Generation of Multicomponent Motional Coherent and Squeezed Coherent States of N Trapped Ions by a Dispersive Interaction

Following the recent proposal by Solano E et al. Phys. Rev. Lett. 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) Schrödinger cat states for the vibrational motion of a single ion trapped in a two-dimensional harmonic potential.