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We propose the use of a superconducting charge qubit capacitively coupled totwo resonant nanomechanical resonators to generate Yurke-Stoler states, i.e.quantum superpositions of pairs of distinguishable coherent states 180$^\circ$out of phase with each other. This is achieved by effectively implementing Kerrnonlinearities induced through application of a strong external driving fieldin one of the resonators. A simple study of the effect of dissipation on ourscheme is also presented, and lower bounds of fidelity and purity of thegenerated state are calculated. Our procedure to implement a Kerr nonlinearityin this system may be used for high precision measurements in nanomechanicalresonators.

Kerr nonlinearities and nonclassical states with superconducting qubits and nanomechanical resonators