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We present a scheme to generate an arbitrary two-dimensional quantum state ofmotion of a trapped ion. This proposal is based on a sequence of laser pulses,which are tuned appropriately to control transitions on the sidebands of twomodes of vibration. Not more than $(M+1)(N+1)$ laser pulses are needed togenerate a pure state with upper phonon number $M$ and $N$ in the $x$ and $y$direction respectively.Comment: to appear in PR

Generation of arbitrary two-dimensional motional states of a trapped ion