  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.
