Synchronizing Quantum Harmonic Oscillators through Two-Level Systems

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of $N$ oscillators and $M(<N)$ two-level systems.