Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection

Abstract

We show that conditional photon detection induces instantaneous phase synchronization between two decoupled quantum limit-cycle oscillators. We consider two quantum van der Pol oscillators without mutual coupling, each with additional single-photon dissipation, and perform continuous measurement of photon counting on the output fields of the two baths interacting through a beam splitter. It is observed that in-phase or antiphase coherence of the two decoupled oscillators instantaneously increases after photon detection and then decreases gradually in the weak quantum regime or quickly in the strong quantum regime until the next photon detection occurs. In the strong quantum regime, quantum entanglement also increases after photon detection and quickly disappears. We derive the analytical upper bounds for the increases in the quantum entanglement and phase coherence by conditional photon detection in the quantum limit.