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Longhi S. Non-Hermitian dynamical topological winding in photonic mesh lattices. OPTICS LETTERS 2024; 49:3672-3675. [PMID: 38950237 DOI: 10.1364/ol.529632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Accepted: 06/05/2024] [Indexed: 07/03/2024]
Abstract
Topological winding in non-Hermitian systems is generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models, topological winding naturally arises from the dynamical evolution of the system and is related to a new form of geometric phase. Here we investigate dynamical topological winding in non-Hermitian photonic mesh lattices, where the mean survival time of an optical pulse circulating in coupled fiber loops is quantized and robust against Hamiltonian deformations. The suggested photonic model could provide an experimentally accessible platform for the observation of non-Hermitian dynamical topological windings.
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Longhi S. Incoherent non-Hermitian skin effect in photonic quantum walks. LIGHT, SCIENCE & APPLICATIONS 2024; 13:95. [PMID: 38658541 PMCID: PMC11043335 DOI: 10.1038/s41377-024-01438-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Revised: 03/08/2024] [Accepted: 03/25/2024] [Indexed: 04/26/2024]
Abstract
The non-Hermitian skin effect describes the concentration of an extensive number of eigenstates near the boundaries of certain dissipative systems. This phenomenon has raised a huge interest in different areas of physics, including photonics, deeply expanding our understanding of non-Hermitian systems and opening up new avenues in both fundamental and applied aspects of topological phenomena. The skin effect has been associated to a nontrivial point-gap spectral topology and has been experimentally demonstrated in a variety of synthetic matter systems, including photonic lattices. In most of physical models exhibiting the non-Hermitian skin effect full or partial wave coherence is generally assumed. Here we push the concept of skin effect into the fully incoherent regime and show that rather generally (but not universally) the non-Hermitian skin effect persists under dephasing dynamics. The results are illustrated by considering incoherent light dynamics in non-Hermitian photonic quantum walks.
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Affiliation(s)
- Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133, Milano, Italy.
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, E-07122, Palma de Mallorca, Spain.
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Hu YM, Wang HY, Wang Z, Song F. Geometric Origin of Non-Bloch PT Symmetry Breaking. PHYSICAL REVIEW LETTERS 2024; 132:050402. [PMID: 38364141 DOI: 10.1103/physrevlett.132.050402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 11/05/2023] [Accepted: 01/03/2024] [Indexed: 02/18/2024]
Abstract
The parity-time (PT) symmetry of a non-Hermitian Hamiltonian leads to real (complex) energy spectrum when the non-Hermiticity is below (above) a threshold. Recently, it has been demonstrated that the non-Hermitian skin effect generates a new type of PT symmetry, dubbed the non-Bloch PT symmetry, featuring unique properties such as high sensitivity to the boundary condition. Despite its relevance to a wide range of non-Hermitian lattice systems, a general theory is still lacking for this generic phenomenon even in one spatial dimension. Here, we uncover the geometric mechanism of non-Bloch PT symmetry and its breaking. We find that non-Bloch PT symmetry breaking occurs by the formation of cusps in the generalized Brillouin zone (GBZ). Based on this geometric understanding, we propose an exact formula that efficiently determines the breaking threshold. Moreover, we predict a new type of spectral singularities associated with the symmetry breaking, dubbed non-Bloch van Hove singularity, whose physical mechanism fundamentally differs from their Hermitian counterparts. This singularity is experimentally observable in linear responses.
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Affiliation(s)
- Yu-Min Hu
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Hong-Yi Wang
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Zhong Wang
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
| | - Fei Song
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China
- Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences, Beijing, 100190, China
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Lin Q, Yi W, Xue P. Manipulating directional flow in a two-dimensional photonic quantum walk under a synthetic magnetic field. Nat Commun 2023; 14:6283. [PMID: 37805651 PMCID: PMC10560269 DOI: 10.1038/s41467-023-42045-4] [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: 02/17/2023] [Accepted: 09/28/2023] [Indexed: 10/09/2023] Open
Abstract
Matter transport is a fundamental process in nature. Understanding and manipulating flow in a synthetic media often have rich implications for modern device design. Here we experimentally demonstrate directional transport of photons in a two-dimensional quantum walk, where the light propagation is highly tunable through dissipation and synthetic magnetic flux. The directional flow hereof underlies the emergence of the non-Hermitian skin effect, with its orientation continuously adjustable through the photon-loss parameters. By contrast, the synthetic magnetic flux originates from an engineered geometric phase, which, by inducing localized cyclotron orbits, suppresses the bulk flow through magnetic confinement. We further demonstrate how the directional flow and synthetic flux impact the dynamics of the Floquet topological edge modes along an engineered boundary. Our results exemplify an intriguing strategy for engineering directed light transport, highlighting the interplay of non-Hermiticity and gauge fields in synthetic systems of higher dimensions.
