Abstract
The current SI second based on the atomic hyperfine transition in the ground state of 133Cs is expected to be replaced by a new definition based on optical frequency standards, whose estimated uncertainty has now been established two orders of magnitude lower than the accuracy of the best Cs primary standards. However, such a redefinition of the second is hindered by the fact that many atomic species are potential contenders to become the new primary frequency standard. In this paper, we propose to resolve this issue by defining a composite frequency unit based on the weighted geometric mean of the individual frequencies of different atomic transitions. This unit has the property to be realisable with any single clock whose transition composes the unit, provided that at least a few frequency ratios are available, with an accuracy that marginally differs from the nominal clock uncertainty. We show that the unit can be updated as the performances of the contributing transitions evolve, without incurring a drift on the unit itself.
Highlights
Since 1967, the definition of the Système International (SI) unit of time, the second, has been based on the hyperfine energy splitting of the ground state of 133Cs atoms [1]
The current definition of the SI second based on Cs fulfills these requirements: it is realisable with a cold atom atomic fountain clock, and the constant NSI was chosen so that the atomic second defined with Cs would match the previous definition of the SI second based on the ephemeris time [10]
We showed that a frequency unit ν can be defined as the weighted geometric mean of the frequencies of a set C of clock transitions:
Summary
Since 1967, the definition of the Système International (SI) unit of time, the second, has been based on the hyperfine energy splitting of the ground state of 133Cs atoms [1]. The 26th CGPM in 2018 introduced a new wording of the definition of the time unit, in order to make it consistent with the newly adopted definitions of the other base units: The second, symbol s, is the SI unit of time It is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192 631 770 when expressed in the unit Hz, which is equal to s−1. It means that none of these optical transitions currently stands out as an obvious choice for a new definition of the SI second, and the fast evolution of the field of optical frequency metrology makes picking a single atomic species uncertain Facing this situation, it seems unavoidable that a new definition of the SI second should not designate a specific atomic transition as the new standard, but rather define the frequency unit from a weighted mix of the best realised optical trans itions. This article proposes such a definition for a unit of time that can accommodate with the multiplicity of frequency standards and their evolution with time
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