Quantum simulation of the Klein paradox with trapped ions

TL;DR

This paper demonstrates quantum simulations of relativistic scattering, including Klein tunneling, using trapped ions to encode and visualize Dirac equation dynamics in a controllable quantum system.

Contribution

It introduces a novel method for simulating relativistic quantum scattering with trapped ions, enabling visualization and study of phenomena like Klein tunneling.

Findings

Successful simulation of Dirac dynamics in trapped ions

Visualization of relativistic scattering processes

Extension to complex problems beyond classical computing

Abstract

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.