  Self-organized synchronization is a ubiquitous collective phenomenon, in
which each unit adjusts their rhythms to achieve synchrony through mutual
interactions. The optomechanical systems, due to their inherently engineerable
nonlinearities, provide an ideal platform to study self-organized
synchronization. Here, we demonstrate the self-organized synchronization of
phonon lasers in a two-membrane-in-the-middle optomechanical system. The probe
of individual membrane enables to monitor the real-time transient dynamics of
synchronization, which reveal that the system enters into the synchronization
regime via torus birth bifurcation line. The phase-locking phenomenon and the
transition between in-phase and anti-phase regimes are directly observed.
Moreover, such a system greatly facilitate the controllable synchronous states,
and consequently a phononic memory is realized by tuning the system parameters.
This result is an important step towards the future studies of many-body
collective behaviors in multiresonator optomechanics with long distances, and
might find potential applications in quantum information processing and complex
networks.
