We describe a method to engineer giant nonlinearities in, and probes to measure nonlinear observables of, mesoscopic quantum resonators. This involves tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled to the resonator, and has the potential to engineer a wide range of nonlinearities to high accuracy. We give a number of explicit examples, including a readily realizable two-qubit auxiliary system that creates an x;{4} potential and a chi;{(3)} (Kerr) nonlinearity, valid to fifth order in the perturbative coupling.
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Jacobs et al. (2009) studied this question.
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