Quantum state preparation and measurement

Summary form only given. The recent experimental generation of nonclassical states of the motion of an ion in a Paul trap has propelled the field of quantum state preparation into a new era. But how to prove that the ion is indeed in a Fock, a squeezed, or a Schrodinger cat state? How can we measure a motional state which, due to the explicit time dependence of the binding force of the Paul trap, displays a complicated time dependence? In this paper we present the first method that measures a vibratory state of an ion taking into account the complete time dependence of the Paul trap. Moreover our technique operates outside the Lamb-Dicke regime and is not limited to pure states only.