Dressed-state-mediated synchronization in coupled quantum oscillators

We investigate quantum synchronization in coupled self-sustained oscillators interacting via bosonic exchange. Using a phase-distribution-based synchronization measure, we identify bistable phase locking between 0 and $\ensuremath{\pi}$ and uncover an expanded Arnold-tongue structure under finite detuning, indicative of enhanced quantum phase locking. Power spectral analysis reveals dual-frequency locking associated with dressed-state formation, a uniquely quantum effect. This spectral splitting persists even without detuning and increases with coupling strength, signaling coherent hybridization of oscillator modes. A comparison with a classical approximation highlights key differences, including the absence of spectral doublets in the classical regime. Finally, we show that increasing nonlinear damping induces a sharp transition in the preferred phase difference and leads to decoherence through spectral peak broadening, underscoring the critical role of dissipation in shaping quantum synchronization dynamics.