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.

许多现代技术，从数据传输的医疗应用到量子计算的新技术，都依赖于光波导中的光控制。因此，控制机制的任何改进都会产生很大的涟漪。直觉上，为了最大限度地提高任何光学设备的效率，人们会寻求最小化吸收和损耗，几十年来（如果不是几个世纪的话），这一直是控制方案设计的指导原则。直到最近，人们才开始探索使用工程损失来主动控制动态的想法，并导致了大量的新应用。支撑这些想法的数学是从基础量子物理学中借来的，该领域被称为非厄米和PT对称量子理论。在过去的十年里，在波导中实现由非厄米哈密顿产生的量子动力学已经是一个重大的成功故事，但许多重要的方面仍然没有探索。特别是显式时间依赖计划的应用是非常重要的损失的情况下，一直很少调查，由于其非平凡的基础数学。为了将应用推进到下一个水平，必须理解时间相关的非厄米量子系统的数学基础，并使物理应用的从业者能够访问。该补助金的主要目标是分类，然后利用丰富的数学性质的系统所描述的非厄米哈密顿与明确的时间相关的参数。这是一个具有挑战性的任务，因为量子绝热定理，提供了大多数厄米特系统的基础，在非厄米特的情况下失败。最近，我们能够取得实质性的进展，为特定的模型系统，使用语言的动力系统和工具，从几何和群论。我们将以此为基础，实现为下一代非厄米波导应用提供数学基础的愿景。