Quantum simulation of the Dirac equation

TL;DR

This paper demonstrates a quantum simulation of the one-dimensional Dirac equation using a single trapped ion, enabling observation of relativistic quantum effects like Zitterbewegung and the transition to nonrelativistic dynamics.

Contribution

It introduces a novel method to simulate relativistic quantum effects with high control using trapped ions, bridging theoretical predictions and experimental observation.

Findings

Successful simulation of the Dirac equation in a trapped ion system

Observation of Zitterbewegung for different initial states

Analysis of the transition from relativistic to nonrelativistic regimes

Abstract

The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it is able to reproduce accurately the spectrum of the hydrogen atom and its realm, relativistic quantum mechanics, is considered as the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects such as Klein's paradox and Zitterbewegung, an unexpected quivering motion of a free relativistic quantum particle first examined by Schr\"odinger. These and other predictions would be difficult to observe in real particles, while constituting key fundamental examples to understand relativistic quantum effects. Recent years have seen an increased interest in simulations of relativistic quantum effects in different physical setups, where parameter tunability allows accessibility to different physical regimes. Here, we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion, which is set to behave as a free relativistic quantum particle. We measure as a function of time the particle position and study Zitterbewegung for different initial superpositions of positive and negative energy spinor states, as well as the cross-over from relativistic to nonrelativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate elegant textbook examples of relativistic quantum physics.