Quantum topology with strong light-matter coupling (Ref: 4170)

支撑拓扑物质的数学是一个巨大的和日益增长的兴趣，特别是自2016年诺贝尔物理学奖授予英国理论物理学家索利斯、霍尔丹和科斯特利茨“对拓扑相变和物质拓扑相的理论发现”以来。从本质上讲，拓扑物理学允许人们非常简单地解释复杂系统的行为，通常是通过一些重要的数字：一个所谓的拓扑不变量。著名的例子是著名的量子霍尔效应，材料中的电阻惊人地在某些整数值处趋于稳定。这种有趣的现象可以通过被称为陈氏数的拓扑数来理解。到目前为止，我们只讨论了传统材料，这些材料主要是由它们的组成电子的行为决定的。然而，当光的粒子（光子）在系统中起着重要作用时，我们所知道的就少得多了。在量子纳米光子学领域，我们关注的是纳米尺度材料，其中光-物质相互作用是决定性的。特别地，在强光-物质耦合状态下，电子和光子可能杂交形成新的粒子，同时携带其两个组成部分的理想特性。这为提出的项目奠定了基础，该项目旨在在拓扑量子纳米光子学中取得基础数学进展。也就是说，受到拓扑理论在描述电子系统方面的成功的启发，我们将发展在纳米尺度上描述和利用拓扑光的理论。我们将开发能够描述玻色子粒子（如光）的拓扑不变量，并创建模型来解释拓扑光如何在下一代量子技术中使用，包括量子电路、通信和信息。

The mathematics underpinning topological matter is of a large and growing interest, especiallysince the Nobel Prize in Physics was awarded in 2016 to the British theoretical physicistsThouless, Haldane and Kosterlitz "for theoretical discoveries of topological phase transitionsand topological phases of matter".At its heart, topological physics allows one to explain the behavior of complicated systemsvery simply, usually through some important number: a so-called topological invariant. Afamous example is in the much celebrated quantum Hall effect, where the resistance in thematerial surprisingly plateaus at certain integer values. This intriguing phenomenon can beunderstood elegantly through topological numbers known as Chern numbers.We have so far only talked about conventional materials, which are primarily governed by thebehaviour of their constituent electrons. However, much less is known when it is the particleof light (the photon) which instead plays an important role in the system. In the field ofquantum nanophotonics, we are concerned with nanoscale materials where the light-matterinteraction is decisive. In particular, in the strong light-matter coupling regime, electrons andphotons may hybridize to form a new particle, carrying desirable traits of both of its componentparts.This sets the stage for the proposed project, which aims to make fundamental mathematicaladvances in topological quantum nanophotonics. Namely, inspired by the success of topologicaltheories in describing electronic systems, we will develop theories to describe and exploittopological light at the nanoscale. We will develop topological invariants capable ofdescribing bosonic particles such as light, and create models which explain how topologicallight may be used in the next generation of quantum technology, including quantum circuitry,communications and information.