Collaborative Research: Science and Engineering of Topological Acoustics and Mechanics

传播、干涉和散射是声波和其他机械波波动性的基本表现。几个世纪以来，人类一直利用这些特性在一定程度上控制和操纵声音，例如实现乐器，音乐霍尔斯和耳语画廊。然而，最近在凝聚态物理学中发现了一种基于先进拓扑概念的物质组织新原理。在物理学和工程学的不同分支工作的科学家受到这些概念的激励。通过利用适当设计的复合材料系统的分散中的拓扑约束，可以实现对波传播特性中的扰动具有异常稳定性的高度非局部响应。本项目的目的是将这些概念转化为声学和机械系统。其目标是重新定义对波动现象的理解，并极大地扩展操纵机械波和声波的能力。这项研究的结果将扩大工程工具包，改善机械和声学设备的架构，例如通过减少不同组件（包括换能器，接收器和谐振元件）之间的不良相互作用。这种方法将赋予机械波传播拓扑保护，使单向引导沿着任意形状的路径没有背反射，并使其强大的缺陷和混乱。由于该项目跨越了材料科学、物理学和工程学等多个学科，其多学科性质将产生积极的教育影响。该项目将拓宽背景，并改善参与该项目的学生的准备，而且，由于与包括音乐和声音工程在内的不同学科的广泛重叠，它将扩大代表性不足的少数群体对研究和教育的参与，将拓扑秩序概念应用于声音和机械波的想法在许多科学研究领域开辟了场所，从基础科学到应用物理学和工程学。该研究计划受到量子系统中发现的拓扑鲁棒性的独特性质的启发，设想了可以在人工声晶格和合成弹性介质中设计的拓扑声波，并且不受设备制造或阻抗失配缺陷引起的不必要的散射和背反射的影响。声波和机械波的拓扑序的方法利用了两个基于合成规范场的先进概念。第一种方法依赖于通过施加基于机械或时空调制的角动量偏置来打破时间反演对称性，从而模拟直流磁场的效果。第二种方法依赖于合成自旋-轨道耦合的原理，作用于在具有保留的时间反演对称性的机械系统中设计的伪自旋。基于这两种机制，具有单向和螺旋边缘传输的声学系统和装置的工程是先进的。由于对局部缺陷和无序的固有鲁棒性，各种具有拓扑保护的新型设备将被设计成沿着二维和三维的任意路径引导声音和机械波，从而增加带宽，多路复用，可重构性和声学系统的新型架构。

Propagation, interference and scattering are basic manifestations of the wave nature of acoustic and other mechanical waves. For centuries, humans have used these properties to control and manipulate sound to a certain degree, for instance to realize musical instruments, music halls and whispering galleries. However, a new principle of organization of matter based on advanced topological concepts has been recently discovered in condensed matter physics. Scientists working in different branches of physics and engineering are motivated by these concepts. By exploiting topological constraints in the dispersion of suitably engineered composite material systems, it is possible to realize highly nonlocal responses with unusual stability to perturbations in their wave propagation characteristics. The aim of this project is to translating these concepts to acoustic and mechanical systems. The goals are to redefine the understanding of wave phenomena and to dramatically expand the ability to manipulate mechanical and acoustic waves. Results from this research will expand the engineering toolkit, improving the architecture of mechanical and acoustic devices, for instance by reducing undesirable interactions between different components, including transducers, receivers, and resonant elements. This approach will endow mechanical wave propagation with topological protection, enabling one-way guiding along arbitrarily shaped pathways without back-reflection, and making it robust to defects and disorder. Since this project bridges several disciplines, including material science, physics and engineering, its multi-disciplinary character will have positive educational impact. The project will widen the background and improve the preparation of students involved into this project, and, due to the broad overlap with diverse disciplines, including engineering of music and sound, it will broaden participation of underrepresented minorities in research and education.The idea of applying the concepts of topological order to sound and mechanical waves opens venues in a multitude of scientific fields of research, from basic science to applied physics and engineering. The research plan, inspired by the unique properties of topological robustness discovered in quantum systems, envisions topological acoustic waves that can be engineered in artificial acoustic lattices and synthetic elastic media, and that are immune to unwanted scattering and back-reflection caused by imperfections in device fabrication or impedance mismatch. The approaches to topological order for sound and mechanical waves exploit two advanced concepts based on synthetic gauge fields. The first approach relies on breaking time-reversal symmetry by applying an angular momentum bias based on mechanical or spatio-temporal modulation, emulating the effect of a dc magnetic field. The second approach relies on the principle of synthetic spin-orbital coupling, acting on a pseudo-spin engineered in mechanical systems with preserved time-reversal symmetry. Building upon these two mechanisms, the engineering of acoustic systems and devices with one-way and helical edge transport is advanced. Thanks to the inherent robustness against local defects and disorder, a variety of novel devices with topological protection will be engineered to steer sound and mechanical waves along arbitrary pathways in two and three dimensions, leading to increased bandwidth, multiplexing, reconfigurability and novel architectures for acoustic systems.