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For atomic frequency standards in which fluctuations of the local oscillator(LO) frequency are the dominant noise source, we examine the role of the servoalgorithm that predicts and corrects these frequency fluctuations. We derivethe optimal linear prediction algorithm, showing how to measure the relevantspectral properties of the noise and optimise servo parameters while thestandard is running, using only the atomic error signal. We find that, forrealistic LO noise spectra, a conventional integrating servo with a properlychosen gain performs nearly as well as the optimal linear predictor. Usingsimple analytical models and numerical simulations, we establish optimum probetimes as a function of clock atom number and of the dominant noise type in thelocal oscillator. We calculate the resulting LO-dependent scaling of achievableclock stability with atom number for product states as well as formaximally-correlated states.

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