  Coupling, synchronization, and non-linear dynamics of resonator modes are
omnipresent in nature and highly relevant for a multitude of applications
ranging from lasers to Josephson arrays and spin torque oscillators.
Nanomechanical resonators are ideal candidates to study these effects on a
fundamental level and to realize all-mechanical platforms for information
processing and storage. For larger resonator networks, however, this requires
the ability to tune the mode frequencies selectively and to operate the
resonators in the strong coupling regime. Here, we present a proof-of-principle
realization of a resonator network consisting of two high-quality nanostring
resonators, coupled mechanically by a shared support. First, we demonstrate
that we can control the fundamental mode frequencies of both nanostrings
independently by a strong drive tone resonant with one of the higher harmonics
of the network, rendering local control gates redundant. The tuning mechanism
relies on an effective increase of the pre-stress in a highly excited
nanostring, known as geometric nonlinearity. Using this selective frequency
control of the individual nanomechanical resonators, we investigate the
coherent dynamics of the resonator network, which is a classical model system
showing several of the characteristic features of strongly coupled quantum
systems. In particular, we demonstrate mode splitting, classical Rabi
oscillations, as well as adiabatic and diabatic transitions between the coupled
states representing the classical analog of Landau-Zener tunneling. Therefore,
this coupling and tuning concept opens the path to a selective phonon transfer
between two spatially separated mechanical resonators.
