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

支撑拓扑学的数学越来越受到人们的关注，特别是自从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，以表彰他们对拓扑相变和拓扑相的理论发现。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，通常是通过一个重要的数字：所谓的拓扑不变量。另一个例子是非常著名的量子霍尔效应，材料中的电阻在某些整数值时出人意料地停滞不前。这一有趣的现象可以通过被称为陈数的拓扑数来优雅地理解。到目前为止，我们只讨论了传统材料，这些材料主要由其组成电子的行为决定。然而，当光的粒子(光子)在系统中扮演重要角色时，我们所知的要少得多。在量子纳米光子学领域，我们关注的是纳米材料，其中光与物质的相互作用是决定性的。特别是，在强光-物质耦合的情况下，电子和光子可能会杂交形成一种新的粒子，携带其两个组成部分的理想特性。这为拟议的项目奠定了基础，该项目旨在拓扑量子纳米光子学的基础数学方面取得进展。也就是说，受拓扑学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用于下一代量子技术，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.