1
|
Liu W, Yan W, Cheng W, Zhang B, Wu B, Zhu H, Chu L, Jia Y, Chen F. Observation of multiple topological bound states in the continuum in the photonic bilayer trimer lattice. OPTICS LETTERS 2024; 49:5587-5590. [PMID: 39353012 DOI: 10.1364/ol.538623] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2024] [Accepted: 09/07/2024] [Indexed: 10/04/2024]
Abstract
A topological bound state in the continuum (TBIC) is a novel topological phase that has attracted significant attention. Different from conventional topological insulators (TIs), where boundary states reside within gaps, TBICs can support unconventional boundary states that remain isolated from the surrounding bulk states. In this work, we experimentally demonstrate multiple TBICs in photonic bilayer trimer lattices using femtosecond laser writing technology. By modulating the interlayer coupling between two trimer chains, we observe the emergence of two distinct types of TBICs. Moreover, we experimentally achieve the coexistence of in-gap topological states and TBICs and demonstrate the transformation between them. Our work unveils new insights into the flexible construction of TBICs, and this method can be easily applied to other one-dimensional topological structures, offering promising avenues for further research.
Collapse
|
2
|
Roy K, Roy S, Basu S. Quasiperiodic disorder induced critical phases in a periodically driven dimerized p-wave Kitaev chain. Sci Rep 2024; 14:20603. [PMID: 39232007 PMCID: PMC11375019 DOI: 10.1038/s41598-024-70995-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 08/22/2024] [Indexed: 09/06/2024] Open
Abstract
The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties.
Collapse
Affiliation(s)
- Koustav Roy
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India.
| | - Shilpi Roy
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India
- Department of Physics, National University of Singapore, 117542, Singapore, Singapore
| | - Saurabh Basu
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India
| |
Collapse
|
3
|
Medina-Vázquez JA, González-Ramírez EY, Murillo-Ramírez JG. Topological Fano-resonance with type-II and type-III corner states. OPTICS LETTERS 2024; 49:3263-3266. [PMID: 38824379 DOI: 10.1364/ol.524980] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Accepted: 05/21/2024] [Indexed: 06/03/2024]
Abstract
Topological corner states have been used to develop topologically robust Fano-resonant systems immune to structural perturbations while preserving the ultra-sensitive profiles under external factors. In this work, we have extended the possibility of obtaining Fano-resonant systems by introducing type-II and type-III corner states with a large modal surface to this class of resonance. Through photonic lattices with low symmetry, such as C2, it is easy to obtain type-II and type-III corner states due to the tailoring of long-range interactions. Subsequently, one can combine topological cavities of type-II and type-III corner modes with topological waveguides obtained from a first-order topological insulating phase. Our results may pave the way to generate devices suitable for creating non-classical light applicable in quantum computing and ultra-sensitive sensors employing large-area topological states.
Collapse
|
4
|
Zhang H, Wang WW, Qiao C, Zhang L, Liang MC, Wu R, Wang XJ, Liu XJ, Zhang X. Topological spin-orbit-coupled fermions beyond rotating wave approximation. Sci Bull (Beijing) 2024; 69:747-755. [PMID: 38331706 DOI: 10.1016/j.scib.2024.01.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Revised: 12/24/2023] [Accepted: 01/15/2024] [Indexed: 02/10/2024]
Abstract
The realization of spin-orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation (RWA). By neglecting the counter-rotating terms, RWA characterizes a single near-resonant spin-orbit (SO) coupling in a two-level system. Here, we propose and experimentally realize a new scheme for achieving a pair of two-dimensional (2D) SO couplings for ultracold fermions beyond RWA. This work not only realizes the first anomalous Floquet topological Fermi gas beyond RWA, but also significantly improves the lifetime of the 2D-SO-coupled Fermi gas. Based on pump-probe quench measurements, we observe a deterministic phase relation between two sets of SO couplings, which is characteristic of our beyond-RWA scheme and enables the two SO couplings to be simultaneously tuned to the optimum 2D configurations. We observe intriguing band topology by measuring two-ring band-inversion surfaces, quantitatively consistent with a Floquet topological Fermi gas in the regime of high Chern numbers. Our study can open an avenue to explore exotic SO physics and anomalous topological states based on long-lived SO-coupled ultracold fermions.
Collapse
Affiliation(s)
- Han Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Wen-Wei Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Chang Qiao
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
| | - Long Zhang
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; Hefei National Laboratory, Hefei 230088, China
| | - Ming-Cheng Liang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Rui Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xu-Jie Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Hefei National Laboratory, Hefei 230088, China; International Quantum Academy, Shenzhen 518048, China.
| | - Xibo Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; Hefei National Laboratory, Hefei 230088, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China.
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Chen Q, Zhang Z, Qin H, Bossart A, Yang Y, Chen H, Fleury R. Anomalous and Chern topological waves in hyperbolic networks. Nat Commun 2024; 15:2293. [PMID: 38480697 PMCID: PMC10937626 DOI: 10.1038/s41467-024-46551-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 03/01/2024] [Indexed: 03/17/2024] Open
Abstract
Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior.
Collapse
Affiliation(s)
- Qiaolu Chen
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Zhe Zhang
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Haoye Qin
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Aleksi Bossart
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, ZJU-UIUC Institute, Zhejiang University, Hangzhou, China
| | - Romain Fleury
- Laboratory of Wave Engineering, School of Electrical Engineering, EPFL, Lausanne, Switzerland.
| |
Collapse
|
7
|
Fritzsche A, Biesenthal T, Maczewsky LJ, Becker K, Ehrhardt M, Heinrich M, Thomale R, Joglekar YN, Szameit A. Parity-time-symmetric photonic topological insulator. NATURE MATERIALS 2024; 23:377-382. [PMID: 38195865 PMCID: PMC11349580 DOI: 10.1038/s41563-023-01773-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Accepted: 11/28/2023] [Indexed: 01/11/2024]
Abstract
Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.
Collapse
Affiliation(s)
- Alexander Fritzsche
- Institute of Physics, University of Rostock, Rostock, Germany
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, Würzburg, Germany
| | | | | | - Karo Becker
- Institute of Physics, University of Rostock, Rostock, Germany
| | - Max Ehrhardt
- Institute of Physics, University of Rostock, Rostock, Germany
| | | | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, Würzburg, Germany
| | - Yogesh N Joglekar
- Department of Physics, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, IN, USA.
| | - Alexander Szameit
- Institute of Physics, University of Rostock, Rostock, Germany.
