Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

TL;DR

This paper improves the accuracy of the NPL-CsF2 cesium fountain clock by evaluating and reducing the uncertainties from distributed cavity phase and microwave lensing frequency shifts through measurements and theoretical modeling.

Contribution

It provides a detailed experimental and theoretical analysis of cavity-related frequency shifts, significantly reducing the clock's overall frequency uncertainty.

Findings

Distributed cavity phase uncertainty reduced to 1.1×10⁻¹⁶

Microwave lensing shift estimated at 6.2×10⁻¹⁷

Overall frequency uncertainty lowered to 2.3×10⁻¹⁶

Abstract

We evaluate the distributed cavity phase and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 cesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the distributed cavity phase uncertainty to $1.1 \times 10^{-16}$. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of $6.2 \times 10^{-17}$. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to $2.3 \times 10^{-16}$, nearly a factor of two lower than its most recent complete evaluation.