# Optical simulation of the free Dirac equation

## TL;DR

This paper demonstrates a classical optics setup that simulates the one-dimensional Dirac equation, allowing observation of relativistic quantum phenomena like zitterbewegung using tunable optical components.

## Contribution

It introduces a novel optical simulation method for the Dirac equation that does not require specially engineered media, enabling study of relativistic effects in a controllable classical system.

## Key findings

- Observed zitterbewegung oscillations in the optical setup
- Measured mean-position operator without oscillations
- Demonstrated tunable simulation of relativistic quantum phenomena

## Abstract

We present a classical optics simulation of the one-dimensional Dirac equation for a free particle. Positive and negative energy components are represented by orthogonal polarizations of a free propagating beam, while the spatial profile represents the spatial wave function of the particle. Using a completely tunable time parameter, we observed the oscillation of the average value of the Dirac position operator - known as zitterbewegung (ZB). We are also able to measure the so called mean-position operator which is a single-particle observable and presents no oscillations. Our work opens the way for optical simulation of interesting phenomenon of relativistic systems, as well as condensed-matter physics, without any requirement for specially engineered medium.