  We investigate the dynamics of a cold trapped ion coupled to the quantized
field inside a high-finesse cavity. We have used an approach for preparing the
SC states of motion of ion. This approach, based on unitary transformating the
Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke
aproximation. We show that is possible to generate a SC states having rather
simple initial state preparation, e.g., the vacuum sate for both cavity field
and the ion motion.
