Quantum simulation of 2D Weyl equation in a magnetic field*

Quantum simulation of relativistic quantum mechanics has been proposed and performed in well-controlled quantum systems like trapped ions. However, previous experiments only study 1D spatial dynamics, while properties like spin dynamics and response to magnetic fields that appear only in higher spatial dimensions remain unexplored. Here we simulate the dynamics of a Weyl particle in 2D, which is a minimal model to demonstrate nontrivial spin dynamics and coupling to external magnetic fields. We show the linear dispersion relation of free Weyl particles and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity can be verified. Our work demonstrates the trapped-ion system as a powerful quantum simulator, and extends its application in particle physics with the additional spatial and spin degrees of freedom.