Spontaneous synchronization is a collective phenomenon that can occur in both dynamical classical and quantum systems. Here, we analyze the spontaneous synchronization dynamics of vibrations assisting energy transfer in a bio-inspired system. We find the emergence of a constant nonzero “synchronization phase” between synchronized vibrational displacements as the natural frequencies of the oscillators are detuned. This phase difference arises from the asymmetric participation of local modes in the long-lived synchronized state. Furthermore, we investigate the relationships between the synchronization phase, detuning and the degree of quantum correlations between the synchronizing subsystems and find that the synchronization phase captures how quantum correlations persistently exceed classical correlations during the dynamics. We show that our analysis applies to a variety of spontaneously synchronizing open quantum systems. Our work therefore opens up a promising avenue to investigate nontrivial quantum phenomena in complex biomolecular and nanoscale chemical systems
