Coherent manipulation of two-dipole-dipole interacting ions

We investigate to what extent two trapped ions can be manipulated coherentl y when their coupling is mediated by a dipole-dipole interaction. We will s how how the resulting level shift induced by this interaction can be used t o create entanglement, while the decay of the states remains nearly negligi ble. This will allow us to implement conditional dynamics (a CNOT gate) and single qubit operations. We propose two different experimental realization s 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 realiza tion.