Supersymmetric Isophase Acoustic Potentials

In the quest for manipulating sound propagation, innovative approaches in acoustics, inspired by quantum phenomena, have yielded remarkable functionalities. Despite these advances in acoustics, the potential of supersymmetry, a powerful tool for shaping a system's Hamiltonian, remains untapped. In this Letter, we demonstrate the application of supersymmetric transformations in acoustics through the creation of supersymmetric isophase acoustic potentials. Our theoretical exploration centers on isospectral supersymmetric transformations within an acoustic wave equation framework, enabling the generation of isophase acoustic potentials that preserve both transmission and reflection characteristics. Experimentally, we have developed a reconfigurable acoustic metamaterial platform to validate isophase scattering characteristics facilitated by the principles of supersymmetry. This design strategy offers a general method to create a family of continuously variable acoustic structures that remain indistinguishable under broadband acoustic wave probing, holding great promise for the future of sonar technology.