Quantum entanglement has been focus of fundamental debate since the original paper of Einstein, Podolsky and Rosen [1] and the work of Bell [2], discussing its implications on fundamental issues related to the concepts of physical reality and locality. It has only been during the last few years when it has been recognized that this feature of Quantum Mechanics may also have important applications in the fields of communication and computation. In particular, it has been shown that using entanglement would (...) allow to perform certain computational tasks, such as factoring, much faster. On the other hand, it provides the basis for provably secure secret communication and cryptography. (shrink)

We show that transverse phonons in a set of trapped ions under the action of lasers are described by an interacting boson model whose parameters can be externally adjusted. If the radial trapping frequency is large enough, the system is described by a Bose–Hubbard model, in which hopping of the phonons between different ions is provided by the Coulomb interaction. On the other hand, the non-linear terms in the interaction of the ions with a standing-wave provide us with the phonon–phonon (...) interaction. We investigate the possibility of observing several quantum many—body phenomena, including (quasi)Bose–Einstein Condensation as well as a superfluid-Mott insulator quantum phase transition. (shrink)