  We theoretically propose a unifying expression for synchronization dynamics
between two-level constituents. Although synchronization phenomena require some
substantial mediators, the distinct repercussions of their propagation delays
remain obscure, especially in open systems. Our scheme directly incorporates
the details of the constituents and mediators in an arbitrary environment. As
one example, we demonstrate the synchronization dynamics of optical emitters on
a dielectric microsphere. We reveal that the whispering gallery modes (WGMs)
bridge the well-separated emitters and accelerate the synchronized
fluorescence, known as superfluorescence. The emitters are found to overcome
the significant and nonuniform retardation, and to build up their pronounced
coherence by the WGMs, striking a balance between the roles of resonator and
intermediary. Our work directly illustrates the dynamical aspects of many-body
synchronizations and contributes to the exploration of research paradigms that
consider designed open systems.
