Langevin model for soliton molecules in ultrafast fiber ring laser cavity: investigating experimentally the interplay between noise and inertia

The dynamics of soliton molecules in ultrafast fiber ring laser cavity is strongly influenced by noise. We show how a parsimonious Langevin model can be constructed from experimental data, resulting in a mathematical description that encompasses both the deterministic and stochastic properties of the evolution of the soliton molecules. In particular, we were able to probe the response dynamics of the soliton molecule to an external kick in a sub-critical approach, namely without the need to actually disturb the systems under investigation. Moreover, the noise experienced by the dissipative solitonic system, including its distribution and correlation, can now be also analyzed in details. Our strategy can be applied to any systems where the individual motion of its constitutive particles can be traced; the case of optical solitonic-system laser presented here serving as a proof-of-principle demonstration.