MOTION TOMOGRAPHY OF A SINGLE TRAPPED ION

A method for the experimental reconstruction of the quantum state of m otion for a single trapped ion is proposed. It is based on the measure ment of the ground-state population of the trap after a sudden change of the trapping potential. In particular, we show how the Q(alpha) fun ction and the quadrature distribution P(x, theta) can be measured dire ctly. In an example we demonstrate the principle and analyze the sensi tivity of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to th e Lamb-Dicke Limit and works in one or more dimensions.