Most synchronization realizations occur when the oscillation frequencies involved are barely dissimilar. With the recent convergence among optical, mechanical and electrical waves using scalable microfabrication technologies, synchronization has emerged as a powerful tool targeted not only at technological applications, such as phase-lock loops in radio-based communications 6, 7, 8, but also at developing the fundamentals of chaotic systems 9, injection locking 10, 11, 12, electro and optomechanical devices 13, 14, 15, 16, 17, 18, 19, 20, nonlinear dynamics 21, 22, 23, 24, 25, 26, network coupling 27, 28, 29, 30, and quantum synchronization 31, 32, 33, 34, 35, 36. Since its observation by Huygens in the 17th century, the synchronization of widely distinct systems has been shown to share remarkably universal features 1, 2, fostering its exploration across many disciplines 3, 4, 5. In a nutshell, synchronization occurs when an oscillatory system has its bare frequency entrained by a weak external signal, which may have a slightly different tempo. Synchronization lies at the core of time keeping and underpins a vast class of natural phenomena, from life cycles to precision measurements 1. Further developments could harness these effects towards frequency synthesizers, phase-sensitive amplification and nonlinear sensing. Exploring this effect, we also experimentally demonstrate a purely optomechanical RF frequency divider, where we performed frequency division up to a 4:1 ratio, i.e., from 128 MHz to 32 MHz.

Here, we experimentally demonstrate entrainment of a silicon-nitride optomechanical oscillator driven up to the fourth harmonic of its 32 MHz fundamental frequency. In its simplest form, synchronization occurs when an oscillator is entrained by a signal with frequency nearby the oscillator’s tone, and becomes increasingly challenging as their frequency detuning increases. Cavity optomechanical devices have played an important role in this scenario, with the perspective of bridging optical and radio frequencies through nonlinear classical and quantum synchronization concepts. Experimental exploration of synchronization in scalable oscillator microsystems has unfolded a deeper understanding of networks, collective phenomena, and signal processing.

Octave frequencies