  Synchronization in oscillatory systems is a frequent natural phenomenon and
is becoming an important concept in modern physics. Nanomechanical resonators
are ideal systems for studying synchronization due to their controllable
oscillation properties and engineerable nonlinearities. Here we demonstrate
synchronization of two nanomechanical oscillators via a photonic resonator,
enabling optomechanical synchronization between mechanically isolated
nanomechanical resonators. Optical backaction gives rise to both reactive and
dissipative coupling of the mechanical resonators, leading to coherent
oscillation and mutual locking of resonators with dynamics beyond the widely
accepted phase oscillator (Kuramoto) model. Besides the phase difference
between the oscillators, also their amplitudes are coupled, resulting in the
emergence of sidebands around the synchronized carrier signal.
