{"title":"通过广义彼得曼因子检测非赫米提系统中的体例外点和边缘例外点","authors":"Yue-Yu Zou, Yao Zhou, Li-Mei Chen, Peng Ye","doi":"10.1007/s11467-023-1337-8","DOIUrl":null,"url":null,"abstract":"<div><p>Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity. In this paper, we introduce an interesting quantity (denoted as <i>η</i>) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both <i>η</i> and its first-order derivative (denoted as <i>∂η</i>) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of <i>η</i> as a function of the model parameter, which is dubbed “edge state transition”. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points (EPs) in topological edge states. Regarding the discontinuity of <i>∂η</i>, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of <i>∂η</i> and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of <i>∂η</i>, implying the existence of EPs in bulk states.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":573,"journal":{"name":"Frontiers of Physics","volume":null,"pages":null},"PeriodicalIF":6.5000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors\",\"authors\":\"Yue-Yu Zou, Yao Zhou, Li-Mei Chen, Peng Ye\",\"doi\":\"10.1007/s11467-023-1337-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity. In this paper, we introduce an interesting quantity (denoted as <i>η</i>) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both <i>η</i> and its first-order derivative (denoted as <i>∂η</i>) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of <i>η</i> as a function of the model parameter, which is dubbed “edge state transition”. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points (EPs) in topological edge states. Regarding the discontinuity of <i>∂η</i>, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of <i>∂η</i> and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of <i>∂η</i>, implying the existence of EPs in bulk states.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>\",\"PeriodicalId\":573,\"journal\":{\"name\":\"Frontiers of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.5000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Frontiers of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11467-023-1337-8\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11467-023-1337-8","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity. In this paper, we introduce an interesting quantity (denoted as η) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both η and its first-order derivative (denoted as ∂η) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of η as a function of the model parameter, which is dubbed “edge state transition”. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points (EPs) in topological edge states. Regarding the discontinuity of ∂η, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of ∂η and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of ∂η, implying the existence of EPs in bulk states.
期刊介绍:
Frontiers of Physics is an international peer-reviewed journal dedicated to showcasing the latest advancements and significant progress in various research areas within the field of physics. The journal's scope is broad, covering a range of topics that include:
Quantum computation and quantum information
Atomic, molecular, and optical physics
Condensed matter physics, material sciences, and interdisciplinary research
Particle, nuclear physics, astrophysics, and cosmology
The journal's mission is to highlight frontier achievements, hot topics, and cross-disciplinary points in physics, facilitating communication and idea exchange among physicists both in China and internationally. It serves as a platform for researchers to share their findings and insights, fostering collaboration and innovation across different areas of physics.