Following the recent proposal by Solano E et al. [Phys. Rev. Left. 87 (2001) 060402] a procedure is proposed to generate arbitrary discrete multicomponent motional coherent and squeezed coherent states of N trapped ions by additionally using a dispersive bichromatic interaction in a long-living and fast way. In this procedure, two lasers in the Raman configuration are tuned quasiresonant and resonant with N two-level ions under different conditions, respectively. Furthermore, we show how the idea can be used for the generation of two-mode SU(2) Schrdinger cat states for the vibrational motion of a single ion trapped in a two-dimensional harmonic potential.
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