  We investigate to what extent two trapped ions can be manipulated coherently
when their coupling is mediated by a dipole-dipole interaction. We will show
how the resulting level shift induced by this interaction can be used to create
entanglement, while the decay of the states remains nearly negligible. This
will allow us to implement conditional dynamics (a CNOT gate) and single qubit
operations. We propose two different experimental realisations where a large
level shift can be achieved and discuss both the strengths and weaknesses of
this scheme from the point of view of a practical realization.