- Department of Life, Light and Matter, University of Rostock, Rostock, Germany.
| |
Collapse
|
8
|
Wu HC, Xu HS, Xie LC, Jin L. Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:083801. [PMID: 38457698 DOI: 10.1103/physrevlett.132.083801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 01/10/2024] [Indexed: 03/10/2024]
Abstract
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.
Collapse
Affiliation(s)
- H C Wu
- School of Physics, Nankai University, Tianjin 300071, China
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - H S Xu
- School of Physics, Nankai University, Tianjin 300071, China
| | - L C Xie
- School of Physics, Nankai University, Tianjin 300071, China
| | - L Jin
- School of Physics, Nankai University, Tianjin 300071, China
| |
Collapse
|
9
|
Yang J, Li Y, Yang Y, Xie X, Zhang Z, Yuan J, Cai H, Wang DW, Gao F. Realization of all-band-flat photonic lattices. Nat Commun 2024; 15:1484. [PMID: 38374147 PMCID: PMC10876559 DOI: 10.1038/s41467-024-45580-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: 04/07/2023] [Accepted: 01/25/2024] [Indexed: 02/21/2024] Open
Abstract
Flatbands play an important role in correlated quantum matter and have promising applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such methods can only obtain a few flatbands with most bands remaining dispersive. Here we realize all-band-flat photonic lattices of an arbitrary size by precisely controlling the coupling strengths between lattice sites to mimic those in Fock-state lattices. This allows us to go beyond the perturbative regime of strain engineering and group all eigenmodes in flatbands, which simultaneously achieves high band flatness and large usable bandwidth. We map out the distribution of each flatband in the lattices and selectively excite the eigenmodes with different chiralities. Our method paves a way in controlling band structure and topology of photonic lattices.
Collapse
Affiliation(s)
- Jing Yang
- Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou, China
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China
| | - Yuanzhen Li
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China
| | - Yumeng Yang
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China
| | - Xinrong Xie
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China
| | - Zijian Zhang
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China
| | - Jiale Yuan
- Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou, China
| | - Han Cai
- Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou, China
- College of Optical Science and Engineering, Zhejiang University, Hangzhou, China
| | - Da-Wei Wang
- Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou, China.
- College of Optical Science and Engineering, Zhejiang University, Hangzhou, China.
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China.
| | - Fei Gao
- Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou, China.
- ZJU-Hangzhou Global Science and Technology Innovation Center, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China.
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, China.
| |
Collapse
|
10
|
Slager RJ, Bouhon A, Ünal FN. Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems. Nat Commun 2024; 15:1144. [PMID: 38326295 PMCID: PMC10850167 DOI: 10.1038/s41467-024-45302-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 01/18/2024] [Indexed: 02/09/2024] Open
Abstract
While a significant fraction of topological materials has been characterized using symmetry requirements1-4, the past two years have witnessed the rise of novel multi-gap dependent topological states5-9, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium10-15, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an 'anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.
Collapse
Affiliation(s)
- Robert-Jan Slager
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
| | - Adrien Bouhon
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - F Nur Ünal
- TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom.
| |
Collapse
|
11
|
Kim TB, Song H, Huculak P, Van V. Broadband frequency generation by four-wave mixing in an all-bands-flat Floquet-Lieb topological insulator. OPTICS LETTERS 2024; 49:634-637. [PMID: 38300077 DOI: 10.1364/ol.515231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 01/07/2024] [Indexed: 02/02/2024]
Abstract
All-bands-flat topological photonic insulators are photonic lattices with all dispersionless bulk bands separated by nontrivial bandgaps. A distinct feature of these systems is that the edge modes can be excited across the flatband frequencies without scattering into the localized bulk modes, thus allowing the edge mode spectrum to extend beyond the gap size. Here we exploit the wide edge mode spectrum of a Floquet-Lieb topological insulator with all flatbands to achieve broadband frequency generation by four-wave mixing on a topological silicon photonic platform. Our all-bands-flat Floquet insulator is based on a Lieb lattice of microring resonators with perfect couplings, which provides a wide frequency generation bandwidth spanning more than six microring's free spectral ranges. The all-bands-flat microring lattice can also serve as a robust topological platform for other broadband nonlinear processes such as stimulated Raman scattering, frequency comb generation, supercontinuum generation, and soliton propagation based on topologically protected edge modes.
Collapse
|
12
|
Zhang JH, Mei F, Xiao L, Jia S. Dynamical Detection of Topological Spectral Density. PHYSICAL REVIEW LETTERS 2024; 132:036603. [PMID: 38307045 DOI: 10.1103/physrevlett.132.036603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 12/18/2023] [Indexed: 02/04/2024]
Abstract
Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.
Collapse
Affiliation(s)
- Jia-Hui Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| |
Collapse
|
13
|
Ghosh AK, Nag T, Saha A. Generation of higher-order topological insulators using periodic driving. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:093001. [PMID: 37983922 DOI: 10.1088/1361-648x/ad0e2d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 11/20/2023] [Indexed: 11/22/2023]
Abstract
Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.
Collapse
Affiliation(s)
- Arnob Kumar Ghosh
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
| | - Tanay Nag
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
- Department of Physics, BITS Pilani-Hyderabad Campus, Telangana 500078, India
| | - Arijit Saha
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| |
Collapse
|
14
|
Li M, Li C, Yan L, Li Q, Gong Q, Li Y. Fractal photonic anomalous Floquet topological insulators to generate multiple quantum chiral edge states. LIGHT, SCIENCE & APPLICATIONS 2023; 12:262. [PMID: 37914682 PMCID: PMC10620381 DOI: 10.1038/s41377-023-01307-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Revised: 10/08/2023] [Accepted: 10/14/2023] [Indexed: 11/03/2023]
Abstract
Anomalous Floquet topological insulators with vanishing Chern numbers but supporting chiral edge modes are attracting more and more attention. Since the existing anomalous Floquet topological insulators usually support only one kind of chiral edge mode even at a large lattice size, they are unscalable and unapplicable for multistate topological quantum systems. Recently, fractal topological insulators with self-similarity have been explored to support more nontrivial modes. Here, we demonstrate the first experimental realization of fractal photonic anomalous Floquet topological insulators based on dual Sierpinski carpet consisting of directional couplers using the femtosecond laser direct writing. The fabricated lattices support much more kinds of chiral edge states with fewer waveguides and enable perfect hopping of quantum states with near unit transfer efficiency. Instead of zero-dimensional bound modes for quantum state transport in previous laser direct-written topological insulators, we generate multiple propagating single-photon chiral edge states in the fractal lattice and observe high-visibility quantum interferences. These suggest the successful realization of highly indistinguishable single-photon chiral edge states, which can be applied in various quantum operations. This work provides the potential for enhancing the multi-fold manipulation of quantum states, enlarging the encodable quantum information capacity in a single lattice via high-dimensional encoding and many other fractal applications.
