  Synchronisation is a collective phenomenon widely investigated in classical
oscillators and, more recently, in quantum systems. However, it remains unclear
what features distinguish synchronous behaviour in these two scenarios. Recent
works have shown that investigating the dynamics of synchronisation in open
quantum systems can give insight into this issue. Here we study transient
synchronisation in a bio-inspired vibronic dimer, where the dynamics of
electronic excitation is mediated by coherent interactions with intramolecular
vibrational modes. We show that the synchronisation dynamics of the
displacement of these local modes exhibit a rich behaviour which arises
directly from the distinct time-evolutions of different vibronic quantum
coherences. Furthermore, our study shows that coherent energy transport in this
bio-inspired system is concomitant with the emergence of positive
synchronisation between mode displacements. Our work provides further
understanding of the relations between quantum coherence and synchronisation in
open quantum systems and suggests an interesting role for coherence in
biomolecules, that is promoting the synchronisation of vibrational motions
driven out of thermal equilibrium.
