Critical thermal drifts in external fiber amplifiers limit optical frequency metrology

Relying on the nonlinear optical effect of difference-frequency generation, passively carrier-envelope stabilized comb systems are currently considered the simplest option for generating combs with zero carrier-envelope offset frequency ${f_{{\mathbf{ceo}}}}$, that is, without relying on electronic servo loops or additional acousto-optic shifters. However, recent measurements indicated statistically significant deviations from a perfect vanishing ${f_{{\mathbf{ceo}}}}$. Here, we show that temperature-drift-induced refractive index changes in subsequent distribution or booster amplifiers may give rise to an effective Doppler shift of the measured ${f_{{\mathbf{ceo}}}}$, thwarting precision frequency measurements up to the mHz level. Comparing this hypothesis with temperature-dependent refractive index data and gain spectra, we find excellent quantitative agreement with measurements. Mitigating these problems by allowing for sufficient warm-up times of the external amplifiers, the ${f_{{\mathbf{ceo}}}}$ mean value of a difference frequency comb is measured as -0.55 ± 1.55 µHz, which is statistically equivalent to 0. The corresponding stability supersedes the current best optical clocks by an order of magnitude, with an overlapping Allan deviation of <1·10^-17 at 1 s and 5.36 × 10^-21 at 100,000 s. Previously often considered negligible, the temperature drift of external distribution or booster amplifiers plays a critical role in obtaining similar stabilities in frequency metrology for all kinds of ${f_{{\mathbf{ceo}}}}$-stabilized combs.