  In this work we explore the limits of synchronization of mutually coupled
oscillators at the crossroads of classical and quantum physics. In order to
address this uncovered regime of synchronization we apply electrically driven
quantum dot micropillar lasers operating in the regime of cavity quantum
electrodynamics. These high-$\beta$ microscale lasers feature cavity enhanced
coupling of spontaneous emission and operate at output powers on the order of
100 nW. We selected pairs of micropillar lasers with almost identical optical
properties in terms of the input-output dependence and the emission energy
which we mutually couple over a distance of about 1\~m and bring into spectral
resonance by precise temperature tuning. By excitation power and detuning
dependent studies we unambiguously identify synchronization of two mutually
coupled high-$\beta$ microlasers via frequency locking associated with a
sub-GHz locking range. A detailed analysis of the synchronization behavior
includes theoretical modeling based on semi-classical stochastic rate equations
and reveals striking differences from optical synchronization in the classical
domain with negligible spontaneous emission noise and optical powers usually
well above the mW range. In particular, we observe deviations from the
classically expected locking slope and broadened locking boundaries which are
successfully explained by the fact the quantum noise plays an important role in
our cavity enhanced optical oscillators. Beyond that, introducing additional
self-feedback to the two mutually coupled microlasers allows us to realize
zero-lag synchronization. Our work provides important insight into
synchronization of optical oscillators at ultra-low light levels and has high
potential to pave the way for future experiments in the quantum regime of
synchronization.
