  Dissipative Kerr soliton offers broadband coherent and low-noise frequency
comb and stable temporal pulse train, having shown great potential applications
in spectroscopy, communications, and metrology. Breathing soliton is a
particular dissipative Kerr soliton that the pulse duration and peak intensity
show periodic oscillation. However, the noise and stability of the breathing
soliton is still remaining unexplored, which would be the main obstacle for
future applications. Here, we have investigated the breathing dissipative Kerr
solitons in the silicon nitride (SiN) microrings, while the breather period
shows uncertainties around MHz in both simulation and experiments. By applying
a modulated pump, the breathing frequency can be injectively locked to the
modulation and tuned over tens of MHz with frequency noise significantly
suppressed. Our demonstration offers an alternative knob for the controlling of
soliton dynamics in microresonator and paves a new avenue towards practical
applications of breathing soliton.
