  Networks of coupled resonators are an ubiquitous concept in physics, forming
the basis of synchronization phenomena, metamaterial formation, nonreciprocal
behavior and topological effects. Such systems are typically explored using
optical or microwave resonators. In recent years, mechanical resonators have
entered the stage as universal building block for resonator networks, both for
their well-controlled mechanical properties and for their eigenfrequencies
conveniently located in the radio-frequency regime. Vertically oriented
nanomechanical pillar resonators are ideally suited for the dense integration
into large resonator networks. However, to realize the potential of these
promising systems, an intrinsic coupling mechanism needs to be established.
Here, we demonstrate strain-induced, strong coupling between two adjacent
nanomechanical pillar resonators. The coupling is mediated through the strain
distribution in the joint substrate caused by the flexural vibration of the
pillars, such that the coupling strength can be controlled by the geometric
properties of the nanopillars as well as their separation. Both, mode
hybridization and the formation of an avoided level crossing in the response of
the nanopillar pair are experimentally observed. The coupling mechanism is
readily scalable to large arrays of nanopillars, enabling all-mechanical
resonator networks for the investigation of a broad range of collective
dynamical phenomena.
