Abstract
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.
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