Liouvillian analysis of dynamics at exceptional points incorporating quantum jumps

结合量子跃迁的特殊点动力学的刘维尔分析

• 批准号: 22K03473
• 负责人: ガーモン サバンナスターリング
• 金额: $ 2.66万
• 依托单位: Osaka Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2022
• 资助国家: 日本
• 起止时间: 2022-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22K03473/
• 关键词: exceptional point; microscopic dynamics; structured reservoir; topological insulator; Lindblad; Exceptional point; non-Markovian dynamics; Lindblad operator; non-Hermitian physics; quantum jump

In this year, I have made progress on two tracks related to the dynamical problem at the exceptional point. While the original intention was to focus on the exceptional point dynamics at the level of the Liouvillian, I have found a new discovery that redirects my focus somewhat. I have found an extension of a simple model for a topological insulator that gives rise to an exceptional point with unique properties.Usually the model for a topological insulator is finite and exhibits edge states (or zero-energy modes) that have nearly zero energy eigenvalue and act as conducting surface states despite that the bulk of the system behaves as a conductor. These states are partially protected against disorder. I have found that by taking a semi-infinite extension of the Su-Schrieffer-Heeger (SSH) model, which has alternating couplings along a 1-D lattice, I can obtain an edge state with eigenvalue exactly zero such that the protection against disorder is maximized. Further, by introducing an impurity at the endpoint of the system, I can show that two new parameter regimes appear that have no correspondence in the uniform lattice. Further, all of the eigenvalues appear inside the bulk gap in these two regions, which are separated from the 'trivial' parameter space by an exceptional point that has topological properties.On a separate track, I have also made some preliminary progress on the problem of writing the Lindblad equation for a simple system and will consider how to extend this to incorporate quantum jumps at exceptional point in future work.

这一年，我在与特异点动力学问题相关的两个轨道上取得了进展。 虽然最初的目的是关注刘维尔水平的特殊点动力学，但我发现了一个新发现，在某种程度上改变了我的注意力。 我发现了拓扑绝缘体简单模型的扩展，它产生了具有独特属性的例外点。通常拓扑绝缘体的模型是有限的，并且表现出能量特征值接近零的边缘态（或零能量模式），并且尽管系统的大部分表现为导体，但仍充当导电表面态。 这些州受到部分保护，免受混乱。 我发现，通过采用 Su-Schrieffer-Heeger (SSH) 模型的半无限扩展（该模型沿一维晶格具有交替耦合），我可以获得特征值恰好为零的边缘态，从而最大限度地防止无序。 此外，通过在系统的端点引入杂质，我可以证明出现了两个新的参数状态，它们在均匀晶格中没有对应关系。 此外，所有特征值都出现在这两个区域的体间隙内，它们通过具有拓扑性质的异常点与“平凡”参数空间分开。在单独的轨道上，我还在为简单系统编写 Lindblad 方程的问题上取得了一些初步进展，并将考虑如何扩展它以在未来的工作中纳入异常点处的量子跃迁。