Relativistic motion of an Airy wavepacket in a lattice potential

TL;DR

This paper demonstrates that Airy wavepackets in a lattice potential exhibit relativistic-like dynamics, enabling control and simulation of relativistic quantum phenomena through Floquet engineering.

Contribution

It reveals that lattice-bound Airy wavepackets follow relativistic equations of motion, allowing novel control and simulation of relativistic effects in quantum systems.

Findings

Wavepackets exhibit relativistic equations of motion in lattice potentials.

Lattice control enables mimicking of negative refraction.

Airy wavepackets can simulate relativistic quantum systems.

Abstract

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schr\"odinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.