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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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2
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Zhou L, Zhang DJ. Non-Hermitian Floquet Topological Matter-A Review. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1401. [PMID: 37895522 PMCID: PMC10606436 DOI: 10.3390/e25101401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Revised: 09/19/2023] [Accepted: 09/27/2023] [Indexed: 10/29/2023]
Abstract
The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.
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Affiliation(s)
- Longwen Zhou
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, China
- Key Laboratory of Optics and Optoelectronics, Qingdao 266100, China
- Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE, Qingdao 266100, China
| | - Da-Jian Zhang
- Department of Physics, Shandong University, Jinan 250100, China
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3
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Zhou L, Gu Y. Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:115402. [PMID: 34933286 DOI: 10.1088/1361-648x/ac4530] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Accepted: 12/21/2021] [Indexed: 06/14/2023]
Abstract
Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.
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Affiliation(s)
- Longwen Zhou
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, People's Republic of China
| | - Yongjian Gu
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, People's Republic of China
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Wang K, Li T, Xiao L, Han Y, Yi W, Xue P. Detecting Non-Bloch Topological Invariants in Quantum Dynamics. PHYSICAL REVIEW LETTERS 2021; 127:270602. [PMID: 35061422 DOI: 10.1103/physrevlett.127.270602] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks, revealed through the biorthogonal chiral displacement, and crosschecked with the dynamic spin textures in the generalized quasimomentum-time domain following a quantum quench. Both detection schemes are robust against symmetry-preserving disorders, and yield consistent results with theoretical predictions. Our experiments are performed far away from any boundaries, and therefore underline non-Bloch topological invariants as intrinsic properties of the system that persist in the thermodynamic limit. Our work sheds new light on the experimental investigation of non-Hermitian topology.
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Affiliation(s)
- Kunkun Wang
- Beijing Computational Science Research Center, Beijing 100084, China
- School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China
| | - Tianyu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Lei Xiao
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Yiwen Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, 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, Hefei 230026, China
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China
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5
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Ge H, Xu XY, Liu L, Xu R, Lin ZK, Yu SY, Bao M, Jiang JH, Lu MH, Chen YF. Observation of Acoustic Skyrmions. PHYSICAL REVIEW LETTERS 2021; 127:144502. [PMID: 34652207 DOI: 10.1103/physrevlett.127.144502] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 08/18/2021] [Indexed: 06/13/2023]
Abstract
Despite a long history of studies, acoustic waves are generally regarded as spinless scalar waves, until recent research revealed their rich structures. Here, we report the experimental observation of skyrmion configurations in acoustic waves. We find that surface acoustic waves trapped by a designed hexagonal acoustic metasurface give rise to skyrmion lattice patterns in the dynamic acoustic velocity fields (i.e., the oscillating acoustic air flows). Using an acoustic velocity sensing technique, we directly visualize a Néel-type skyrmion configuration of the acoustic velocity fields. We further demonstrate, respectively, the controllability and robustness of the acoustic skyrmion lattices by tuning the phase differences between the acoustic sources and by introducing local perturbations in our setup. Our study unveils a fundamental acoustic phenomenon that may enable unprecedented manipulation of acoustic waves and may inspire future technologies including advanced acoustic tweezers for the control of small particles.
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Affiliation(s)
- Hao Ge
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
| | - Xiang-Yuan Xu
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Le Liu
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
| | - Rui Xu
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
| | - Zhi-Kang Lin
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Si-Yuan Yu
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Ming Bao
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Jian-Hua Jiang
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Ming-Hui Lu
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing, Jiangsu 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Yan-Feng Chen
- National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing, Jiangsu 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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6
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Qu D, Wang K, Xiao L, Zhan X, Xue P. Experimental demonstration of strong unitary uncertainty relations. OPTICS EXPRESS 2021; 29:29567-29575. [PMID: 34615065 DOI: 10.1364/oe.438774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 08/21/2021] [Indexed: 06/13/2023]
Abstract
Uncertainty relations are one of the most important foundations of quantum physics. In the textbook literatures, uncertainty relations usually refer to the preparation uncertainty. Its original formulation based on variances of two observables limits on the ability to prepare an ensemble of quantum systems for which non-commuting observables will have arbitrary uncertainty. The preparation uncertainty relation has been widely investigated. On the other hand, a unitary operator is a fundamental tenet of quantum theory. Every evolution of a closed quantum system is governed by acting unitary operators on the state of the system and the evolution of an open system can be represented by acting unitary operators on an enlarged system consisting of the quantum system as a subsystem. Therefore, naturally, to understand and quantitatively capture the essence of uncertainty relations for unitary operators is important and timely. Here we report an experimental investigation of a set of uncertainty relations for two unitary operators, which are theoretically derived by using a sequence of fine-grained inequalities. We test these uncertainty relations with single photons and interferometric networks. The unitary uncertainty relation is saturated by any pure qubit state. For higher-dimensional states, it is stronger than the best known bound introduced in the previous literatures. The lower bounds of the unitary uncertainty relations can be even further strengthened by the symmetry of permutation. The experimental findings agree with the predictions of quantum theory and respect the new uncertainty relations.
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Mizoguchi T, Kuno Y, Hatsugai Y. Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:016802. [PMID: 33480756 DOI: 10.1103/physrevlett.126.016802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.
