Page 18 - Fall2021

TOPOLOGICAL ACOUSTICS
Figure 4. a: Parallel array of three elastically coupled waveguides (aluminum rods glued with epoxy), driven at their ends by piezoelectric transducers (black structures at the bottom right of picture), designed to support acoustic analogues of quantum Bell states (Hasan et al., 2019). b and d: Color maps of the magnitude of the displacement field calculated using the finite-element method in the array of coupled waveguides in separable orbital angular momentum (OAM) and plane wave states. Red and blue, large and low magnitudes of displacement, respectively. Separability is visualized as symmetric color patterns across the array of rods. c: A nonseparable linear combination of waves, each with a different momentum and OAM degrees of freedom. The loss of symmetry in the color pattern across the array of rods is indicative of nonseparability.
quantum phenomena in classical settings. For instance, optical metamaterials have been able to simulate a quan- tum algorithm with electromagnetic waves (Cheng et al., 2020). However, these simulations have relied on wave superposition and interference to realize algorithms that do not require entanglement. In contrast to electromag- netic waves, the stronger nonlinearities and robustness arising in topological acoustics offer unique oppor- tunities to realize nonseparable states for algorithms harnessing entanglement to speed up computational tasks beyond Boolean operations.
Sensing with Topological Sound
Topological acoustic attributes, such as pseudospin as well as amplitude, wavelength, and the frequency of sound, provide access to the global physical properties of a material or of a system. This allows transduction and encoding of infor- mation over a broad range of frequencies and implies the
ability of observing features at multiple length scales and resolutions. Thus, the ability to observe and measure these attributes holds the promise for unparalleled sensitivity and resolution in acoustic-based sensing and imaging. For exam- ple, the emerging literature on the sensitivity to the geometric phase as a form of acoustic pseudospin is already making an impact in the areas of ecological and environmental sciences, aimed at measuring changes in temperature, density, or stiff- ness of the underlying medium. A recent study (Lata et al., 2020) has exploited the sensitivity to the geometric phase of ground-supported long-wavelength acoustic waves, such as seismic waves, in a forest environment, an acoustic medium where trees act as scatterers.
In the era of climate change, melting permafrost poses significant challenges to local Arctic communities. New technologies are needed to provide reliable ways to moni- tor and characterize the global properties of permafrost such as temperature and thawing state. This is vital to the management of natural and built environments in Arctic regions. Current techniques relying on data collected through boreholes and drilling sites produce rough perma- frost maps and are not suitable for continuous monitoring. Also, remote sensing based on aerial and satellite imaging that indirectly measures ground characteristics through the reflection of electromagnetic waves, for example, using LiDAR technology, require a direct field of view and there- fore are not suitable for forested areas. In contrast, the variation of the geometric phase as a function of frequency is experimentally measurable through distributed arrays of ground transducers. These can operate in active mode, according to pulse/echo schemes that employ transmit- ter and receiver transducer pairs, or in a passive modality, whereby the transducers receive and correlate the diffuse acoustic field corresponding to the ambient seismic noise. Through geometric phase monitoring, large detectable changes in phase in response to changes in ground stiff- ness/temperature (up to 3π/1°C have been predicted for frequencies near resonance of trees (Figure 5a).
Topological acoustic attributes may also be employed for monitoring any type of built or natural structures in the broader context of acoustics-based nondestructive test- ing, which is a multibillion industry. For example, recent findings in the field of topological physics have revealed how enhanced sensing may be achieved by exploiting the unprecedented sensitivity around EPs to perturba- tions associated with small changes in physical properties
18 Acoustics Today • Fall 2021