EXPERIMENTAL-DETERMINATION OF THE MOTIONAL QUANTUM STATE OF A TRAPPEDATOM

We reconstruct the density matrices and Wigner functions for various q uantum states of motion of a harmonically bound Be-9(+) ion. We apply coherent displacements of different amplitudes and phases to the input state and measure the number state populations. Using novel reconstru ction schemes we independently determine both the density matrix in th e number state basis and the Wigner function. These reconstructions ar e sensitive indicators of decoherence in the system.