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Affiliation(s)
- Tomonari Mizoguchi
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
| | - Yoshihito Kuno
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
| | - Yasuhiro Hatsugai
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
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8
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Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder. ENTROPY 2020; 22:e22070746. [PMID: 33286522 PMCID: PMC7517290 DOI: 10.3390/e22070746] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Revised: 07/05/2020] [Accepted: 07/06/2020] [Indexed: 11/16/2022]
Abstract
Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants (w0,wπ)∈2Z×2Z. Under the open boundary condition, these invariants further predict the number of zero- and π-quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.
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9
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Gupta SK, Zou Y, Zhu XY, Lu MH, Zhang LJ, Liu XP, Chen YF. Parity-Time Symmetry in Non-Hermitian Complex Optical Media. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1903639. [PMID: 31830340 DOI: 10.1002/adma.201903639] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2019] [Revised: 09/25/2019] [Indexed: 06/10/2023]
Abstract
The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.
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Affiliation(s)
- Samit Kumar Gupta
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Yi Zou
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Xue-Yi Zhu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences, Nanjing University, Nanjing, 210093, P. R. China
| | - Ming-Hui Lu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Li-Jian Zhang
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Xiao-Ping Liu
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
| | - Yan-Feng Chen
- National Laboratory of Solid-State Microstructures, College of Engineering and Applied Sciences and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, P. R. China
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10
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Hu H, Zhao E. Topological Invariants for Quantum Quench Dynamics from Unitary Evolution. PHYSICAL REVIEW LETTERS 2020; 124:160402. [PMID: 32383903 DOI: 10.1103/physrevlett.124.160402] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 03/30/2020] [Indexed: 05/22/2023]
Abstract
Recent experiments began to explore the topological properties of quench dynamics, i.e., the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well-established theory for static band insulators or periodically driven systems, at present it is not clear whether, and how, topological invariants can be defined for a general quench of band insulators. Previous work solved a special case of this problem beautifully using Hopf mapping of two-band Hamiltonians in two dimensions. However, it only works for a topologically trivial initial state and is hard to generalize to multiband systems or other dimensions. Here we introduce the concept of loop unitary constructed from the unitary time-evolution operator and show its homotopy invariant fully characterizes the dynamical topology. For two-band systems in two dimensions, we prove that the invariant is precisely equal to the change in the Chern number across the quench, regardless of the initial state. We further show that the nontrivial dynamical topology manifests as hedgehog defects in the loop unitary and also as winding and linking of its eigenvectors along a curve where dynamical quantum phase transition occurs. This opens up a systematic route to classify and characterize quantum quench dynamics.
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Affiliation(s)
- Haiping Hu
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Erhai Zhao
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
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11
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Xie D, Deng TS, Xiao T, Gou W, Chen T, Yi W, Yan B. Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2020; 124:050502. [PMID: 32083915 DOI: 10.1103/physrevlett.124.050502] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Accepted: 01/15/2020] [Indexed: 05/22/2023]
Abstract
We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.
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Affiliation(s)
- Dizhou Xie
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tian-Shu Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Teng Xiao
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Wei Gou
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tao Chen
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, 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, Hefei 230026, China
| | - Bo Yan
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
- Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Key Laboratory of Quantum Optics, Chinese Academy of Sciences, Shanghai 200800, China
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12
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Xiao L, Wang K, Zhan X, Bian Z, Kawabata K, Ueda M, Yi W, Xue P. Observation of Critical Phenomena in Parity-Time-Symmetric Quantum Dynamics. PHYSICAL REVIEW LETTERS 2019; 123:230401. [PMID: 31868428 DOI: 10.1103/physrevlett.123.230401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Indexed: 06/10/2023]
Abstract
We experimentally simulate nonunitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time- (PT-)symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and PT-broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT-symmetric nonunitary quantum dynamics.
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Affiliation(s)
- Lei Xiao
- Beijing Computational Science Research Center, Beijing 100084, China
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Kunkun Wang
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Xiang Zhan
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Zhihao Bian
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Kohei Kawabata
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - 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, Hefei 230026, China
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China
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13
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Qiu X, Deng TS, Hu Y, Xue P, Yi W. Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench. iScience 2019; 20:392-401. [PMID: 31622880 PMCID: PMC6818370 DOI: 10.1016/j.isci.2019.09.037] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 08/23/2019] [Accepted: 09/24/2019] [Indexed: 11/26/2022] Open
Abstract
We identify dynamic topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time (PT) symmetry. Their occurrences in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the density matrices do not evolve in time. Based on our theoretical formalism characterizing topological properties of non-unitary dynamics, we prove the existence of fixed points for quenches between distinct static topological phases in the PT-symmetry-preserving regime, thus unveiling the interplay between dynamic topological phenomena and PT symmetry. Interestingly, non-Hermiticity of the driving Hamiltonian gives rise to rich dynamic topological phenomena which are different, either qualitatively or quantitatively, from their counterparts in unitary dynamics. Our work sheds light on dynamic topological phenomena in open systems and is readily accessible in experiments.
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Affiliation(s)
- Xingze Qiu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Tian-Shu Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Ying Hu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China.
| | - Peng Xue
- Beijing Computational Science Research Center, Beijing 100084, China; Department of Physics, Southeast University, Nanjing 211189, China; State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, 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, Hefei 230026, China.
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