Wannier-Stark ladders in one-dimensional elastic systems

TL;DR

This paper demonstrates an elastic system that mimics quantum Wannier-Stark ladders using torsional vibrations, providing new experimental insights into wave localization and amplitude measurement.

Contribution

It introduces a novel elastic realization of Wannier-Stark ladders and measures wave amplitudes directly, which was not possible in previous quantum or optical systems.

Findings

Wave amplitudes are spatially localized.

Measured amplitudes match theoretical predictions.

Elastic rods can localize different frequencies spatially.

Abstract

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa.