Breather molecular complexes in a passively mode-locked fiber laser

Breathing solitons are nonlinear waves in which the energy concentrates in a localized and oscillatory fashion. Similarly to stationary solitons, breathers in dissipative systems can form stable bound states displaying molecule-like dynamics, which are frequently called breather molecules. So far, the experimental observation of optical breather molecules and the real-time detection of their dynamics are limited to diatomic molecules, that is, bound states of only two breathers. In this work, the observation of different types of breather complexes in a mode-locked fiber laser: multibreather molecules, and molecular complexes originating from the binding of two breather-pair molecules or a breather pair molecule and a single breather is reported. The intermolecular temporal separation of the molecular complexes attains several hundreds of picoseconds, which is more than an order of magnitude larger than that of their stationary soliton counterparts and is a signature of long-range interactions. Numerical simulations of the laser model support the experimental findings. Moreover, nonequilibrium dynamics of breathing solitons are also observed, including breather collisions and annihilation. This work opens the possibility of studying the dynamics of many-body systems in which breathers are the elementary constituents.