We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on twoion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows that the distribution rate of entanglement achievable with such an ion-based quantum repeater protocol is higher by orders of magnitude than the rates that are achievable with the best known schemes based on atomic ensemble memories and linear optics. The main reason is that for trapped ions the entanglement swapping operations are performed deterministically, in contrast to success probabilities below 50 percent per swapping with linear optics. The scheme requires efficient collection of the emitted photons, which can be achieved with cavities, and efficient conversion of their wavelength, which can be done via stimulated parametric down-conversion. We also suggest how to realize temporal multiplexing, which offers additional significant speed-ups in entanglement distribution, with trapped ions.

We present the first experimental realization of a two-dimensional quantum gas in a purely magnetic trap dressed by a radio frequency field in the presence of gravity. The resulting potential is extremely smooth and very close to harmonic in the two-dimensional plane of confinement. We fully characterize the trap and demonstrate the confinement of a quantum gas to two dimensions. The trap geometry can be modified to a large extent, in particular in a dynamical way. Taking advantage of this possibility, we study the monopole and the quadrupole modes of a two-dimensional Bose gas.