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We experimentally demonstrate the synchronization of regularly vibrating soliton molecules by means of an injected modulated signal. Such synchronization is analyzed in real time through the sensitive balanced optical correlation technique. We also unveil the existence of chaotic intra-molecular vibrations, to which we successfully apply a similar control strategy. These findings strengthen the hypothesis of internal dynamics of soliton molecules essentially ruled by a reduced number of degrees of freedom, allowing applicative prospects.

We propose a theoretical method to model the complex phenomenon of oscillating ultrashort pulse pair molecules. Using a phenomenological viewpoint, we construct effective dynamical systems, whose degrees of freedom are the inter-pulse timing and overall phase. The effective dynamical system is characterized by a limit cycle attractor that is fit to the experimentally measured soliton oscillation using data-driven methods. Good agreement is achieved between the dynamical system orbits and experimental observations made in a mode-locked fiber laser.