Controlled fast wavepackets in non-Hermitian lattices

TL;DR

This paper demonstrates how non-Hermitian lattices can control and enhance wavepacket group velocities beyond Hermitian limits, using a classical system inspired by quantum models, with experimental validation in topoelectrical metamaterials.

Contribution

It introduces a method to achieve superluminal-like wavepacket propagation in classical non-Hermitian lattices through a quantum-inspired mapping, ensuring stability and experimental realization.

Findings

Group velocity depends on non-Hermiticity parameters, exceeding Hermitian limits.

Square root dependence of group velocity on gain/loss parameter.

Experimental demonstration in topoelectrical metamaterials with embedded operational amplifiers.

Abstract

We report the propagation of fast wavepackets in classical non-Hermitian lattices, where the group velocity is controlled by the non-Hermiticity parameters, and can be made higher than in the Hermitian counterpart. Specifically, we obtain a square root dependence of the group velocity on the gain/loss parameter, similarly to the dependence of quantum wavepackets in stretched graphene-like lattices subjected to gain and loss. We derive a targeted mapping from the quantum to the classical Hamiltonian to realize this phenomenon in a dynamically stable form. As a result, fast wavepackets of any frequency supported by the lattice are propagating in time domain with a non-growing amplitude. We demonstrate the system experimentally in a topoelectrical metamaterial, where the non-Hermiticity is generated by embedded operational amplifiers in a feedback setup. Our design paves the way to realize increased group velocities, and other wave phenomena inspired by quantum systems in a form that preserves the original system properties, while supporting an inherently stable dynamics.