  We propose to synthesize arbitrary nonclassical motional states in
optomechanical systems by using sideband excitations and photon blockade. We
first demonstrate that the Hamiltonian of the optomechanical systems can be
reduced, in the strong single-photon optomechanical coupling regime when the
photon blockade occurs, to one describing the interaction between a driven
two-level trapped ion and the vibrating modes, and then show a method to
generate target states by using a series of classical pulses with desired
frequencies, phases, and durations. We further analyze the effect of the photon
leakage, due to small anharmonicity, on the fidelity of the expected motional
state, and study environment induced decoherence. Moreover, we also discuss the
experimental feasibility and provide operational parameters using the possible
experimental data.
