  Bound states of solitons (molecules) occur in various settings, playing an
important role in the operation of fiber lasers, optical emulations, encoding,
and communications. Soliton interactions are generally related to breathing
dynamics in nonlinear dissipative systems, maintaining potential applications
in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are
created in a synchronized mode-locked fiber laser. Real-time delay-shifting
interference spectra are measured to display the temporal evolution of the
DBMs, that cannot be observed by means of the usual real-time spectroscopy. As
a result, robust out-of-phase vibrations are found as a typical intrinsic mode
of DBMs. The same bound states are produced numerically in the framework of a
model combining equations for the population inversion in the mode-locked laser
and XPM-coupled complex Ginzburg-Landau equations for amplitudes of the optical
fields in the fiber segments of the laser cavity. The results demonstrate that
the Q-switching instability induces the onset of breathing oscillations. The
findings offer new possibilities for the design of various regimes of the
operation of ultrafast lasers.
