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We show that conditional photon detection induces instantaneous phasesynchronization between two decoupled quantum limit-cycle oscillators. Weconsider two quantum van der Pol oscillators without mutual coupling, each withan additional linearly coupled bath, and perform continuous measurement ofphoton counting on the output fields of the two baths interacting through abeam splitter. It is observed that in-phase or anti-phase coherence of the twodecoupled oscillators instantaneously increases after the photon detection andthen decreases gradually in the weak quantum regime or quickly in the strongquantum regime until the next photon detection occurs. In the strong quantumregime, quantum entanglement also increases after the photon detection andquickly disappears. We derive the analytical upper bounds for the increases inthe quantum entanglement and phase coherence by the conditional photondetection in the quantum limit.

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