Synchronization of the internal dynamics of optical soliton molecules

Compact bound states of light pulses in ultrafast lasers are known as optical soliton molecules. They constitute nonlinear superstructures of choice to investigate complex dynamical phenomena that manifest similarly in a wide range of nonlinear systems. Akin to matter molecules, optical soliton molecules can feature vibrational motions between their internal constituents. However, these vibrations are intrinsically nonlinear, with oscillation frequencies sensitive to system parameters. Therefore, vibrating soliton molecules present an opportunity for control. We here investigate the precise control of their oscillation frequencies through the universal mechanism of synchronization between master and slave oscillators. Self-oscillating soliton molecules are prepared within a passively mode-locked fiber laser. We experimentally demonstrate the synchronization of the internal vibrations of soliton molecules through the optical injection of a master oscillator signal. Direct observation of the synchronization process is enabled by balanced optical crosscorrelation detection, a technique allowing real-time detection of intramolecular separation with femtosecond temporal resolution. We show efficient sub-harmonic, fundamental, and super-harmonic synchronization, forming a pattern of Arnold tongues with respect to the injection strength. Numerical simulations support experimental observations. By retrieving these universal synchronization features, the role of the soliton molecule as a nonlinear dynamical system of chief importance is further highlighted