Collapse
Affiliation(s)
- Meng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China.
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China.
| | - Chu Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China
| | - Linyu Yan
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China
| | - Qiang Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China
| | - Qihuang Gong
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi, 030006, China
- Hefei National Laboratory, Hefei, 230088, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, 226010, China
| | - Yan Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China.
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing, 100871, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi, 030006, China.
- Hefei National Laboratory, Hefei, 230088, China.
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, 226010, China.
| |
Collapse
|
15
|
Li T, Hu H. Floquet non-Abelian topological insulator and multifold bulk-edge correspondence. Nat Commun 2023; 14:6418. [PMID: 37828030 PMCID: PMC10570273 DOI: 10.1038/s41467-023-42139-z] [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: 04/14/2023] [Accepted: 09/28/2023] [Indexed: 10/14/2023] Open
Abstract
Topological phases characterized by non-Abelian charges are beyond the scope of the paradigmatic tenfold way and have gained increasing attention recently. Here we investigate topological insulators with multiple tangled gaps in Floquet settings and identify uncharted Floquet non-Abelian topological insulators without any static or Abelian analog. We demonstrate that the bulk-edge correspondence is multifold and follows the multiplication rule of the quaternion group Q8. The same quaternion charge corresponds to several distinct edge-state configurations that are fully determined by phase-band singularities of the time evolution. In the anomalous non-Abelian phase, edge states appear in all bandgaps despite trivial quaternion charge. Furthermore, we uncover an exotic swap effect-the emergence of interface modes with swapped driving, which is a signature of the non-Abelian dynamics and absent in Floquet Abelian systems. Our work, for the first time, presents Floquet topological insulators characterized by non-Abelian charges and opens up exciting possibilities for exploring the rich and uncharted territory of non-equilibrium topological phases.
Collapse
Affiliation(s)
- Tianyu Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China
| | - Haiping Hu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China.
| |
Collapse
|
16
|
Arkhipova AA, Zhang Y, Kartashov YV, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Zadkov VN. Observation of π solitons in oscillating waveguide arrays. Sci Bull (Beijing) 2023; 68:2017-2024. [PMID: 37573247 DOI: 10.1016/j.scib.2023.07.048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Revised: 06/23/2023] [Accepted: 07/18/2023] [Indexed: 08/14/2023]
Abstract
Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.
Collapse
Affiliation(s)
- Antonina A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Faculty of Physics, Higher School of Economics, Moscow 105066, Russia
| | - Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices (Ministry of Education), School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | | | - Sergei A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Nikolay N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Ivan V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Alexander A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Sergei P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
| | - Victor O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia
| | - Sergey V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia
| | - Victor N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 108840, Russia; Faculty of Physics, Higher School of Economics, Moscow 105066, Russia
| |
Collapse
|
17
|
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.
Collapse
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
| |
Collapse
|
18
|
Wang N, Ping Wang G. Broadband frequency translation by space-time interface with weak permittivity temporal change. OPTICS LETTERS 2023; 48:4436-4439. [PMID: 37656522 DOI: 10.1364/ol.494957] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 07/31/2023] [Indexed: 09/03/2023]
Abstract
Breaking spatial and temporal homogeneities simultaneously incurs the combination of wavenumber and frequency translations. In this work, broadband frequency translations with both redshifts and blueshifts triggered by a single photonic space-time interface (PSTI) with weak temporal change of permittivity across which a homogeneous medium suddenly becomes a one-dimensional photonic crystal is proposed. Mode conversions induced by the PSTI are analyzed, according to which the frequency translation amplitudes are independent of the change of permittivity and the initial frequency but are given by the product of the phase speed of the homogeneous medium and the spatial modulation frequency of the photonic crystal. Hence, a static field can be partially converted into dynamic fields by imposing the PSTI. Our findings pave the way for the study of PSTIs and provide a new scheme to realize broadband frequency translations.
Collapse
|
19
|
Jin KH, Jiang W, Sethi G, Liu F. Topological quantum devices: a review. NANOSCALE 2023; 15:12787-12817. [PMID: 37490310 DOI: 10.1039/d3nr01288c] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/26/2023]
Abstract
The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.
Collapse
Affiliation(s)
- Kyung-Hwan Jin
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
| | - Wei Jiang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Gurjyot Sethi
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA.
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA.
| |
Collapse
|
20
|
Ren B, Arkhipova AA, Zhang Y, Kartashov YV, Wang H, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Zadkov VN. Observation of nonlinear disclination states. LIGHT, SCIENCE & APPLICATIONS 2023; 12:194. [PMID: 37558694 PMCID: PMC10412544 DOI: 10.1038/s41377-023-01235-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 07/10/2023] [Accepted: 07/14/2023] [Indexed: 08/11/2023]
Abstract
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.
Collapse
Affiliation(s)
- Boquan Ren
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Antonina A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
| | - Yiqi Zhang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
| | - Hongguang Wang
- Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Sergei A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Nikolay N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Ivan V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Alexander A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Sergei P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Victor O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Sergey V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
| | - Victor N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
- Faculty of Physics, Higher School of Economics, Moscow, 105066, Russia
| |
Collapse
|
21
|
Wang Y, Wang HX, Liang L, Zhu W, Fan L, Lin ZK, Li F, Zhang X, Luan PG, Poo Y, Jiang JH, Guo GY. Hybrid topological photonic crystals. Nat Commun 2023; 14:4457. [PMID: 37491343 PMCID: PMC10368673 DOI: 10.1038/s41467-023-40172-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 07/14/2023] [Indexed: 07/27/2023] Open
Abstract
Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.
Collapse
Affiliation(s)
- Yanan Wang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Hai-Xiao Wang
- School of Physical Science and Technology, Guangxi Normal University, Guilin, 541004, China.
| | - Li Liang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Weiwei Zhu
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, 266100, China
| | - Longzhen Fan
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Zhi-Kang Lin
- School of Physical Science and Technology, & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, 215006, China
| | - Feifei Li
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Xiao Zhang
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China
| | - Pi-Gang Luan
- Department of Optics and Photonics, National Central University, Jhongli, 32001, Taiwan
| | - Yin Poo
- School of Electronic Science and Engineering, Nanjing University, Nanjing, 210093, China.
| | - Jian-Hua Jiang
- School of Physical Science and Technology, & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, 215006, China.
