Generation of Pair Coherent States in Two Dimensional Trapped Ion

We consider a two-dimensional (2D) trapped ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level of the ion. Due to the coherent superposition of two sub-Rabi oscillations involved in the bimodal vibrations, the Rabi frequency degeneration and offset may occur in this model. This provides a possibility to generate the pair coherent state in the 2D trapped ion.