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Quantum synchronization has been a central topic in quantum nonlineardynamics. Despite rapid development in this field, very few have studied how toefficiently boost synchronization. Homodyne measurement emerges as one of thesuccessful candidates for this task, but preferably in the semi-classicalregime. In our work, we focus on the phase synchronization of a harmonic-drivenquantum Stuart-Landau oscillator, and show that the enhancement induced byhomodyne measurement persists into the quantum regime. Interestingly, optimaltwo-photon damping rates exist when the oscillator and driving are at resonanceand with a small single-photon damping rate. We also report noise-inducedenhancement in quantum synchronization when the single-photon damping rate issufficiently large. Apart from these results, we discover that adding asqueezing Hamiltonian can further boost synchronization, especially in thesemi-classical regime. Furthermore, the addition of squeezing causes theoptimal two-photon pumping rates to shift and converge.

Enhancing quantum synchronization through homodyne measurement, noise and squeezing