Sub-Hz Stability and Correlation in Pair-Generated Primary Kerr Comb Tones

Kerr microcombs provide a compact route to broadband optical frequency grids, yet the primary comb states formed at the onset of Kerr-comb generation have received little attention as metrological objects. Here we characterize the coherence and frequency stability of pair-generated primary-comb tones in a silicon nitride microresonator using synchronized multi-channel frequency counting referenced to a hydrogen-maser-stabilized difference-frequency comb, enabling direct measurement of temporal fluctuations and correlations among the pump, signal, and idler tones. We show that the generated tones are strongly constrained by parametric energy conservation: under weakly locked conditions with MHz-level frequency excursions, the residual deviation from $2f_p=f_s+f_i$ remains sub-hertz in the mean, and the signal-idler regression deviates from the ideal $-1$ response by only $2.4\times10^{-9}$. When two of the three tones are tightly phase-locked, the energy-conservation residual of the full pump-signal-idler triad, equivalently the deviation of the measured idler from the value inferred from the locked pump and signal, reaches a fractional-instability floor near $6 \times 10^{-16}$ at $\tau\approx100~\mathrm{s}$. This demonstrates metrological-level preservation of the parametric constraint while revealing subtle mode-dependent noise transfer. Together, these results establish primary Kerr tones as a strongly correlated chip-scale parametric frequency triad suitable for demanding precision-frequency applications.