Quantum Synchronization in Presence of Shot Noise

Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or platform specific are timely questions of fundamental interest. Here, we present a new approach to model incoherently driven dissipative quantum systems susceptible to synchronization within the framework of Josephson photonics devices, where a dc-biased Josephson junction creates (non-classical) light in a microwave cavity. The combined quantum compound constitutes a self-sustained oscillator with a neutrally stable phase. Linking current noise to the full counting statistics of photon emission allows us to capture phase diffusion, but moreover permits phase locking to an ac-signal and mutual synchronization of two such devices. Thereby one can observe phase stabilization leading to a sharp emission spectrum as well as unique photon emission statistics revealing shot noise induced phase slips. Two-time perturbation theory is used to obtain a reduced description of the oscillators phase dynamics in form of a Fokker-Planck equation in generalization of classical synchronization theories.