- Suzhou Institute for Advanced Reseach, University of Science and Technology of China, Suzhou, 215123, China.
| | - Guang-Yu Guo
- Department of Physics, National Taiwan University, Taipei, 10617, Taiwan.
- Physics Division, National Center for Theoretical Sciences, Taipei, 10617, Taiwan.
| |
Collapse
|
22
|
Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
Collapse
Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
| |
Collapse
|
23
|
Wu J, Ghosh S, Gan Y, Shi Y, Mandal S, Sun H, Zhang B, Liew TCH, Su R, Xiong Q. Higher-order topological polariton corner state lasing. SCIENCE ADVANCES 2023; 9:eadg4322. [PMID: 37224247 DOI: 10.1126/sciadv.adg4322] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 04/20/2023] [Indexed: 05/26/2023]
Abstract
Unlike conventional laser, the topological laser is able to emit coherent light robustly against disorders and defects because of its nontrivial band topology. As a promising platform for low-power consumption, exciton polariton topological lasers require no population inversion, a unique property that can be attributed to the part-light-part-matter bosonic nature and strong nonlinearity of exciton polaritons. Recently, the discovery of higher-order topology has shifted the paradigm of topological physics to topological states at boundaries of boundaries, such as corners. However, such topological corner states have never been realized in the exciton polariton system yet. Here, on the basis of an extended two-dimensional Su-Schrieffer-Heeger lattice model, we experimentally demonstrate the topological corner states of perovskite polaritons and achieved polariton corner state lasing with a low threshold (approximately microjoule per square centimeter) at room temperature. The realization of such polariton corner states also provides a mechanism of polariton localization under topological protection, paving the way toward on-chip active polaritonics using higher-order topology.
Collapse
Affiliation(s)
- Jinqi Wu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Sanjib Ghosh
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
| | - Yusong Gan
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ying Shi
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Subhaskar Mandal
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Handong Sun
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
| | - Timothy C H Liew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
| | - Rui Su
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
- MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
- School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
| | - Qihua Xiong
- Beijing Academy of Quantum Information Sciences, Beijing 100193, P.R. China
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, P.R. China
- Collaborative Innovation Center of Quantum Matter, Beijing, P.R. China
| |
Collapse
|
24
|
Wang S, Qin C, Zhao L, Ye H, Longhi S, Lu P, Wang B. Photonic Floquet Landau-Zener tunneling and temporal beam splitters. SCIENCE ADVANCES 2023; 9:eadh0415. [PMID: 37134159 PMCID: PMC10156109 DOI: 10.1126/sciadv.adh0415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Landau-Zener tunneling (LZT), i.e., the nonadiabatic transition under strong parameter driving in multilevel systems, is ubiquitous in physics, providing a powerful tool for coherent wave control both in quantum and classical systems. While previous works mainly focus on LZT between two energy bands in time-invariant crystals, here, we construct synthetic time-periodic temporal lattices from two coupled fiber loops and demonstrate dc- and ac-driven LZTs between periodic Floquet bands. We show that dc- and ac-driven LZTs display distinctive tunneling and interference characteristics, which can be harnessed to realize fully reconfigurable LZT beam splitter arrangements. As a potential application to signal processing, we realize a 4-bit temporal beam encoder for classical light pulses using a reconfigurable LZT beam splitter network. Our work introduces and experimentally demonstrates a new class of reconfigurable linear optics circuits harnessing Floquet LZT, which may find versatile applications in temporal beam control, signal processing, quantum simulations, and information processing.
Collapse
Affiliation(s)
- Shulin Wang
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Chengzhi Qin
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Lange Zhao
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Han Ye
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Stefano Longhi
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain
| | - Peixiang Lu
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan 430205, China
| | - Bing Wang
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| |
Collapse
|
25
|
Adiyatullin AF, Upreti LK, Lechevalier C, Evain C, Copie F, Suret P, Randoux S, Delplace P, Amo A. Topological Properties of Floquet Winding Bands in a Photonic Lattice. PHYSICAL REVIEW LETTERS 2023; 130:056901. [PMID: 36800474 DOI: 10.1103/physrevlett.130.056901] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
The engineering of synthetic materials characterized by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterized by a winding number. The winding emerges from the breakup of inversion symmetry, and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enriches the variety of topological phases available in lattices subject to Floquet driving and suggests the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.
Collapse
Affiliation(s)
- Albert F Adiyatullin
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Lavi K Upreti
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
| | - Corentin Lechevalier
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Clement Evain
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Francois Copie
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Pierre Suret
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Stephane Randoux
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Pierre Delplace
- ENS de Lyon, CNRS, Laboratoire de physique (UMR CNRS 5672), F-69342 Lyon, France
| | - Alberto Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| |
Collapse
|
26
|
Zhang JY, Yi CR, Zhang L, Jiao RH, Shi KY, Yuan H, Zhang W, Liu XJ, Chen S, Pan JW. Tuning Anomalous Floquet Topological Bands with Ultracold Atoms. PHYSICAL REVIEW LETTERS 2023; 130:043201. [PMID: 36763419 DOI: 10.1103/physrevlett.130.043201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Revised: 11/08/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
The Floquet engineering opens the way to create new topological states without counterparts in static systems. Here, we report the experimental realization and characterization of new anomalous topological states with high-precision Floquet engineering for ultracold atoms trapped in a shaking optical Raman lattice. The Floquet band topology is manipulated by tuning the driving-induced band crossings referred to as band inversion surfaces (BISs), whose configurations fully characterize the topology of the underlying states. We uncover various exotic anomalous topological states by measuring the configurations of BISs that correspond to the bulk Floquet topology. In particular, we identify an unprecedented anomalous Floquet valley-Hall state that possesses anomalous helical-like edge modes protected by valleys and a chiral state with high Chern number.
