Raman motional displacements of a trapped ion in the strong excitation regime

We consider the first-sideband Raman excitations of a trapped ion in the strong Raman coupling regime on the basis of the splitting approximation. It is demonstrated that not only weak but strong Raman excitations can be used to displace the motional ground state to some well-localized motional states under appropriate conditions. Nonlinear and nonresonant effects are taken into account for the Raman sideband transitions. The condition and limitation for the Raman vibrational excitations to be used for preparing Schrödinger cat motional states are analyzed. Quantum interference between the displaced motional states is discussed.