Generation of two-mode SU(2) and SU(1,1) cat states in a two-dimensional anisotropic ion trap

A scheme is proposed for generating two-mode SU(2) and SU(1,1) cat states for an ion trapped in a two-dimensional (2D) anisotropic harmonic potential trap. In the scheme the ion is excited by two laser beams in the trap plane. After an interaction time, a measurement on the internal state collapses the ion motion onto a superposition of two SU(2) or SU(1,1) coherent states depending on the laser frequencies. This work was supported by the National Natural Science Foundation of China under Grant No. 60008003, Fujian Provincial Natural Science Foundation of China under Grant Nos. K20004 and F0110027, and Funds from Fuzhou University.