Quantum synchronization in nanoscale heat engines

Owing to the ubiquity of synchronization in the classical world, it is interesting to study its behavior in quantum systems. Though quantum synchronization has been investigated in many systems, a clear connection to quantum technology applications is lacking. We bridge this gap and show that nanoscale heat engines are a natural platform to study quantum synchronization and always possess a stable limit cycle. Furthermore, we demonstrate an intimate relationship between the power of a coherently driven heat engine and its phase-locking properties by proving that synchronization places an upper bound on the achievable steady-state power of the engine. We also demonstrate that such an engine exhibits finite steady-state power if and only if its synchronization measure is nonzero. Finally, we show that the efficiency of the engine sets a point in terms of the bath temperatures where synchronization vanishes. We link the physical phenomenon of synchronization with the emerging field of quantum thermodynamics by establishing quantum synchronization as a mechanism of stable phase coherence.