Wavefront Curvature in Optical Atomic Beam Clocks

TL;DR

This paper models the effects of wavefront curvature on optical atomic beam clocks, revealing how laser geometry influences frequency stability and proposing optimal configurations to minimize inhomogeneity and shifts.

Contribution

It introduces a new model for Ramsey-Bordé interferometry with curved wavefronts, explaining experimental anomalies and guiding optimal laser geometry for atomic clocks.

Findings

Signal-to-noise ratio maximized with uncollimated laser beams.

Gouy phase identified as primary source of frequency shifts.

Optimal waist size depends on laser inhomogeneity and atomic velocity distribution.

Abstract

Atomic clocks provide a reproducible basis for our understanding of time and frequency. Recent demonstrations of compact optical clocks, employing thermal atomic beams, have achieved short-term fractional frequency instabilities in the $10^{-16}$, competitive with the best international frequency standards available. However, a serious challenge inherent in compact clocks is the necessarily smaller optical beams, which results in rapid variation in interrogating wavefronts. This can cause inhomogeneous excitation of the thermal beam leading to long term drifts in the output frequency. Here we develop a model for Ramsey-Bord\'e interferometery using optical fields with curved wavefronts and simulate the $^{40}$Ca beam clock experiment described in [Olson et al., Phys. Rev. Lett. 123, 073202 (2019)]. Olson et al.'s results had shown surprising and unexplained behaviour in the response of the atoms in the interrogation. Our model predicts signals consistent with experimental data and can account for the significant sensitivity to laser geometry that was reported. We find the signal-to-noise ratio is maximised when the laser is uncollimated at the interrogation zones to minimise inhomogeneity, and also identify an optimal waist size determined by both laser inhomogeneity and the velocity distribution of the atomic beam. We investigate the shifts and stability of the clock frequency, showing that the Gouy phase is the primary source of frequency variations arising from laser geometry.