Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials

TL;DR

This paper models the Dirac equation in metamaterials to simulate Zitterbewegung, enabling direct experimental probing of the wavefunction through electromagnetic field measurements, and verifies the phenomenon with simulations and analytic solutions.

Contribution

It introduces a dynamic effective Dirac theory in metamaterials linking wavefunction to electromagnetic fields, allowing experimental observation of relativistic quantum effects.

Findings

Zitterbewegung emerges in simulations of the effective theory

The wavefunction can be directly measured via electromagnetic fields

Analytic solutions confirm the simulation results

Abstract

We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the experimental setup, which means that the wavefunction of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion, which ravels the identification of Dirac spinors with single-frequency excitations of the electro-magnetic field in the metamaterial. The characteristic Zitterbewegung is shown to emerge in simulations of the effective theory and we verify this signature with an analytic solution.