Relativistic motion of an Airy wave packet in a lattice potential

Abstract

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