Quantum nondemolition measurements of vibrational populations in ionic traps

We discuss a simple implementation of a quantum nondemolition measurement of the vibronic state of a trapped ion, This scheme allows the production of Fock states associated to the center-of-mass motion and the determination of the population distribution of the trap levels, and is based on the vibronic level dependence of the frequency of Rabi oscillations between two internal states of the ion, induced by a resonant carrier field. The same scheme can be used to produce a Schrodinger-cat-like state after a single interaction between the trapped ion and the carrier pulse, followed by the detection of the ionic internal state.