  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.
