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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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Oliver C, Mukherjee S, Rechstman MC, Carusotto I, Price HM. Artificial gauge fields in the t- z mapping for optical pulses: Spatiotemporal wave packet control and quantum Hall physics. SCIENCE ADVANCES 2023; 9:eadj0360. [PMID: 37862408 PMCID: PMC10588944 DOI: 10.1126/sciadv.adj0360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 09/18/2023] [Indexed: 10/22/2023]
Abstract
We extend the t-z mapping of time-dependent paraxial optics by engineering a synthetic magnetic vector potential, leading to a nontrivial band topology. We consider an inhomogeneous 1D array of coupled optical waveguides and show that the wave equation describing paraxial propagation of optical pulses can be recast as a Schrödinger equation, including a synthetic magnetic field whose strength can be controlled via the spatial gradient of the waveguide properties across the array. We use an experimentally motivated model of a laser-written array to demonstrate that this synthetic magnetic field can be engineered in realistic setups and can produce interesting physics such as cyclotron motion, a controllable Hall drift of the pulse in space or time, and propagation in chiral edge states. These results substantially extend the physics that can be explored within propagating geometries and pave the way for higher-dimensional topological physics and strongly correlated fluids of light.
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Affiliation(s)
- Christopher Oliver
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| | | | - Mikael C. Rechstman
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Iacopo Carusotto
- Pitaevskii BEC Center, INO-CNR and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
| | - Hannah M. Price
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
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Huang JY, Xu XF, Zhang H, Zhai N, Liu YQ. Topological boundary states of two-dimensional restricted isosceles triangular photonic crystals. APPLIED OPTICS 2022; 61:1254-1260. [PMID: 35201178 DOI: 10.1364/ao.447528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
We propose an all-media photonic crystal (PC) composed of isosceles triangle dielectric cylinders that realizes the topological phase transition by simply rotating the isosceles triangular dielectric cylinders. Additionally, the topological phase transition is closely linked with the size parameters and rotation angle of the isosceles triangle. The topological boundary states with lossless transmission are constructed on the interface of two different topological structures, and the optical quantum spin Hall effect is simulated. Further, we verified that the boundary state is unidirectional and immune to disorder, cavity, and sharp bend defects. By rotating the angle of the triangle to control the transmission path of the pseudo-spin state, we realize diverse transport pathways of light, such as the "straight line" shape, "Z" shape, "U" shape, and "Y" shape. This topological system shows a higher degree of freedom, which can promote the research on topological boundary states and the development of topological insulators in practical applications.
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Afzal S, Zimmerling TJ, Ren Y, Perron D, Van V. Realization of Anomalous Floquet Insulators in Strongly Coupled Nanophotonic Lattices. PHYSICAL REVIEW LETTERS 2020; 124:253601. [PMID: 32639778 DOI: 10.1103/physrevlett.124.253601] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2019] [Accepted: 05/21/2020] [Indexed: 06/11/2023]
Abstract
We experimentally realized Floquet topological photonic insulators using a square lattice of direct-coupled octagonal resonators. Unlike previously reported topological insulator systems based on microring lattices, the nontrivial topological behaviors of our system arise directly from the periodic evolution of light around each octagon to emulate a periodically driven system. By exploiting asynchronism in the evanescent coupling between adjacent octagonal resonators, we could achieve strong and asymmetric couplings in each unit cell, which are necessary for realizing anomalous Floquet insulator behaviors. Direct imaging of scattered light from fabricated samples confirmed the existence of chiral edge states as predicted by the topological phase map of the lattice. In addition, by exploiting the frequency dispersion of the coupling coefficients, we could also observe topological phase changes of the lattice from a normal insulator to Chern and Floquet insulators. Our lattice thus provides a versatile nanophotonic system for investigating 2D Floquet topological insulators.
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Affiliation(s)
- Shirin Afzal
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
| | - Tyler J Zimmerling
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
| | - Yang Ren
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
| | - David Perron
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
| | - Vien Van
- Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4, Canada
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Mukherjee S, Rechtsman MC. Observation of Floquet solitons in a topological bandgap. Science 2020; 368:856-859. [PMID: 32439788 DOI: 10.1126/science.aba8725] [Citation(s) in RCA: 59] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2020] [Accepted: 04/14/2020] [Indexed: 02/01/2023]
Abstract
Topological protection is a universal phenomenon that applies to electronic, photonic, ultracold atomic, mechanical, and other systems. The vast majority of research in these systems has explored the linear domain, where interparticle interactions are negligible. We experimentally observed solitons-waves that propagate without changing shape as a result of nonlinearity-in a photonic Floquet topological insulator. These solitons exhibited distinct behavior in that they executed cyclotron-like orbits associated with the underlying topology. Specifically, we used a waveguide array with periodic variations along the waveguide axis, giving rise to nonzero winding number, and the nonlinearity arose from the optical Kerr effect. This result applies to a range of bosonic systems because it is described by the focusing nonlinear Schrödinger equation (equivalently, the attractive Gross-Pitaevskii equation).
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Affiliation(s)
- Sebabrata Mukherjee
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.
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Wang H, Gupta SK, Xie B, Lu M. Topological photonic crystals: a review. FRONTIERS OF OPTOELECTRONICS 2020; 13:50-72. [PMID: 36641586 PMCID: PMC9743952 DOI: 10.1007/s12200-019-0949-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Accepted: 10/16/2019] [Indexed: 06/13/2023]
Abstract
The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.
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Affiliation(s)
- Hongfei Wang
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Samit Kumar Gupta
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Biye Xie
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Minghui Lu
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210093, China.
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Lv X, Sun C, Ye F, Ma B, Deng D. Statistical properties of a controllable partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherence lattice in anisotropic ocean turbulence. OPTICS EXPRESS 2019; 27:26532-26546. [PMID: 31674533 DOI: 10.1364/oe.27.026532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Accepted: 08/12/2019] [Indexed: 06/10/2023]
Abstract
The optical coherent lattice (OCL) with periodic reciprocity has been previously proposed for free-space information transfer and optical communications. Here, a new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherent lattice (PCRPREGOCL and PCAPREGOCL) is introduced. Based on the extended Huygens-Fresnel principle and the spatial power spectrum of the anisotropic ocean turbulence, the analytical expressions of the average intensity of the PCRPREGOCL and the PCAPREGOCL through the anisotropic ocean turbulence are obtained. The effects of elliptical coefficients, lattice constants, the number of lattice lobes, wavelengths and anisotropic ocean turbulence parameters on the statistical properties of the PCRPREGOCL and the PCAPREGOCL are studied in detail. It is found that each sub-pattern in the PCRPREGOCL maintains a controllable rotation within a certain distance, which plays an important role in resisting the influence of turbulence. When the propagation distance increases, the PCRPREGOCL and the PCAPREGOCL gradually change from two elliptical Gaussian patterns into a coherent array with periodic reciprocity and eventually evolves into a Gaussian-like pattern. Our work provides new thoughts in applying OCL to overcome turbulence influence in underwater optical communication and underwater laser radar.
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Ünal FN, Seradjeh B, Eckardt A. How to Directly Measure Floquet Topological Invariants in Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 122:253601. [PMID: 31347903 DOI: 10.1103/physrevlett.122.253601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 06/10/2023]
Abstract
The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the gaps. We propose a feasible scheme for measuring these winding numbers in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a by-product, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.
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Affiliation(s)
- F Nur Ünal
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
| | - Babak Seradjeh
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Department of Physics, Indiana University, 727 E Third Street, Bloomington, Indiana 47405, USA
| | - André Eckardt
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
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