry of mirror surface was introduced by mechanically grinding off one side of a cylindrical mirror substrate without degrading the original mirror quality. The bases of the resulting Hermite-Gaussian modes were aligned with respect to the direction of grinding, making it possible to prescribe the mirror principal axes.
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Affiliation(s)
- J Kim
- School of Physics and Astronomy, Seoul National University, Seoul, South Korea
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43
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Liertzer M, Ge L, Cerjan A, Stone AD, Türeci HE, Rotter S. Pump-induced exceptional points in lasers. PHYSICAL REVIEW LETTERS 2012; 108:173901. [PMID: 22680867 DOI: 10.1103/physrevlett.108.173901] [Citation(s) in RCA: 106] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2011] [Revised: 01/20/2012] [Indexed: 05/09/2023]
Abstract
We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser nonuniformly. At these singularities, the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In their vicinity, the laser may turn off even when the overall pump power deposited in the system is increased. Such signatures of a pump-induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.
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Affiliation(s)
- M Liertzer
- Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria, EU.
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Dietz B, Harney HL, Kirillov ON, Miski-Oglu M, Richter A, Schäfer F. Exceptional points in a microwave billiard with time-reversal invariance violation. PHYSICAL REVIEW LETTERS 2011; 106:150403. [PMID: 21568534 DOI: 10.1103/physrevlett.106.150403] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2010] [Indexed: 05/30/2023]
Abstract
We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and nonsymmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.
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Affiliation(s)
- B Dietz
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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45
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Kang S, Lim S, Hwang M, Kim W, Kim JR, An K. Controlled generation of single photons in a coupled atom-cavity system at a fast repetition-rate. OPTICS EXPRESS 2011; 19:2440-2447. [PMID: 21369063 DOI: 10.1364/oe.19.002440] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We have demonstrated high-speed controlled generation of single photons in a coupled atom-cavity system. A single 85Rb atom, pumped with a nanosecond-pulse laser, generates a single photon into the cavity mode, and the photon is then emitted out the cavity rapidly. By employing cavity parameters for a moderate coupling regime, the single-photon emission process was optimized for both high efficiency and fast bit rates up to 10 MHz. The temporal single-photon wave packet was studied by means of the photon-arrival-time distribution relative to the pump pulse and the efficiency of the single-photon generation was investigated as the pump power. The single-photon nature of the emission was confirmed by the second-order correlation of emitted photons.
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Affiliation(s)
- Sungsam Kang
- Department of Physics and Astronomy, Seoul National University, Seoul 151-742, South Korea
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46
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Ryu JW, Lee SY. Quasiscarred modes and their branching behavior at an exceptional point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:015203. [PMID: 21405736 DOI: 10.1103/physreve.83.015203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2010] [Indexed: 05/30/2023]
Abstract
We study quasiscarring phenomena and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by short-time ray dynamics near the critical line. As cavity deformation increases, high-Q and low-Q QS modes are branching in opposite ways, at an EP, into two robust mode types showing QS and diamond patterns, respectively. Similar branching behavior can also be found at another EP appearing at a higher deformation. This branching behavior of QS modes has its origin in the fact that an EP is a square-root branch point.
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Affiliation(s)
- Jung-Wan Ryu
- Max-Planck Institute for Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden, Germany
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