  We propose a scheme to generate nonclassical states of a quantum system,
which is composed of the one-dimensional trapped ion motion and a single cavity
field mode. We show that two-mode SU(2) Schr\"odinger-cat states, entangled
coherent states, two-mode squeezed vacuum states and their superposition can be
generated. If the vibration mode and the cavity mode are used to represent
separately a qubit, a quantum phase gate can be implemented.
