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Synchronization, quantum correlations and entanglement in oscillator networks

Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.