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，都依赖于对光波导中的光的控制。因此，控制机制的任何改进都会对效果产生很大的影响。直觉上，为了最大化任何光学设备的效率，人们会寻求将吸收和损失降至最低，几十年(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，利用工程损失来主动控制动态的想法才被探索出来，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用来的，该领域被称为非厄米和PT对称量子理论。尽管在过去的十年中，非厄米哈密顿量在波导中产生的量子动力学的实现已经取得了很大的成功，但许多重要的方面仍然没有被探索。特别是在没有损失的情况下，显式时间相关格式的应用很少被研究，因为它的基础数学不是平凡的。为了将应用推向下一个层次，必须理解依赖时间的非厄米量子系统的数学基础，并使物理应用中的实践者能够访问该系统。这项资助的主要目标是分类，然后利用非厄米特哈密顿描述的系统的丰富数学性质，这些系统具有明确的时间依赖参数。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系统中崩溃了。最近，我们能够利用动力系统的语言以及几何和群论的工具，对特定的模型系统取得实质性的进展。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。