Evaluating and Minimizing Distributed Cavity Phase Errors in Atomic Clocks

TL;DR

This paper analyzes distributed cavity phase errors in atomic clocks using 3D finite element calculations, identifying key error sources and proposing cavity design improvements to enhance clock accuracy.

Contribution

It introduces a detailed modeling approach for cavity phase errors and demonstrates cavity optimization techniques to minimize systematic errors in atomic clocks.

Findings

Sharp cavity structures do not cause large frequency errors at moderate powers.

Phase imbalances can lead to significant cavity phase errors, especially with larger couplings.

Optimized cavity geometries significantly reduce systematic phase errors.

Abstract

We perform 3D finite element calculations of the fields in microwave cavities and analyze the distributed cavity phase errors of atomic clocks that they produce. The fields of cylindrical cavities are treated as an azimuthal Fourier series. Each of the lowest components produces clock errors with unique characteristics that must be assessed to establish a clock's accuracy. We describe the errors and how to evaluate them. We prove that sharp structures in the cavity do not produce large frequency errors, even at moderately high powers, provided the atomic density varies slowly. We model the amplitude and phase imbalances of the feeds. For larger couplings, these can lead to increased phase errors. We show that phase imbalances produce a novel distributed cavity phase error that depends on the cavity detuning. We also design improved cavities by optimizing the geometry and tuning the mode spectrum so that there are negligible phase variations, allowing this source of systematic error to be dramatically reduced.