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的波动性质的基本表现。几个世纪以来，人类已经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，音乐厅和低语画廊。然而，最近在凝聚态物理中发现了一种基于先进拓扑概念的新的物质组织原理。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。通过利用适当工程复合材料系统色散中的拓扑约束，可以实现对其波传播特性扰动具有异常稳定性的高度非局部响应。这个项目的目的是将这些概念转化为声学和机械系统。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展工程工具包，改进机械和声学设备的结构，例如通过减少不同组件之间的不良相互作用，包括换能器、接收器和谐振元件。这种方法将赋予机械波传播以拓扑保护，使其能够沿着任意形状的路径进行单向引导而没有反向反射，并使其对缺陷和无序具有鲁棒性。由于该项目是材料科学、物理和工程等多学科的桥梁，其多学科性质将产生积极的教育影响。该项目将扩大背景并改善参与该项目的学生的准备工作，并且由于与不同学科（包括音乐和声音工程）的广泛重叠，它将扩大代表性不足的少数民族在研究和教育中的参与。将拓扑秩序的概念应用于声音和机械波的想法在从基础科学到应用物理和工程的众多科学研究领域开辟了场所。该研究计划受到量子系统中发现的拓扑鲁棒性的独特特性的启发，设想拓扑声波可以在人工声晶格和合成弹性介质中设计，并且不受器件制造缺陷或阻抗不匹配引起的不必要的散射和反向反射的影响。声波和机械波的拓扑顺序研究方法利用了基于合成规范场的两个先进概念。第一种方法依赖于通过应用基于机械或时空调制的角动量偏置来打破时间反转对称性，模拟直流磁场的影响。第二种方法依赖于合成自旋-轨道耦合原理，作用于机械系统中保留时间反转对称性的伪自旋。在这两种机制的基础上，提出了具有单向和螺旋边缘传输的声学系统和装置的工程。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器件将被设计成沿着二维和三维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.