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### Abstract:

GPS Precision Point Positioning (PPP) has become a standard method for the time and frequency transfer which is especially useful for inter-continental frequency comparisons of atomic clocks. Moreover, the GPS PPP link has been used for the TAI computation for the last decade which provides a direct link to the TAI/UTC for the National Metrology time laboratories. Here we report on a new absolute frequency measurement of the NRC’s strontium ion atomic clock reference transition using the GPS PPP method. We use the GPS PPP link to determine the frequency as well as the drift of the flywheel oscillator, an active hydrogen maser, against TAI/UTC over a period of about 200 days. This frequency drift function was then used to calculate the frequency difference between the Sr+ ion clock and the flywheel oscillator. The low 2 × 10^-16 uncertainty of the PPP link was achieved by using the month-long frequency averaging interval. The NRC’s Sr+ ion clock has a systematic uncertainty of 1.5 × 10^-17 and its reference transition frequency has been recommended as a secondary representation of the SI second by the CIPM [1, 2]. The frequency measurement campaign of the Sr+ ion clock happened in June 2017 and lasted for 13 days with a total up time of 91.73 hours. Two active hydrogen masers (SM1 for the first 3 days and VM1 for the last 10 days) were used as the reference for the optical frequency comb which was used for the Sr+ ion frequency measurement. The data analysis is based on the accurate determination of the absolute frequency of maser VM1, which was used as a flywheel oscillator for the ion clock frequency measurement, through the GPS PPP link over a period of about 200 days. The PPP link was used to transfer the local UTC time, UTC(NRC), to compare to TAI/UTC. On the other hand, the frequency between VM1 and UTC(NRC) was continuously measured and, therefore, could be linked to TAI/UTC. We found that the frequency drift of maser VM1 can be better modeled using a quadratic function instead of just a linear one, indicating the presence of maser settling (or aging). We chose Circular T #354 (MJD 57904 – 57934) as the ion clock frequency evaluation period. The mean frequency difference between the ion clock and maser VM1 was found by the weighted fit of the intermittent frequency measurements using the maser drift function with the measurement durations as the weights. The uncertainty due to the ion clock measurement down times was estimated using the noise model of the VM1. The mean frequency difference between VM1 and TAI/UTC was found using the above mentioned frequency modeling method for the 30 days evaluation period. Traceability to the SI second is completed by taking into account the scale interval d of TAI for the Circular T #354 taken from the BIPM Circular T website. The systematic and statistical uncertainties of each step were carefully calculated. The preliminary absolute frequency of the Sr+ ion reference transition was found to be in excellent agreement with our previous work [3], with a total fractional frequency uncertainty of 3.8 × 10^-16 representing a fourfold improvement over our previous results. The contributions of the statistical uncertainty are from data extrapolation caused by the measurement down times of the Sr+ ion clock (2.4 × 10^-16), the GPS PPP link uncertainty (2.0 × 10^-16), and the statistical uncertainty of the TAI scale interval d (2.0 × 10^-16). The systematic uncertainty is dominated by that of the SI second realization from the primary/secondary frequency standards (1.0 × 10^-16). This accurate measurement of the reference transition frequency is critical for the NRC’s Sr+ ion atomic clock as a candidate for a future re-definition of the SI second. References: [1]. A. A. Madej, P. Dubé P, Z. Zhou, J. E. Bernard, and M. Gertsvolf, Phys. Rev. Lett. 109 203002, 2012 [2]. P. Dubé, A. A. Madej, Z. Zhou, and J. E. Bernard, Phys. Rev. A 87 023806, 2013