AI 中文总结
研究氮化硅微谐振器中一对产生的初级克尔梳状波的相干性和频率稳定性，用同步多通道频率计数表征其时间波动和相关性，结果表明产生的频率受参数能量守恒约束，确立其为适用于精密频率应用的芯片级参数频率三元组。
AI 中文摘要
克尔微梳为宽带光学频率网格提供了一条紧凑的途径，然而，在克尔梳产生开始时形成的初级梳状态作为计量对象却很少受到关注。在此，我们使用参考氢脉泽稳定差频梳的同步多通道频率计数，来表征氮化硅微谐振器中一对产生的初级梳状波的相干性和频率稳定性，从而能够直接测量泵浦、信号和闲频之间的时间波动和相关性。我们表明，产生的频率受到参数能量守恒的强烈约束：在具有兆赫兹级频率偏移的弱锁定条件下，与\(2f_p=f_s+f_i\)的剩余偏差平均仍保持在亚赫兹水平，并且信号 - 闲频回归仅偏离理想的\(-1\)响应\(2.4×10^{-9}\)。当三个频率中的两个紧密锁相时，整个泵浦 - 信号 - 闲频三元组的能量守恒剩余，等效于测量的闲频与从锁定的泵浦和信号推断的值之间的偏差，在\(\tau\approx100 s\)时达到接近\(6×10^{-16}\)的分数不稳定性下限。这证明了参数约束在计量水平上的保持，同时揭示了微妙的模式相关噪声传递。这些结果共同确立了初级克尔频率作为一个强相关的芯片级参数频率三元组，适用于要求苛刻的精密频率应用。
英文摘要
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 $τ\approx100~\mathrm{s}$. 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.
Comments8 pages, 5 figures