Collapse
Affiliation(s)
- Jin-Yi Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chang-Rui Yi
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Long Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Rui-Heng Jiao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Kai-Ye Shi
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Huan Yuan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Wei Zhang
- Department of Physics, Renmin University of China, Beijing 100872, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Shuai Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| |
Collapse
|
27
|
Jang J, Jeong M, Lee J, Kim S, Yun H, Rho J. Planar Optical Cavities Hybridized with Low-Dimensional Light-Emitting Materials. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2203889. [PMID: 35861661 DOI: 10.1002/adma.202203889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Revised: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Low-dimensional light-emitting materials have been actively investigated due to their unprecedented optical and optoelectronic properties that are not observed in their bulk forms. However, the emission from low-dimensional light-emitting materials is generally weak and difficult to use in nanophotonic devices without being amplified and engineered by optical cavities. Along with studies on various planar optical cavities over the last decade, the physics of cavity-emitter interactions as well as various integration methods are investigated deeply. These integrations not only enhance the light-matter interaction of the emitters, but also provide opportunities for realizing nanophotonic devices based on the new physics allowed by low-dimensional emitters. In this review, the fundamentals, strengths and weaknesses of various planar optical resonators are first provided. Then, commonly used low-dimensional light-emitting materials such as 0D emitters (quantum dots and upconversion nanoparticles) and 2D emitters (transition-metal dichalcogenide and hexagonal boron nitride) are discussed. The integration of these emitters and cavities and the expect interplay between them are explained in the following chapters. Finally, a comprehensive discussion and outlook of nanoscale cavity-emitter integrated systems is provided.
Collapse
Affiliation(s)
- Jaehyuck Jang
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Minsu Jeong
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Jihae Lee
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Seokwoo Kim
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Huichang Yun
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Junsuk Rho
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
- POSCO-POSTECH-RIST Convergence Research Center for Flat Optics and Metaphotonics, Pohang, 37673, Republic of Korea
| |
Collapse
|
28
|
Photonic Topological Insulator Based on Frustrated Total Internal Reflection in Array of Coupled Prism Resonators. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Total internal reflection occurs at the interface between two media with different refractive indices during propagation of light rays from a medium with a higher refractive index to a medium with a lower refractive index. If the thickness of the second medium is comparable to a specific light wavelength, then total internal reflection is violated partially or completely. Based on the frustrated total internal reflection, herein we discuss a two-dimensional photonic topological insulator in an array consisting of triangular, quadrangular, or hexagonal transparent prism resonators with a narrow gap between them. An array of prism resonators allows topologically stable edge solutions (eigenwaves) similar to those studied in ring resonators. Moreover, total internal reflection occurs at different angles of incidence of light. This makes it possible to obtain a set of fundamentally new edge solutions. The light is presumably concentrated at the surface; however, in the new solutions it penetrates relatively deep into the photonic topological insulator and excites several layers of prisms positioned beyond the surface. Remarkably, the direction of light propagation is precisely biased, and therefore new solutions exhibit lower symmetry than the resonator array symmetry.
Collapse
|
29
|
Petiziol F, Eckardt A. Cavity-Based Reservoir Engineering for Floquet-Engineered Superconducting Circuits. PHYSICAL REVIEW LETTERS 2022; 129:233601. [PMID: 36563197 DOI: 10.1103/physrevlett.129.233601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 09/20/2022] [Accepted: 10/25/2022] [Indexed: 06/17/2023]
Abstract
Considering the example of superconducting circuits, we show how Floquet engineering can be combined with reservoir engineering for the controlled preparation of target states. Floquet engineering refers to the control of a quantum system by means of time-periodic forcing, typically in the high-frequency regime, so that the system is governed effectively by a time-independent Floquet Hamiltonian with novel interesting properties. Reservoir engineering, on the other hand, can be achieved in superconducting circuits by coupling a system of artificial atoms (or qubits) dispersively to pumped leaky cavities, so that the induced dissipation guides the system into a desired target state. It is not obvious that the two approaches can be combined, since reaching the dispersive regime, in which system and cavities exchange excitations only virtually, can be spoiled by driving-induced resonant transitions. However, working in the extended Floquet space and treating both system-cavity coupling as well as driving-induced excitation processes on the same footing perturbatively, we identify regimes, where reservoir engineering of targeted Floquet states is possible and accurately described by an effective time-independent master equation. We successfully benchmark our approach for the preparation of the ground state in a system of interacting bosons subjected to Floquet-engineered magnetic fields in different lattice geometries.
Collapse
Affiliation(s)
- Francesco Petiziol
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, Berlin 10623, Germany
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, Berlin 10623, Germany
| |
Collapse
|
30
|
Park J, Cho H, Lee S, Lee K, Lee K, Park HC, Ryu JW, Park N, Jeon S, Min B. Revealing non-Hermitian band structure of photonic Floquet media. SCIENCE ADVANCES 2022; 8:eabo6220. [PMID: 36206346 PMCID: PMC9544314 DOI: 10.1126/sciadv.abo6220] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
Periodically driven systems are ubiquitously found in both classical and quantum regimes. In the field of photonics, these Floquet systems have begun to provide insight into how time periodicity can extend the concept of spatially periodic photonic crystals and metamaterials to the time domain. However, despite the necessity arising from the presence of nonreciprocal coupling between states in a photonic Floquet medium, a unified non-Hermitian band structure description remains elusive. We experimentally reveal the unique Bloch-Floquet and non-Bloch band structures of a photonic Floquet medium emulated in the microwave regime with a one-dimensional array of time-periodically driven resonators. These non-Hermitian band structures are shown to be two measurable distinct subsets of complex eigenfrequency surfaces of the photonic Floquet medium defined in complex momentum space.
Collapse
Affiliation(s)
- Jagang Park
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Hyukjoon Cho
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Seojoo Lee
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Kyungmin Lee
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Kanghee Lee
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| | - Hee Chul Park
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Jung-Wan Ryu
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Namkyoo Park
- Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Republic of Korea
| | - Sanggeun Jeon
- School of Electrical Engineering, Korea University, Seoul 02841, Republic of Korea
| | - Bumki Min
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
| |
Collapse
|
31
|
Leng B, Van V. N-band photonic Hopf insulators based on 2D microring lattices. OPTICS LETTERS 2022; 47:5128-5131. [PMID: 36181203 DOI: 10.1364/ol.471454] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 09/08/2022] [Indexed: 06/16/2023]
Abstract
Hopf insulators are topological insulators whose topological behavior arises from the nontrivial mapping from a 3D sphere to a 2D sphere, known as the Hopf map. The Hopf map, typically encountered in the study of spinor and Skyrmion systems, is classified topologically by an integer invariant called the Hopf index. Here we show that, owing to the periodic circulation of light inside each microring, a 2D lattice of microring resonators can emulate an N-band photonic Hopf insulator with nontrivial Hopf index. In particular, we show by numerical computation and direct analytical proof that the N-band Hopf index of the microring lattice is identical to its winding number. The result shows that the Hopf index is an alternative topological invariant for classifying 2D microring photonic lattices and establishes a correspondence between the Hopf insulator phase and the anomalous Floquet insulator phase of the lattice. More generally, our work shows that 2D microring lattices can provide a versatile nanophotonic platform for studying non-Abelian topological photonic systems.