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Affiliation(s)
- Quan Lin
- Beijing Computational Science Research Center, 100084, Beijing, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, 230026, Hefei, China.
| | - Peng Xue
- Beijing Computational Science Research Center, 100084, Beijing, China.
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Li Z, Luo XW, Lin D, Gharajeh A, Moon J, Hou J, Zhang C, Gu Q. Topological Microlaser with a Non-Hermitian Topological Bulk. PHYSICAL REVIEW LETTERS 2023; 131:023202. [PMID: 37505939 DOI: 10.1103/physrevlett.131.023202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 05/25/2023] [Indexed: 07/30/2023]
Abstract
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.
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Affiliation(s)
- Zhitong Li
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Dayang Lin
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Abouzar Gharajeh
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Jiyoung Moon
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chuanwei Zhang
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Qing Gu
- Department of Electrical and Computer Engineering, The University of Texas at Dallas, Richardson, Texas 75080, USA
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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Wang HY, Zhao XM, Zhuang L, Liu WM. Non-Floquet engineering in periodically driven dissipative open quantum systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:365402. [PMID: 35760065 DOI: 10.1088/1361-648x/ac7c4e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 06/27/2022] [Indexed: 06/15/2023]
Abstract
Floquet engineering plays a key role in realizing novel dynamical topological states. The conventional Floquet engineering, however, only applies to time-periodic non-dissipative Hermitian systems, and for the open quantum systems, non-Hermitian processes usually occur. So far, it remains unclear how to characterize the topological phases of time-periodic open quantum systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to solve the problem and illustrate it by a continuously time-periodic non-Hermitian bipartite chain. In non-Floquet theory, a temporal non-unitary transformation is exercised on the Floquet states, and the transformed Floquet spectrum restores the form of the Wannier-Stark ladder. Besides, we also show that different choices of the starting points of the driving period can result in different localization behavior, effects of which can reversely be utilized to design quantum detectors of phases in dissipative oscillating fields. Our methods are capable of describing topological features in dynamical open quantum systems with various driving types and can find its applications to construct new types of dynamical topological materials.
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Affiliation(s)
- Huan-Yu Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Xiao-Ming Zhao
- Department of Physics, Institute of Theoretical physics, University of Science and Technology Beijing, Beijing, 100083, People's Republic of China
| | - Lin Zhuang
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
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Longhi S. Non-Hermitian topological mobility edges and transport in photonic quantum walks. OPTICS LETTERS 2022; 47:2951-2954. [PMID: 35709023 DOI: 10.1364/ol.460484] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 05/20/2022] [Indexed: 06/15/2023]
Abstract
In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in the complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e., the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e., asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice: while ballistic transport is allowed in the former case, pseudo-dynamical localization is observed in the latter case. The results are illustrated by considering non-Hermitian photonic quantum walks in synthetic mesh lattices.
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Longhi S. Selective and tunable excitation of topological non-Hermitian quasi-edge modes. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0927] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially localized states, dubbed non-Hermitian quasi-edge modes. Quasi-edge states arise rather generally in systems displaying the non-Hermitian skin effect and can be predicted from the non-trivial topology of the energy spectrum under periodic boundary conditions via a bulk-edge correspondence. However, the selective excitation of the system in one among the infinitely many topological quasi-edge states is challenging both from practical and conceptual viewpoints. In fact, in any realistic system with a finite lattice size most of the quasi-edge states collapse and become metastable states. Here we suggest a route toward the selective and tunable excitation of topological quasi-edge states that avoids the collapse problem by emulating semi-infinite lattice boundaries via tailored on-site potentials at the edges of a finite lattice. We illustrate such a strategy by considering a non-Hermitian topological interface obtained by connecting two Hatano–Nelson chains with opposite imaginary gauge fields, which is amenable for a full analytical treatment.
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Affiliation(s)
- Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, Italy
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, Palma de Mallorca 07122, Spain
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Longhi S. Self-Healing of Non-Hermitian Topological Skin Modes. PHYSICAL REVIEW LETTERS 2022; 128:157601. [PMID: 35499878 DOI: 10.1103/physrevlett.128.157601] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 01/21/2022] [Accepted: 03/22/2022] [Indexed: 06/14/2023]
Abstract
A unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e., the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries. Unlike extended Bloch waves in Hermitian systems, the skin modes are normalizable eigenstates of the Hamiltonian that originate from the intrinsic non-Hermitian point-gap topology of the Bloch band energy spectra. Here, we unravel a fascinating property of NH skin modes, namely self-healing, i.e., the ability to self-reconstruct their shape after being scattered off by a space-time potential.
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Affiliation(s)
- Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy and IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
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