Bichromatic synchronized chaos in coupled optomechanical nanoresonators

Abstract: Synchronization and chaos are two well known and ubiquitous phenomena in nature. Interestingly, under specific conditions, coupled chaotic systems can display synchronization in some of their observables. Here, we experimentally investigate bichromatic synchronization on the route to chaos of two non-identical mechanically coupled optomechanical nanocavities. Electromechanical near-resonant excitation of one of the resonators evidences hysteretic behaviors of the coupled mechanical modes which can, under amplitude modulation, reach the chaotic regime. The observations, allowing to measure directly the full phase space of the system, are accurately modeled by coupled periodically forced Duffing resonators thanks to a complete calibration of the experimental parameters. This shows that, besides chaos transfer from the mechanical to the optical frequency domain, spatial chaos transfer between the two nonidentical subsystems occurs. Upon simultaneous excitations of the coupled membranes modes, we also demonstrate bichromatic chaos synchronization between quadratures at the two distinct carrier frequencies of the normal modes. Their respective quadrature amplitudes are consistently synchronized thanks to the modal orthogonality breaking induced by the nonlinearity. Meanwhile, their phases show complex dynamics with imperfect synchronization in the chaotic regime. Our generic model agrees again quantitatively with the observed synchronization dynamics. These results set the ground for the experimental study of yet unexplored collective dynamics of e.g synchronization in arrays of strongly coupled, nanoscale nonlinear oscillators for applications ranging from precise measurements to multispectral chaotic encryption and random bit generation, and to analog computing, to mention a few.