# On-Line Estimation of Local Oscillator Noise and Optimisation of Servo Parameters in Atomic Clocks

## TL;DR

This paper develops an optimal linear prediction method for local oscillator noise in atomic clocks, enabling real-time servo parameter optimization to improve clock stability.

## Contribution

It introduces a practical optimal prediction algorithm and analytical models for tuning servo parameters based on LO noise spectra in atomic clocks.

## Key findings

- Properly tuned conventional integrators perform nearly as well as optimal predictors.
- Optimal probe times depend on atom number and noise type.
- LO noise spectra influence the scaling of clock stability with atom number.

## Abstract

For atomic frequency standards in which fluctuations of the local oscillator (LO) frequency are the dominant noise source, we examine the role of the servo algorithm that predicts and corrects these frequency fluctuations. We derive the optimal linear prediction algorithm, showing how to measure the relevant spectral properties of the noise and optimise servo parameters while the standard is running, using only the atomic error signal. We find that, for realistic LO noise spectra, a conventional integrating servo with a properly chosen gain performs nearly as well as the optimal linear predictor. Using simple analytical models and numerical simulations, we establish optimum probe times as a function of clock atom number and of the dominant noise type in the local oscillator. We calculate the resulting LO-dependent scaling of achievable clock stability with atom number for product states as well as for maximally-correlated states.