Towards linear phononics and non-locality tests in ion traps

The possibility to manipulate the "transverse" motional degrees of freedom of trapped ions is explored in detail. In particular, it is shown that, if local control of the trapping frequencies is achieved, one can reproduce the full toolbox of linear optics on transverse phonon modes. Furthermore, assuming only global control of the trapping potential, unprecedented degrees of continuous variable entanglement can be obtained and nonlocality tests with massive degrees of freedom can be carried out.