On a definition of the SI second with a set of optical clock transitions

TL;DR

This paper proposes a new composite frequency unit based on multiple optical clock transitions to define the SI second, enabling flexible and precise redefinition as optical standards improve.

Contribution

It introduces a composite frequency unit derived from multiple atomic transitions, allowing adaptable and accurate SI second redefinition with various optical clocks.

Findings

The composite unit can be realized with any single clock from the set of transitions.

The unit can be updated as clock performances improve without drifting.

The approach reduces reliance on a single atomic transition for the SI second.

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.