Stimulated Emission and Stochastic Cooling of a Single Ion

Recently several proposals haw been made to m e a " the quantum &ate of the vibrational motion of a single trapped atom [I] and of a cavity radiation-mode [2,3]. On the other hand, we have propmed the mwurement of quasiprobability distributioits of a light mode via unbalanced homodyniq 141, where the determination of the quantum state is haved on a coherent displacement (due to the local millator) and the measurement of the photon-number statkticu. In the present mntribution we consider the application of similar methods for the determination of quasiprobability distributions for cavity fields and the motion of trapped atoms.