Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

Abstract

Strong field processes which occur in intense laser fields are a test area for relativistic quantum field theory, but difficult to study experimentally and theoretically. Thus, modelling relativistic quantum dynamics and therewith the Dirac equation can help to understand quantum field theory. We develop a dynamic description of an effective Dirac theory in metamaterials in which the wave function is modelled by the corresponding electric and magnetic field in the metamaterial. This electromagnetic field can be probed in the experimental setup, which means that the wave function of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion which establishes the identification of Dirac spinors with single-frequency excitations of the electromagnetic field in the metamaterial. We check the validity of our relativistic quantum dynamics simulation by demonstrating the emergence of Zitterbewegung and verifying it with an analytic solution.

Keywords

• Zitterbewegung
• metamaterials
• electrodynamics
• 42.70.Qs
• 78.67.Pt
• 81.05.Xj