Controlling light with non-Hermitian Schrödinger dynamics

用非厄米薛定谔动力学控制光

• 批准号: EP/X032256/1
• 负责人: Eva-Maria Graefe
• 金额: $ 10.19万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX032256%2F1
• 关键词: Controlling; light; non; Hermitian; Schr

Much of modern technology, ranging from medical applications over data transmission to novel technologies for quantum computing, rely on the control of light in optical waveguides. Thus, any improvement in the control mechanisms has a large ripple on effect. Intuitively, to maximise efficiency of any optical device, one would seek to minimise absorption and losses, and for decades (if not centuries) this has been a guiding principle in the design of control schemes. Only fairly recently has the idea of using engineered losses to actively control dynamics been explored, and has led to a spectacular amount of new applications. The mathematics underpinning these ideas is borrowed from fundamental quantum physics from a field known as non-Hermitian and PT-symmetric quantum theory. While the implementation of quantum dynamics generated by non-Hermitian Hamiltonians in waveguides has been a major success story over the last decade, many important aspects remain unexplored. In particular the application of explicitly time-dependent schemes that are of great importance in the absence of losses, has been little investigated, due to its nontrivial underlying mathematics. To propel the applications to the next level, it is imperative that the mathematical foundations of time-dependent non-Hermitian quantum systems are understood and made accessible to practitioners in physical applications. The main goal of this grant is to categorise and then exploit the rich mathematical nature of systems described by non-Hermitian Hamiltonians with explicitly time-dependent parameters. This is a challenging task, since the quantum adiabatic theorem, that provides the foundations of most Hermitian systems, breaks down in the non-Hermitian case. Recently we were able to make substantial progress for specific model systems, using the language of dynamical systems and tools from geometry and group theory. We will build on this to realise the vision of providing the mathematical foundations for next generation non-Hermitian waveguide applications.

从数据传输上的医疗应用到用于量子计算的新技术，许多现代技术都依赖于光学波导中的光的控制。因此，控制机制的任何改进都具有巨大的作用连锁反应。直观地，为了最大程度地提高任何光学设备的效率，人们会寻求最大程度地减少吸收和损失，并且数十年（如果不是几个世纪），这一直是控制方案设计的指导原理。只有最近，只有使用工程损失来积极控制动力学的想法，并导致了大量的新应用程序。这些思想的基础数学是从基本量子物理学中借来的，该量子物理学是从一个名为非热和PT对称量子理论的领域借来的。在过去的十年中，非热汉密尔顿人在波导中产生的量子动态的实施一直是一个重要的成功故事，但许多重要方面仍未得到探索。特别是，由于其非平凡的潜在数学数学，在没有损失的情况下，在没有损失的情况下非常重要的显式依赖时间方案的应用。为了将应用推动到一个新的水平，必须理解与时间相关的非量子量子系统的数学基础，并可以在物理应用中可用于实践者。这项赠款的主要目标是对非热汉密尔顿人描述的系统的丰富数学性质进行分类，然后使用明确的时间依赖性参数描述的系统。这是一项具有挑战性的任务，因为在非赫米特式案例中，量子绝热定理（量子绝热定理）破裂了。最近，我们能够使用几何和群体理论的动态系统和工具的语言对特定模型系统取得了重大进展。我们将在此基础上实现为下一代非富裕波导应用提供数学基础的愿景。