  We demonstrate various regimes of synchronization in systems of two coupled
cavity soliton-based Kerr frequency combs. We show sub-harmonic, harmonic and
harmonic-ratio synchronization of coupled microresonators, and reveal their
dynamics in the form of Arnold tongues, structures that are ubiquitous in
nonlinear dynamical systems. Our experimental results are well corroborated by
numerical simulations based on coupled Lugiato-Lefever equations. This study
illustrates the newfound degree of flexibility in synchronizing Kerr combs
across a wide range of comb spacings and could find applications in time and
frequency metrology, spectroscopy, microwave photonics, optical communications,
and astronomy.
