  We study how quantum and thermal noise affects synchronization of two
optomechanical limit-cycle oscillators. Classically, in the absence of noise,
optomechanical systems tend to synchronize either in-phase or anti-phase.
Taking into account the fundamental quantum noise, we find a regime where
fluctuations drive transitions between these classical synchronization states.
We investigate how this "mixed" synchronization regime emerges from the
noiseless system by studying the classical-to-quantum crossover and we show how
the time scales of the transitions vary with the effective noise strength. In
addition, we compare the effects of thermal noise to the effects of quantum
noise.
