Engineering quantum states of a nanoresonator via a simple auxiliary system.

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