Modern technological advances combined with new design principles allow for the engineering of media with global degrees of freedom that can be manipulated as if additional synthetic dimensions open up. Based on such principles, the physics of 2D and 4D quantum Hall effect has been accessed from lower physical dimensions. In special cases, a synthetic dimension can be rendered in the physical space and this has been achieved with photonics and cold atomic gases, but acoustics has seen little to no progress in this direction, because acoustic wave-guides cannot be weakly coupled in a continuous fashion.In this work, we present a distinct strategy that functions in the opposite regime, where the wave-guides are replaced by chains of coupled discrete resonators and strong couplings and modulations are also established in the transversal direction. In fact, the strategy we are proposing here can be better described as horizontal acoustic crystals carrying different phason values that are stacked and coupled with each other. By slowly varying the phason along the stacking direction, we demonstrate here that, with such approach, we can explore any continuous orbit inside the phason space, and even control the speed along this path to control the shape of the pumped pattern. As a result, we can render these abstract trajectories, occurring in the synthetic dimensions, on the physical dimension along the stackings. In turn, this enables us to control the propagation of the acoustic modes in space as well as the temporal phases of the signals. In contrast to the previous photonic waveguide&nbsp;experiments, where the samples had to be sliced for data acquisition, our designs enable a "non-demolition"&nbsp;measurement procedure which does not disrupt or alter the wave propagation.With the unprecedented control over the phason, we demonstrate edge-to-edge topological pumping of sound in 1D modulated acoustic crystals, as well as edge-to-edge topological and corner-to-corner topological pumping in 2D modulated acoustic crystals. The higher-order topological corner-to-corner modes &nbsp;in &nbsp;our &nbsp;system &nbsp;are &nbsp;principally &nbsp;different &nbsp;from conventional realizations. We demonstrate for the first time for these type of pumping processes that the topological sound transport is robust against random fluctuations in the resonator couplings. We also demonstrate that the pumping along a given orbit in the phason space occurs only in specific space directions. We delineate the generated 2D and 4D quantum Hall systems by calculating first and second Chern numbers. We also discuss various ways in which we can control these pumping processes and, moreover, we discuss new topological mode steerings in 2D modulated acoustic crystals that are entirely specific to the 4D quantum Hall physics. The principles of synthetic dimensions demonstrated by our work could provide a powerful way for acoustic topological wave steering and open up a new platform to explore higher-order topological matter in dimensions four and higher.

Physical Rendering of Synthetic Spaces for Topological Sound Transport

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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