Synchronization of many nanomechanical resonators coupled via a common cavity field

Using amplitude equations, we show that groups of identical nanomechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the squared sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behavior which, when analyzed using amplitude equations, can be shown to exhibit multistability. In contrast, groups of sufficiently dissimilar nanomechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further, the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.