Superlocalization reveals long-range synchronization of vibrating soliton molecules

We implement a super-localization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with inter-molecules oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characteristic ranges, timescales, strengths, and physical origins.