Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels

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.