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We show how to engineer an extensive range of non-linear Hamiltonians for anano-mechanical resonator. The technique requires only a time dependent driveapplied to a Cooper-pair box or second oscillator to which the nano-resonatoris coupled. This method allows one to generate a large number of non-classicalstates, as well as Hamiltonians whose classical counterparts are chaotic.

Engineering Quantum States of a Nano-Resonator via a Simple Auxiliary System