Quantum harmonic oscillator state synthesis and analysis

Experiments are described in which a single, harmonically bound, beryllium ion in a Paul trap is put into Fock, thermal, coherent, squeezed, and Schroedinger cat states. Experimental determinations of the density matrix and the Wigner function are described. A simple calculation of the decoherence of a superposition of coherent states due to an external electric field is given.