We propose a scheme to generate various nonclassical vibrational states in the collective motion of two trapped ions, such as squeezed states, Schrödinger 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.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.