Klein tunneling and Dirac potentials in trapped ions

TL;DR

This paper demonstrates how to simulate the Dirac equation with various potentials using trapped ions, enabling the study of relativistic quantum effects like Klein tunneling in a controllable quantum system.

Contribution

It introduces a method to engineer scalar and pseudoscalar potentials in a trapped-ion setup for simulating relativistic quantum phenomena.

Findings

Successful simulation of Dirac equation with engineered potentials

Observation of Klein tunneling in a trapped-ion system

High spatial resolution potential engineering achieved

Abstract

We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scaterring and the Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the 1+1 Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states of one ion, while its position and momentum are described by those of a collective motional mode. The second ion is used to build the desired potentials with high spatial resolution.