Collapse
|
32
|
Li C, Kartashov YV, Konotop VV. Topological Floquet bound states in the continuum. OPTICS LETTERS 2022; 47:5160-5163. [PMID: 36181211 DOI: 10.1364/ol.470762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
A honeycomb array of helical waveguides with zigzag-zigzag edges and a refractive index gradient orthogonal to the edges may support Floquet bound states in the continuum (BICs). The gradient of the refractive index leads to strong asymmetry of the Floquet-Bloch spectrum. The mechanism of creation of such Floquet BICs is understood as emergence of crossings and avoided crossings of the branches supported by spatially limited stripe array. The whole spectrum of a finite array is split into the bulk branches being a continuation of the edge states in the extended zone revealing multiple self-crossings and bulk modes disconnected from the gap states by avoided crossings. Nearly all states in the system are localized due to the gradient, but topological edge states manifest much stronger localization than other states. Such strongly localized Floquet BICs coexist with localized Wannier-Stark-like bulk modes. Robustness of the edge Floquet states is confirmed by their passage through a localized edge defect in the form of a missing waveguide.
Collapse
|
33
|
Photonic topological insulator induced by a dislocation in three dimensions. Nature 2022; 609:931-935. [PMID: 36171384 DOI: 10.1038/s41586-022-05129-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 07/20/2022] [Indexed: 02/01/2023]
Abstract
The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2-4 and are emerging as a promising tool for robust lasers5, quantum devices6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and acoustic waves10-13, where the topological protection in the latter is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14-17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.
Collapse
|
34
|
Zheng S, Man X, Kong ZL, Lin ZK, Duan G, Chen N, Yu D, Jiang JH, Xia B. Observation of fractal higher-order topological states in acoustic metamaterials. Sci Bull (Beijing) 2022; 67:2069-2075. [DOI: 10.1016/j.scib.2022.09.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Revised: 08/20/2022] [Accepted: 09/16/2022] [Indexed: 10/14/2022]
|
35
|
Sheng C, Wang Y, Chang Y, Wang H, Lu Y, Yang Y, Zhu S, Jin X, Liu H. Bound vortex light in an emulated topological defect in photonic lattices. LIGHT, SCIENCE & APPLICATIONS 2022; 11:243. [PMID: 35915073 PMCID: PMC9343378 DOI: 10.1038/s41377-022-00931-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 07/10/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.
Collapse
Affiliation(s)
- Chong Sheng
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yijun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Huiming Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yongheng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Yingyue Yang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Shining Zhu
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Xianmin Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China.
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Hui Liu
- National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu, 210093, China.
| |
Collapse
|
36
|
Jung PS, Pyrialakos GG, Wu FO, Parto M, Khajavikhan M, Krolikowski W, Christodoulides DN. Thermal control of the topological edge flow in nonlinear photonic lattices. Nat Commun 2022; 13:4393. [PMID: 35906224 PMCID: PMC9338248 DOI: 10.1038/s41467-022-32069-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 07/18/2022] [Indexed: 11/29/2022] Open
Abstract
The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics. The nonlinear evolution dynamics in topological photonic lattices is systematically investigated within the framework of optical thermodynamics. This approach allows for the precise prediction of topological currents even under the extreme complexity introduced by nonlinearity.
Collapse
Affiliation(s)
- Pawel S Jung
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
| | - Georgios G Pyrialakos
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Fan O Wu
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Midya Parto
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Mercedeh Khajavikhan
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
| | - Wieslaw Krolikowski
- Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT, 0200, Australia.,Science Program, Texas A&M University at Qatar, Doha, Qatar
| | | |
Collapse
|
37
|
Chen C, Ding X, Qin J, Wu J, He Y, Lu CY, Li L, Liu XJ, Sanders BC, Pan JW. Topological Spin Texture of Chiral Edge States in Photonic Two-Dimensional Quantum Walks. PHYSICAL REVIEW LETTERS 2022; 129:046401. [PMID: 35939012 DOI: 10.1103/physrevlett.129.046401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 06/27/2022] [Indexed: 06/15/2023]
Abstract
Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-spin texture has nontrivial winding. This topological spin winding is protected by a chiral-like symmetry emerging for the low-energy Hamiltonian. Our experiment confirms that two-dimensional anomalous Floquet topological systems exhibit topological spin texture on the boundary, which could inspire novel topology-based spintronic phenomena and devices.
Collapse
Affiliation(s)
- Chao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Xing Ding
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| | - Jian Qin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| | - Jizhou Wu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| | - Yu He
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| | - Xiong-Jun Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Barry C Sanders
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
- Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai Branch, Shanghai 201315, China
- CAS-Alibaba Quantum Computing Laboratory, CAS Centre for Excellence in Quantum Information and Quantum Physics, Shanghai 201315, China
| |
Collapse
|
38
|
Lu M, Reid GH, Fritsch AR, Piñeiro AM, Spielman IB. Floquet Engineering Topological Dirac Bands. PHYSICAL REVIEW LETTERS 2022; 129:040402. [PMID: 35939027 PMCID: PMC9832990 DOI: 10.1103/physrevlett.129.040402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 05/25/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
We experimentally realized a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each with a Floquet winding number. These bands are spin-momentum locked and almost perfectly linear everywhere in the Brillouin zone: a near-ideal realization of the 1D Dirac Hamiltonian. We characterized the Floquet winding number using a form of quantum state tomography, covering the Brillouin zone and following the micromotion through one Floquet period. Last, we altered the modulation timing to lift the topological protection, opening a gap at the Dirac point that grew in proportion to the deviation from the topological configuration.
