Aperiodic quantum optical materials

绝大多数凝聚态物理研究涉及周期性物质——晶体。这是由于这些材料的丰富，以及它们可以被简单地表征。然而，在该学科的前沿，我们发现人工材料的设计和创造，其中非周期结构提供了超越晶体物质的任何可能的进步。一个值得注意的例子是在拓扑量子材料领域，其中“十倍方式”根据某些对称性和它所处的维度数量量化了材料行为的限制。然而，在该方案中，非周期“准晶体”材料已被证明表现得像高维晶体，从而在二维非周期波导阵列中观察到四维量子霍尔效应。光波导已经成为实现新的“非厄米”拓扑物质的主要途径，它与环境积极或耗散地交换能量，导致光增益或损耗。非厄米特征丰富了光子动力学，定义了物质的新拓扑状态。然而，所有的论证都是在周期系统中进行的。本计画涉及新的非周期光子结构的理论设计与实验创造。特别是，学生将探索光子如何在拓扑准晶体中经历增益和损失（经典极限），并将进一步研究相同结构中单光子的动力学（量子极限）。理论工作将涉及非周期环境下基于紧密结合方法的非厄米拓扑材料行为的分析计算，以及非周期结构设计的计算模型的使用。实验工作将涉及非周期波导阵列的创建和表征。

The vast majority of condensed matter physics research concerns periodic matter -- crystals. This is due to both the abundance of such materials, and the simplicity with which they can be characterised. However, at the frontiers of the subject we find the design and creation of artificial materials, where aperiodic structures offer advances beyond anything possible in crystalline matter. A notable example is in the field of topological quantum materials, where the 'tenfold way' quantifies restrictions on a material's behaviour according to certain symmetries and the number of dimensions in which it lives. Yet aperiodic 'quasicrystal' materials have been shown to behave like higher-dimensional crystals in this scheme, leading to the remarkable experimental observation of a four-dimensional quantum Hall effect in a 2D aperiodic waveguide array. Optical waveguides have been the principal route to realising new 'non-Hermitian' topological matter, which exchanges energy with its environment actively or dissipatively leading to optical gain or loss. The non-Hermitian feature enriches the dynamics of photons defining new topological states of matter. However, all demonstrations have been done only in periodic systems.This project concerns the theoretical design, and experimental creation, of new aperiodic photonic structures. In particular, the student will explore how photons travel in topological quasicrystals experiencing gain and loss (classical limit) and will further look at the dynamics of single photons in the same structures (quantum limit). Theoretical work will involve analytical calculations of the behaviour of non-Hermitian topological materials based on a tight-binding approach in aperiodic settings, as well as the use of computational modelling for the design of aperiodic structures. Experimental work will involve the creation and characterization of aperiodic waveguide arrays.