  The phase-coherent frequency division of a stabilized optical reference laser
to the microwave domain is made possible by optical frequency combs (OFCs).
Fundamentally, OFC-based clockworks rely on the ability to lock one comb tooth
to this reference laser, which probes a stable atomic transition. The active
feedback process associated with locking the comb tooth to the reference laser
introduces complexity, bandwidth, and power requirements that, in the context
of chip-scale technologies, complicate the push to fully integrate OFC
photonics and electronics for fieldable clock applications. Here, we
demonstrate passive, electronics-free synchronization of a microresonator-based
dissipative Kerr soliton (DKS) OFC to a reference laser. We show that the Kerr
nonlinearity within the same resonator in which the DKS is generated enables
phase locking of the DKS to the externally injected reference. We present a
theoretical model to explain this Kerr-induced synchronization (KIS), and find
that its predictions for the conditions under which synchronization occur
closely match experiments based on a chip-integrated, silicon nitride microring
resonator. Once synchronized, the reference laser is effectively an OFC tooth,
which we show, theoretically and experimentally, enables through its frequency
tuning the direct external control of the OFC repetition rate. Finally, we
examine the short- and long-term stability of the DKS repetition rate and show
that the repetition rate stability is consistent with the frequency division of
the expected optical clockwork system.
