Mimicking quantum tunneling using active mechanical circuits

The striking analogy between the electronic band structure of solids and the frequency dispersion of classical systems inspired the idea of mimicking quantum effects on classical platforms. For example, a great deal of attention was devoted to mimicking quantum topological phenomena, exploiting the band structure properties to achieve unique functionalities such as beam-like narrow waves, which are immune to backscattering from corners, bents, and structural defects. However, an entire class of quantum phenomena related to tunneling remains significantly under-explored for classical waveguiding. This includes Klein tunneling of relativistic particles through potential barriers of arbitrary heights and widths, tunneling of particles across the event horizon of black holes, tunneling of electron pairs through superconducting junctions, and more. The common property of these effects is an unusual and counterintuitive ability of particles to cross gaps, barriers or interfaces, despite this crossing being seemingly forbidden by energy considerations. Here we derive a classical mechanical analogue of two such effects, tunneling through the event horizon and tunneling of non-Hermitian skin modes, which turn out to require structural couplings that violate the rules of classical dynamics. We show how these effects can be precisely realized using active mechanical circuits, which operate in a real-time-controlled closed loop.