Scheme for direct measurement of the Wigner function of a trapped ion in the intermediate-excitation regime

We propose a scheme to directly measure the Wigner function for the motion of a trapped ion. Unlike the previous scheme [Phys. Rev. Lett. 78, 2547 (1997)], the present scheme works in the intermediate-excitation regime, which may be of experimental importance in view of decoherence. The scheme can also be used to perform a quantum nondemolition measurement of the vibrational energy and prepare motional Schroedinger cat states