Harmonic non-Hermitian skin effect

The non-Hermitian skin effect (NHSE), an exotic phenomenon of localization at the boundary, has recently drawn extensive attention and Floquet engineering offers a powerful approach to expanding its scope. The fundamental role of harmonic response in Floquet systems has nonetheless yet to be elucidated. Here, we introduce the concept of harmonic NHSE and demonstrate it experimentally in an acoustic platform. Within our theoretical framework, we demonstrate that incorporating dynamic couplings into the paradigmatic Hatano-Nelson model causes a single-frequency input to generate multiple harmonics with diverse skin morphologies, each dictated by the underlying spectral winding topology at its respective frequency. Experimentally, we implement the requisite dynamic couplings in an acoustic lattice via programmable unidirectional couplers. By simply reconfiguring the excitation and modulation frequencies, we demonstrate controllable switching of unipolar and bipolar harmonic NHSEs, which exhibit uniform and opposite sound gathering toward the sample boundaries, respectively. By introducing the class of harmonic NHSE, our work sets the stage for further investigating non-Hermitian physics with harmonic effects.