Motional quantum-state engineering and measurement in the strong-excitation regime

We propose a scheme to generate a superposition of several coherent states with arbitrary coefficients on a line in phase space and directly measure the Wigner characteristic function for the motion of a trapped ion. Unlike previous schemes for motional quantum-state engineering and endoscopy, the present scheme works in the strong-excitation regime, which may be of experimental importance in view of decoherence.