Bayesian estimate of the zero-density frequency of a Cs fountain

TL;DR

This paper applies Bayesian analysis to estimate the zero-density frequency of a Cs fountain, improving uncertainty estimates and demonstrating its importance in primary frequency metrology.

Contribution

It introduces a Bayesian approach to estimate atomic density shifts in Cs fountains, incorporating prior knowledge to enhance accuracy over traditional methods.

Findings

Bayesian analysis reduces uncertainty by 28%.

Bayes theorem effectively incorporates prior knowledge.

Application to INRIM data validates the method.

Abstract

Caesium fountain frequency-standards realize the second in the International System of Units with a relative uncertainty approaching 10^-16. Among the main contributions to the accuracy budget, cold collisions play an important role because of the atomic density shift of the reference atomic transition. This paper describes an application of the Bayesian analysis of the clock frequency to estimate the density shift and describes how the Bayes theorem allows the a priori knowledge of the sign of the collisional coefficient to be rigourously embedded into the analysis. As an application, data from the INRIM caesium fountain are used and the Bayesian and orthodox analyses are compared. The Bayes theorem allows the orthodox uncertainty to be reduced by 28% and demonstrates to be an important tool in primary frequency-metrology.