Towards linear phononics and nonlocality tests in ion traps

We explore the possibility to manipulate massive, i.e. motional, degrees of freedom of trapped ions. In particular, we demonstrate that, if local control of the trapping frequencies is achieved, one can reproduce the full toolbox of linear optics on radial modes. Furthermore, assuming only global control of the trapping potential, we show that unprecedented degrees of continuous variable entanglement can be obtained and that nonlocality tests with massive degrees of freedom can be carried out.