Abstract
The seventh lesson focused on the collective manipulation of ions in a linear trap (Boulder group experiments). The description of N symmetrically manipulated ions as an angular momentum J = N/2 was recalled. The states of this angular momentum (Dicke states) were analyzed. The preparation of GHZ states by the action of an effective Hamiltonian in Jy2 was described. Two ways of realizing this Hamiltonian through collective ion addressing have been proposed. A GHZ state preparation experiment with 4,5 and 6 ions was dissected (Boulder experiment). The lecture concluded with a discussion of the successes and limitations of quantum information experiments with ions, and a brief introduction to quantum information with ultra-cold, trapped neutral atoms. In addition to the "bottom-up" approach of trapped ions, there is also a "top-down" approach of building qubit arrays by starting with a sample consisting of a large number of very cold atoms (Bose-Einstein condensate) and ordering these atoms in an optical lattice. These systems will be described in the 2006-2007 lecture.
