Selective interactions in trapped ions: State reconstruction and quantum logic

We propose the implementation of selective interactions of atom-motion subspaces in trapped ions. These interactions yield resonant exchange of population inside a selected subspace, leaving the others in a highly dispersive regime. Selectivity allows us to generate motional Fock (and other nonclassical) states with high purity out of a wide class of initial states, and becomes an unconventional cooling mechanism when the ground state is chosen. Individual population of number states can be distinctively measured, as well as the motional Wigner function. Furthermore, a protocol for implementing quantum logic through a suitable control of selective subspaces is presented.