Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions

We propose an experimental scheme to simulate and observe the Klein tunneling of relativistic Maxwell particles with trapped ions. We explore the scattering dynamics of the pseudospin-one Maxwell particles and demonstrate that the scattered state should be a superposition of a reflection state, a localization state, and a transmission state. The probabilities of these states can be analytically obtained by the approach of Landau-Zener transition. We further show that the Maxwell Hamiltonian and the associated scattering dynamics can be mimicked with two trapped ions. The Maxwell spinors are encoded by three internal states of the first ion, the position and momentum are described by those of the motional modes, and the desired linear potential barrier is built by the second ion.