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We study locking phenomena of two strongly coupled, high-quality factornanomechanical resonator modes subject to a common parametric drive at a singledrive frequency. By controlled dielectric gradient forces we tune the resonancefrequencies of the flexural in-plane and out-of-plane oscillation of the highstress silicon nitride string through their mutual avoided crossing. For thecase of the strong common parametric drive signal-idler generation viaparametric oscillation is observed, analogously to the framework of nonlinearoptical effects in an optical parametric oscillator. Frequency tuning of thesignal and idler resonances is demonstrated. When the resonance frequencies ofsignal and idler get closer to each other, partial injection locking, injectionpulling and complete injection locking to half of the drive frequency occursdepending on the pump strength. Furthermore, satellite resonances,symmetrically off-set from signal and idler by their beat-note, are observedwhich can be attributed to degenerate four-wave-mixing in the highly nonlinearmechanical oscillations.

Parametric oscillation, frequency mixing and injection locking of strongly coupled nanomechanical resonator modes