Validating a lutetium frequency reference

TL;DR

This paper discusses the development and validation of a lutetium-based optical frequency reference, emphasizing its potential for extremely high accuracy and the advantages of using frequency ratios for system comparisons.

Contribution

It presents a detailed analysis of lutetium ion transitions as a frequency reference and proposes a method for comparing remote systems using frequency ratios to ensure accuracy.

Findings

Achievable accuracy at the 10^{-19} level for lutetium transitions.

Frequency ratio measurements are robust against environmental and relativistic effects.

Discrepancies in ratios indicate at least one system's measurement is incorrect.

Abstract

We review our progress in developing a frequency reference with singly ionized lutetium and give estimates of the levels of inaccuracy we expect to achieve in the near future with both the $^1S_0\leftrightarrow{}^3D_1$ and $^1S_0\leftrightarrow{}^3D_2$ transitions. Based on established experimental results, we show that inaccuracies at the low $10^{-19}$ level are readily achievable for the $^1S_0\leftrightarrow{}^3D_1$ transition, and the frequency ratio between the two transitions is limited almost entirely by the BBR shift. We argue that the frequency ratio measured within the one apparatus provides a well-defined metric to compare and establish the performance of remotely located systems. For the measurement of an in situ frequency ratio, relativistic shifts drop out and both transitions experience the same electromagnetic environment. Consequently, the uncertainty budget for the ratio is practically identical to the uncertainty budgets for the individual transitions. If the ratios for two or more systems disagree we can be certain at least one of the clock assessments is incorrect. If they agree, subsequent comparisons on one transition would only differ by relativistic effects. Since motional effects are easily assessed and typically small for a heavy ion, only the differential gravitational red-shift will significantly contribute and this can be confirmed by comparison on the second transition.