Super-resolution acoustic displacement metrology through topological pairs in orbital meta-atoms

The precise measurement of minute displacements using light is a common practice in modern science and technology. The utilization of sound for precision displacement metrology remains scarce due to the diffraction limit of half-wavelength, while it holds crucial applications in some specific scenarios, such as underwater environments, biological tissues, and complex machinery components. Here, we propose an approach to super-resolution acoustic displacement metrology by introducing the concept of topological pairs in orbital meta-atoms, drawing inspiration from the analogy of Cooper pairs observed in spinful electrons. The topological pairs are conjugately formed to create two distinct pathways in mode space that enable robust generation of interference. This allows the realization of acoustic analogue of Malus's law and thereby enhances the resolution of displacement measurements. By incorporating a spiral twist configuration in orbital meta-atoms, we demonstrate the first acoustic prototype of a physical micrometer tailored for micron-scale displacement metrology. We observe experimentally a displacement resolving power of 1.2 μm at an audible frequency of 3.43 kHz, approximately 1/10⁵ of the sound wavelength of 100 mm. Our work implies a new paradigm for precise displacement metrology within classical wave physics and lays the foundation for diverse acoustic applications.