Noise-induced servo errors in optical clocks utilizing Rabi interrogation

TL;DR

This paper investigates how flicker noise in optical clocks with Rabi interrogation causes servo errors, and proposes methods to mitigate these errors by changing probing sequences or normalizing the discriminator.

Contribution

It provides an analytical model of flicker noise-induced servo errors and suggests practical mitigation strategies for optical clock stability.

Findings

Flicker noise causes servo errors at the 10^{-18} level in Rabi interrogation clocks.

Reversing probing order or normalizing the discriminator reduces servo errors.

Analytical expressions match numerical simulations, guiding noise mitigation.

Abstract

We show that in optical clocks based on Rabi interrogation, both laser-frequency and magnetic-field flicker ($1/f$) noise with zero mean can lead to servo errors at the $10^{-18}$ level if the negative-detuning (red) and positive-detuning (blue) sides of the transition are always probed in the same order. This is due to the strong correlations of flicker noise in combination with an imbalance in the response of the servo discriminator to positive and negative differential frequency noise between the red- and blue-side probing. This imbalance is particularly large for a normalized discriminator. We derive an analytical expression for the servo error based on the correlation function of the laser-frequency or magnetic-field noise and compare it to numerical servo simulations to demonstrate how the error depends on the noise level, servo parameters, and probing sequence. We also show that the servo error can be avoided by normalizing the discriminator with a moving mean or by reversing the red/blue probing order for every second servo cycle.