Collapse
Affiliation(s)
- Mingwu Lu
- Joint Quantum Institute, National Institute of Standards and
Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - G. H. Reid
- Joint Quantum Institute, National Institute of Standards and
Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - A. R. Fritsch
- Joint Quantum Institute, National Institute of Standards and
Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - A. M. Piñeiro
- Joint Quantum Institute, National Institute of Standards and
Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA
| | - I. B. Spielman
- Joint Quantum Institute, National Institute of Standards and
Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
39
|
Karni O, Esin I, Dani KM. Through the Lens of a Momentum Microscope: Viewing Light-Induced Quantum Phenomena in 2D Materials. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022:e2204120. [PMID: 35817468 DOI: 10.1002/adma.202204120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Revised: 06/23/2022] [Indexed: 06/15/2023]
Abstract
Van der Waals (vdW) materials at their 2D limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many 2D semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials are reviewed using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. The advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials are discussed. Then, the future research directions opened by these scientific and instrumental advancements are projected for studying the physics of 2D materials and the opportunities to engineer their band-structure and band-topology by laser fields.
Collapse
Affiliation(s)
- Ouri Karni
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Iliya Esin
- Department of Physics, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Keshav M Dani
- Femtosecond Spectroscopy Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa, 904-0495, Japan
| |
Collapse
|
40
|
Pyrialakos GG, Beck J, Heinrich M, Maczewsky LJ, Kantartzis NV, Khajavikhan M, Szameit A, Christodoulides DN. Bimorphic Floquet topological insulators. NATURE MATERIALS 2022; 21:634-639. [PMID: 35484331 DOI: 10.1038/s41563-022-01238-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.
Collapse
Affiliation(s)
- Georgios G Pyrialakos
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, USA
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Julius Beck
- Institute for Physics, University of Rostock, Rostock, Germany
| | | | | | - Nikolaos V Kantartzis
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece
| | - Mercedeh Khajavikhan
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
| | | | | |
Collapse
|
41
|
Khanikaev AB. More nodes bring more Floquet modes. NATURE MATERIALS 2022; 21:618-619. [PMID: 35641562 DOI: 10.1038/s41563-022-01268-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Affiliation(s)
- Alexander B Khanikaev
- Electrical Engineering and Physics, The City College of New York (USA), New York, NY, USA.
| |
Collapse
|
42
|
Kartashov YV, Arkhipova AA, Zhuravitskii SA, Skryabin NN, Dyakonov IV, Kalinkin AA, Kulik SP, Kompanets VO, Chekalin SV, Torner L, Zadkov VN. Observation of Edge Solitons in Topological Trimer Arrays. PHYSICAL REVIEW LETTERS 2022; 128:093901. [PMID: 35302806 DOI: 10.1103/physrevlett.128.093901] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
We report the experimental observation of nonlinear light localization and edge soliton formation at the edges of fs-laser written trimer waveguide arrays, where transition from nontopological to topological phases is controlled by the spacing between neighboring trimers. We found that, in the former regime, edge solitons occur only above a considerable power threshold, whereas in the latter one they bifurcate from linear states. Edge solitons are observed in a broad power range where their propagation constant falls into one of the topological gaps of the system, while partial delocalization is observed when considerable nonlinearity drives the propagation constant into an allowed band, causing coupling with bulk modes. Our results provide direct experimental evidence of the coexistence and selective excitation in the same or in different topological gaps of two types of topological edge solitons with different internal structures, which can rarely be observed even in nontopological systems. This also constitutes the first experimental evidence of formation of topological solitons in a nonlinear system with more than one topological gap.
Collapse
Affiliation(s)
- Y V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - A A Arkhipova
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- Faculty of Physics, Higher School of Economics, 105066 Moscow, Russia
| | - S A Zhuravitskii
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - N N Skryabin
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - I V Dyakonov
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - A A Kalinkin
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - S P Kulik
- Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - V O Kompanets
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - S V Chekalin
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
| | - L Torner
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
| | - V N Zadkov
- Institute of Spectroscopy, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia
- Faculty of Physics, Higher School of Economics, 105066 Moscow, Russia
| |
Collapse
|
43
|
Timms CI, Sieberer LM, Kolodrubetz MH. Quantized Floquet Topology with Temporal Noise. PHYSICAL REVIEW LETTERS 2021; 127:270601. [PMID: 35061414 DOI: 10.1103/physrevlett.127.270601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 01/28/2021] [Accepted: 12/01/2021] [Indexed: 06/14/2023]
Abstract
Time-periodic (Floquet) drive is a powerful method to engineer quantum phases of matter, including fundamentally nonequilibrium states that are impossible in static Hamiltonian systems. One characteristic example is the anomalous Floquet insulator, which exhibits topologically quantized chiral edge states similar to a Chern insulator, yet is amenable to bulk localization. We study the response of this topological system to time-dependent noise, which breaks the topologically protecting Floquet symmetry. Surprisingly, we find that the quantized response, given by partially filling the fermionic system and measuring charge pumped per cycle, remains quantized up to finite noise amplitude. We trace this robust topology to an interplay between diffusion and Pauli blocking of edge state decay, which we expect should be robust against interactions. We determine the boundaries of the topological phase for a system with spatial disorder numerically through level statistics, and corroborate our results in the limit of vanishing disorder through an analytical Floquet superoperator approach. This approach suggests an interpretation of the state of the system as a non-Hermitian Floquet topological phase. We comment on quantization of other topological responses in the absence of Floquet symmetry and potential experimental realizations.
Collapse
Affiliation(s)
- Christopher I Timms
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Lukas M Sieberer
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | | |
Collapse
|
44
|
Ivanov SK, Kartashov YV, Konotop VV. Floquet defect solitons. OPTICS LETTERS 2021; 46:5364-5367. [PMID: 34724476 DOI: 10.1364/ol.441124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 09/26/2021] [Indexed: 06/13/2023]
Abstract
We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such a configuration represents a line defect in the lattice plane, which is periodically modulated along the propagation direction. In the linear limit, such a system sustains line defect modes, whose number coincides with the number of tilted layers. In the presence of nonlinearity, the branches of defect solitons propagating along the defect line bifurcate from each of the linear defect modes. Depending on the effective dispersion induced by the Floquet spectrum of the system, the bifurcating solitons can be either bright or dark. Dynamics and stability of such solitons are studied numerically.
