Photonic realization of the kappa-deformed Dirac equation

TL;DR

This paper demonstrates how to implement a kappa-deformed Dirac equation using photonic waveguide arrays, allowing experimental simulation of noncommutative spacetime effects like Zitterbewegung.

Contribution

It introduces a novel photonic setup with tailored couplings to simulate kappa-deformed Dirac physics in a controllable experimental platform.

Findings

Successful simulation of kappa-deformed Dirac equation in photonic arrays

Control of wave packet dynamics via geometric manipulation of couplings

Observation of deformation effects on Zitterbewegung motion

Abstract

We show an implementation of a kappa-deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to recreate the effects of a flat noncommutative spacetime -i.e., kappa-Minkowski spacetime -in simple experimental setups. We touch upon elastic realizations in the section of Conclusions.