We demonstrate the impact of increasing the White Rabbit SoftPLL bandwidth and the PTP message rate.

We show short term fractional frequency stability of 2×10-12, averaging down to 2×10-15 at one day of integration time, with no frequency shift within the statistical uncertainty. Using fiber spools, we realize a 500 km, four-span cascaded White Rabbit link. We use unidirectional links, to ensure compatibility with active telecommunication networks, and White Rabbit equipment with modifications for improved performance. We perform experiments exploring the use of White Rabbit PTP for time and frequency dissemination over long-distance optical fiber links. We apply the experimentally measured central frequency of the (−1,−1) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 × 10−15, with the uncertainty of 0.10 × 10−15. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. The central fringe of (−1,−1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field “map”. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The result shows that the magnetic field fluctuation is less than 1 nT. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally.

The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (−1,−1) magnetically sensitive Ramsey transition. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (−1,−1) magnetically sensitive Ramsey transition.

Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock.

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