Realization of Nonclassical States and Two-Mode Coupling in the Motion of Two Trapped Ions

We propose a scheme to generate various nonclassical vibrational states in the collective motion of twotrapped ions, such as squeezed states, Schrodinger cat states, and SU(2) states. It is based on Raman-type excitations.Two-mode coupling between the center-of-mass and relative vibrational modes can also be realized.