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

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