Synchronization in Josephson photonics devices in the presence of shot noise

Abstract

For many quantum sources the exploitation and characterization of their quantum properties, such as entanglement and squeezing, is hampered by phase instability. Josephson photonics devices, where microwave radiation is created by inelastic Cooper pair tunneling across a dc-biased Josephson junction in-series with a microwave resonator are particularly vulnerable lacking the reference phase provided by an ac-drive. To counter this issue, sophisticated measurement schemes have been used in [1] to prove entanglement, while in [2] a weak ac-signal was put in to lock phase and frequency of the emission. Intrinsic shot noise of the Josephson-photonics device inevitably diffuses the oscillators phase and requires an extension of classical synchronization theories to the quantum regime. Performing multi-time scale perturbation theory we derive an effective Fokker-Plank equation for the phase to analyze quantum locking and synchronization in an Adler-type equation. Injection locking and synchronization lead to a narrowing of the photon emission statistics, while the shot noise induces phase slips. [1] A. Peugeot et al., Phys. Rev. X 11, 031008 (2021). [2] M. C. Cassidy et al., Science 355, 939 (2017).