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.

从数据传输的医疗应用到量子计算的新技术，许多现代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连锁反应。直观地说，为了最大限度地提高任何光学设备的效率，人们都会寻求最大限度地减少吸收和损耗，几十年来（如果不是几个世纪），这一直是控制方案设计的指导原则。直到最近，人们才探索利用工程损失来主动控制动力学的想法，并带来了大量的新应用。支持这些想法的数学借鉴自非厄米和 PT 对称量子理论领域的基础量子物理学。虽然波导中非厄米哈密顿量产生的量子动力学的实现在过去十年中取得了重大成功，但许多重要方面仍有待探索。特别是在没有损失的情况下非常重要的显式时间相关方案的应用，由于其基础数学并不平凡，因此很少被研究。为了将应用推向新的水平，必须理解时间相关的非厄米量子系统的数学基础，并让物理应用的从业者能够理解它们。该资助的主要目标是对具有明确时间相关参数的非厄米哈密顿量描述的系统进行分类，然后利用其丰富的数学性质。这是一项具有挑战性的任务，因为为大多数厄米系统提供基础的量子绝热定理在非厄米情况下会失效。最近，我们利用动力系统语言以及几何和群论工具，在特定模型系统方面取得了实质性进展。我们将在此基础上实现为下一代非厄米波导应用提供数学基础的愿景。