Dissipative solitons in optical microcavities have attracted significant
attention in recent years due to their direct association with the generation
of optical frequency combs. Here, we address the problem of dissipative soliton
breathers in a microresonator with second-order nonlinearity, operating at the
exact phase-matching for efficient second-harmonic generation. We elucidate the
vital role played by the group velocity difference between the first and second
harmonic pulses for the breather existence. We report the dissipative breather
gas phenomenon, when multiple breathers propagate randomly in the resonator and
collide nearly elastically. Finally, when the breather gas reaches an
out-of-equilibrium statistical stationarity, we show how the velocity locking
between first and second harmonic is still preserved, naming such phenomena
turbulence locking.Comment: 10 pages, 10 figure