Topological concepts for robust directed amplification

稳健定向扩增的拓扑概念

• 批准号: 2895098
• 金额: --
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2895098
• 关键词: Topological; concepts; robust; directed; amplification

Description of Project: Quantum systems can display robust features related to topological properties. These attain precise values that can only change in phase transitions where the states change their topological properties. While the scope of these effects is well understood for electronic and superconducting systems, a much richer range is accounted for photonic and in general bosonic systems. In these systems particles can be created and annihilated, which results in loss, gain, and nonlinearity. Recent years have seen a surge of activity to tailor these bosonic systems to their electronic counterparts, mostly by eliminating the mentioned differences. However, it was soon realised that topological physics extends beyond these mere analogies, leading to experimental demonstrations for laser, microwave resonator arrays, and polaritonic condensates.What is missing is a detailed understanding of the actual scope of these extensions - how to systematically define the topological invariants, and classify systems in the manner achieved in the electronic context. This project tackles this question both generally, as well as practically by examining specific model systems of experimental interest, and inquiring how to increase their robustness for possible applications. The challenge is to fully capture the non-Hermitian, non-reciprocal, and non-linear aspects that characterise these systems. In particular, the project will examine how this interplay unfolds near non-Hermitian spectral degeneracies, known as exceptional points. First, the student will develop a comprehensive framework to evaluate the spectral strength of systems operating in the vicinity of these points, taking the full biorthogonal structure of the involved states into account. These insights will then be applied to nonreciprocal systems, which support a special type of bound state whose biorthogonal states are located at opposite sides of a system, and mediates directed amplification. The ultimate goal is to develop the selfconsistent description of these directed amplifiers, taking quantum noise and nonlinearities into account. This project develops both analytical and numerical modelling skills.

项目简介：量子系统可以显示与拓扑属性相关的健壮特征。这些得到的精确值只能在状态改变其拓扑属性的相变中改变。虽然这些效应的范围对于电子和超导系统是众所周知的，但对于光子系统和一般的玻色子系统来说，这些效应的范围要丰富得多。在这些系统中，粒子可以被产生和湮灭，从而导致损耗、增益和非线性。近年来，针对电子系统定制这些玻色子系统的活动激增，主要是通过消除上述差异。然而，人们很快意识到，拓扑物理超越了这些简单的类比，导致了激光、微波谐振器阵列和极化子凝聚体的实验演示。缺少的是对这些扩展的实际范围的详细了解-如何系统地定义拓扑不变量，并以在电子环境中实现的方式对系统进行分类。这个项目一般地和实际地解决了这个问题，通过检查感兴趣的实验的特定模型系统，并询问如何增加它们对于可能的应用的健壮性。挑战在于完全捕捉这些系统所特有的非厄米特、非互易和非线性方面。特别是，该项目将研究这种相互作用是如何在非厄米光谱简并附近展开的，这些非厄米光谱简并称为例外点。首先，学生将开发一个综合的框架来评估在这些点附近运行的系统的光谱强度，同时考虑到所涉及的态的完全双正交结构。然后，这些洞见将被应用于非互易系统，这些系统支持一种特殊类型的束束态，其双正交态位于系统的相反两边，并中介定向放大。最终目标是发展这些定向放大器的自洽描述，同时考虑量子噪声和非线性。该项目开发了分析和数值建模技能。