Collapse
|
45
|
Superior robustness of anomalous non-reciprocal topological edge states. Nature 2021; 598:293-297. [PMID: 34646003 PMCID: PMC8514337 DOI: 10.1038/s41586-021-03868-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 07/29/2021] [Indexed: 11/08/2022]
Abstract
Robustness against disorder and defects is a pivotal advantage of topological systems1, manifested by the absence of electronic backscattering in the quantum-Hall2 and spin-Hall effects3, and by unidirectional waveguiding in their classical analogues4,5. Two-dimensional (2D) topological insulators4-13, in particular, provide unprecedented opportunities in a variety of fields owing to their compact planar geometries, which are compatible with the fabrication technologies used in modern electronics and photonics. Among all 2D topological phases, Chern insulators14-25 are currently the most reliable designs owing to the genuine backscattering immunity of their non-reciprocal edge modes, brought via time-reversal symmetry breaking. Yet such resistance to fabrication tolerances is limited to fluctuations of the same order of magnitude as their bandgap, limiting their resilience to small perturbations only. Here we investigate the robustness problem in a system where edge transmission can survive disorder levels with strengths arbitrarily larger than the bandgap-an anomalous non-reciprocal topological network. We explore the general conditions needed to obtain such an unusual effect in systems made of unitary three-port non-reciprocal scatterers connected by phase links, and establish the superior robustness of anomalous edge transmission modes over Chern ones to phase-link disorder of arbitrarily large values. We confirm experimentally the exceptional resilience of the anomalous phase, and demonstrate its operation in various arbitrarily shaped disordered multi-port prototypes. Our results pave the way to efficient, arbitrary planar energy transport on 2D substrates for wave devices with full protection against large fabrication flaws or imperfections.
Collapse
|
46
|
Yu J, Zhang RX, Song ZD. Dynamical symmetry indicators for Floquet crystals. Nat Commun 2021; 12:5985. [PMID: 34645782 PMCID: PMC8514516 DOI: 10.1038/s41467-021-26092-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Accepted: 09/15/2021] [Indexed: 11/09/2022] Open
Abstract
Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.
Collapse
Affiliation(s)
- Jiabin Yu
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, USA.
| | - Rui-Xing Zhang
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, USA
- Joint Quantum Institute, University of Maryland, College Park, MD, USA
| | - Zhi-Da Song
- Department of Physics, Princeton University, Princeton, NJ, USA
| |
Collapse
|
47
|
Yu D, Peng B, Chen X, Liu XJ, Yuan L. Topological holographic quench dynamics in a synthetic frequency dimension. LIGHT, SCIENCE & APPLICATIONS 2021; 10:209. [PMID: 34620837 PMCID: PMC8497532 DOI: 10.1038/s41377-021-00646-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2021] [Revised: 09/10/2021] [Accepted: 09/14/2021] [Indexed: 05/06/2023]
Abstract
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of nonequilibrium topological invariants is a central issue and usually necessitates the information of quantum dynamics in both the time and momentum dimensions. Here, we propose the topological holographic quench dynamics in synthetic dimension, and also show it provides a highly efficient scheme to characterize photonic topological phases. A pseudospin model is constructed with ring resonators in a synthetic lattice formed by frequencies of light, and the quench dynamics is induced by initializing a trivial state, which evolves under a topological Hamiltonian. Our key prediction is that the complete topological information of the Hamiltonian is encoded in quench dynamics solely in the time dimension, and is further mapped to lower-dimensional space, manifesting the holographic features of the dynamics. In particular, two fundamental time scales emerge in the dynamical evolution, with one mimicking the topological band on the momentum dimension and the other characterizing the residue time evolution of the state after the quench. For this, a universal duality between the quench dynamics and the equilibrium topological phase of the spin model is obtained in the time dimension by extracting information from the field evolution dynamics in modulated ring systems in simulations. This work also shows that the photonic synthetic frequency dimension provides an efficient and powerful way to explore the topological nonequilibrium dynamics.
Collapse
Affiliation(s)
- Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
| | - Bo Peng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
- Shanghai Research Center for Quantum Sciences, 201315, Shanghai, China
- Jinan Institute of Quantum Technology, 250101, Jinan, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, 250358, Jinan, China
| | - Xiong-Jun Liu
- International Center for Quantum Materials and School of Physics, Peking University, 100871, Beijing, China.
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China.
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China.
| |
Collapse
|
48
|
Jiao ZQ, Longhi S, Wang XW, Gao J, Zhou WH, Wang Y, Fu YX, Wang L, Ren RJ, Qiao LF, Jin XM. Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices. PHYSICAL REVIEW LETTERS 2021; 127:147401. [PMID: 34652196 DOI: 10.1103/physrevlett.127.147401] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 08/27/2021] [Indexed: 06/13/2023]
Abstract
Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.
Collapse
Affiliation(s)
- Zhi-Qiang Jiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - 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
| | - Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jun Gao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yu-Xuan Fu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Li Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruo-Jing Ren
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu-Feng Qiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- TuringQ Co., Ltd., Shanghai 200240, China
| |
Collapse
|
49
|
Esin I, Gupta GK, Berg E, Rudner MS, Lindner NH. Electronic Floquet gyro-liquid crystal. Nat Commun 2021; 12:5299. [PMID: 34489409 PMCID: PMC8421454 DOI: 10.1038/s41467-021-25511-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 08/04/2021] [Indexed: 11/26/2022] Open
Abstract
Floquet engineering uses coherent time-periodic drives to realize designer band structures on-demand, thus yielding a versatile approach for inducing a wide range of exotic quantum many-body phenomena. Here we show how this approach can be used to induce non-equilibrium correlated states with spontaneously broken symmetry in lightly doped semiconductors. In the presence of a resonant driving field, the system spontaneously develops quantum liquid crystalline order featuring strong anisotropy whose directionality rotates as a function of time. The phase transition occurs in the steady state of the system achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. We obtain the phase diagram of the system using numerical calculations that match predictions obtained from a phenomenological treatment and discuss the conditions on the system and the external drive under which spontaneous symmetry breaking occurs. Our results demonstrate that coherent driving can be used to induce non-equilibrium quantum phases of matter with dynamical broken symmetry.
Collapse
Affiliation(s)
- Iliya Esin
- Physics Department, Technion, Haifa, Israel.
- Department of Physics, California Institute of Technology, Pasadena, CA, USA.
| | | | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Mark S Rudner
- Center for Quantum Devices and Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | | |
Collapse
|
50
|
Zhang RX, Das Sarma S. Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure. PHYSICAL REVIEW LETTERS 2021; 127:067001. [PMID: 34420352 DOI: 10.1103/physrevlett.127.067001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel Floquet topological quantum phase transitions driving the system into a myriad of exotic Majorana-carrying Floquet topological superconducting phases. Our theory establishes a new paradigm for realizing Floquet chiral topological superconductivity in solid-state systems, which should be experimentally directly accessible.
Collapse
Affiliation(s)
- Rui-Xing Zhang
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
| | - S Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
| |
Collapse
|