Abstract
We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of equations that are valid for a wide variety of clock architectures, making the comparison of a large number of clocks practical. This formalism suggests a generic data exchange protocol that can be used in clock comparison collaborations, for which data logging and decision taking are completely local procedures, independently implemented by the participants.
Highlights
Worldwide time and frequency comparison of clocks has a long-standing history and is the backbone for steering the International Atomic Time (TAI) by primary and secondary frequency standards using the local implementations UTC(k) as a pivot [1,2]
The reference oscillators x is not connected by a chain of comparator outputs to the other oscillators of the network: the only knowledge about the frequency of x available to the network is contained in the nominal frequency ratio” (NFR) between accurate oscillators, which is chosen such that the reduced frequency ratio” (RFR) between these accurate oscillators is upper bounded
1, that can be exactly calculated from known NFRs; and a correcting factor that depends on the RFR between the accurate oscillators xi and 0
Summary
Worldwide time and frequency comparison of clocks has a long-standing history and is the backbone for steering the International Atomic Time (TAI) by primary and secondary frequency standards using the local implementations UTC(k) as a pivot [1,2]. While it is feasible to work out ad hoc equations to calculate the frequency ratio between two remote optical clocks connected by a single optical fiber link from the output of the experimental apparatuses involved in the comparison, the situation becomes rapidly more complex when a large number of clocks are connected by different links with different architectures, operated by a diverse collaboration, and with multiple intermediate steps where data are collected by various parties. For these comparisons, a more rigorous and generic approach must be followed in order to facilitate the data analysis. In Appendix F we illustrate the equations derived in this paper by applying them to a fictitious network
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