Roadmap towards the redefinition of the second

The NMIs and DIs, as part of their mandates, strive to develop the best realizations of the SI units and build the highest accuracy primary standards. They also typically have the most demanding requirements for accessing accurate time and frequency signals because they provide the highest tier SI dissemination services for their respective countries. The current primary frequency standards have now been surpassed in terms of stability and systematic uncertainty by OFS, and, therefore, the NMIs and DIs are expected to drive the transition to the new state-of-the-art definition.

The implementation of a new definition of the SI second, based on optical standards, and an improved Coordinated Universal Time (UTC) will require the metrology labs to acquire new systems and adopt new methods. The stakeholder survey that was conducted in December 2020–January 2021 showed an overall positive response to the redefinition plans, which indicates high levels of commitment and technical maturity that is essential to support the redefinition work.

Although relatively unknown to the general public, sub-μs timing and synchronization capability has become an essential and crucial feature of most critical infrastructure, including telecommunications, energy, finance, cloud computing, transportation and space activities. Even though these applications do not require the accuracies of the optical clocks today, they, in general, depend on TF metrology.

In addition, many scientific applications require nanosecond levels of stability and/or accuracy such as radio astronomy, particle physics experiments, and time metrology. In the next 5–10 y, the need for higher precision in both time and frequency is estimated to grow across all fields.

Initially, the redefinition of the second, and the development in the time and frequency metrology that this may underpin, will mostly support scientific applications, but industrial ones will arise as the related technology becomes available. For example, quantum communications have some time accuracy and stability requirements at the level of femtoseconds, which are hardly achievable with current technologies, and the stimulus of the redefinition may help their development.

From the CCTF survey and other references [11–14], timing accuracy needs are currently in the range from 1 μs down to 10 ns, while future needs seem to focus below 100 ns for most users. Some scientific users highlighted the need for a sub-nanosecond timing accuracy. The most stringent fractional frequency accuracy needs are currently around 10⁻¹⁴, while future needs are specified up to 10⁻¹⁵ or 10⁻¹⁸ for some specific users.

The most fundamental of the existing scientific applications that will be improved by a redefinition and the resulting improvement in timing infrastructure, are tests of fundamental physics, for which the levels of accuracy achievable with optical clocks can underpin tests of fundamental physical theories, including the investigation of physics beyond the standard model and time variation of the fundamental constants, the search for dark matter, gravitational wave detection, and more [15].

Better clocks will also enable higher-precision atomic and molecular spectroscopy as well as improved time synchronization for high-resolution telescope arrays and future VLBI generations [16], geopotential monitoring with centimetre resolution [17], quantum networks for quantum encrypted communications [18], and others.

These emerging fields of research that already require better TF accuracy or stability than is available today and applications that promise to transition from the research lab into commercial use in the next decades will benefit from the improved accuracy enabled by a redefinition.

A redefinition of the SI second will also lead to timing infrastructure improvements, including improved time scales and frequency transfer methods. These improvements will benefit the wider stakeholder community, including clock and equipment manufacturers and users. The redefinition of the second constitutes a required step in stabilizing and directing the technology development, standardization and adoption.

Table 2 lists the stakeholder requests for their future needs in the accuracy of frequency references. It is clear from the high level of interest in more accurate frequency reference signals that many research opportunities will arise with better access to optical clocks and better dissemination methods.

Due to their demonstrated potential for low fractional frequency instabilities and uncertainties, there is currently considerable research activity directed towards investigating optical transitions to serve as frequency standards. These standards fall into two categories distinguished by the charge state of the atom and the method used for trapping: trapped ion optical clocks and optical lattice clocks with neutral atoms. Presently, ten optical transitions and one microwave transition (⁸⁷Rb) are recommended as SRS, as listed in table 5. We note that due to the lower uncertainties associated with most of the optical standards themselves, the uncertainties for the realizations of the second with these standards as listed in the table are largely determined by the uncertainty of microwave standards based on the Cs transition that enters into the recommended frequencies.

Advances in several key technologies have been critical to the rapid improvement in optical standards. To achieve a low instability, it is necessary to start with an extremely narrow linewidth clock laser. Thus, pre-stabilization of the clock laser to a high-performance optical cavity is a standard component of any high-performance standard. Fractional frequency instabilities as low as 8 × 10⁻¹⁷ on 1 s timescales have been achieved with a clock laser locked to the resonance frequency of a room temperature 48 cm ULE FP cavity (ultra-low expansion Fabry–Perot cavity) [24], while locking to cryogenic single-crystal optical cavities has led to frequency instabilities in the low 10⁻¹⁷ range [25, 26]. In addition, the development of optical frequency combs (OFC) [27, 28], which are needed to link optical frequencies directly with microwave frequencies, has made high-fidelity measurements of absolute optical frequencies at the low 10⁻¹⁶ uncertainty level of fountain clocks feasible. In fact, simultaneous measurements of the same optical frequency ratio with two independent OFCs have shown agreement at the level of 10⁻²¹ [29], thereby confirming the capability of OFCs to support optical frequency ratio measurements at the limit of the uncertainties of current optical clocks. These capabilities have enabled more precise (and more rapid) comparisons between standards, with many of the optical standards realizing SRS as listed in table 5 reaching Type B uncertainties below 10⁻¹⁷.

The current record for systematic uncertainty of an atomic clock is held by the ²⁷Al⁺ quantum logic clock, with a fractional frequency systematic uncertainty of 9.4 × 10⁻¹⁹ [30]. This level of performance is closely followed by that of an Yb optical lattice clock (1.4 × 10⁻¹⁸ [31]), a Sr optical lattice clock (2.0 × 10⁻¹⁸ [32]), an ¹⁷¹Yb⁺ ion clock operated on the octupole (E3) transition (2.7 × 10⁻¹⁸ [33, 34]), and recently a ⁴⁰Ca⁺ ion clock (3.0 × 10⁻¹⁸ [35]). Interestingly, it seems there is not a fundamental limitation for the accuracy of the optical clocks that are being developed based on different ion and neutral atom species. Most of the currently proposed optical transitions can potentially achieve an uncertainty level below 10⁻¹⁸. We note that the lowest instabilities achieved at 1 s averaging time have been observed with optical lattice clocks: 4.8 × 10⁻¹⁷ [36] and 6 × 10⁻¹⁷ [37]. For single ion clocks, the lowest reported instabilities at 1 s are typically around 1 × 10⁻¹⁵ [30, 38].

In order to verify the predicted levels of performance for these standards, there has been a great effort over the past decade to perform measurements of frequency ratios between co-located or remotely located standards. Such comparisons can be based on the same transition or different transitions. Comparing different optical standards based on the same transition provides a way to validate uncertainties by verifying that the realized transition frequencies agree within stated uncertainties. To date, several such comparisons performed within the same institute have reached an overall uncertainty better than 5 × 10⁻¹⁸ [31, 34], with the lowest reaching 1 × 10⁻¹⁸ [31]. Comparisons between standards based on the same transitions from different institutes are at the level of 5 × 10⁻¹⁷ [39]. We note that comparisons between clocks in different locations are much more challenging because they involve either remote comparison, which can be limited by the instability of long-distance time transfer capabilities or transportable standards, which generally have lower levels of performance than their lab-based counterparts. In general, such comparisons are of utmost importance to validate the frequency standards' uncertainties.

Equally valuable are frequency ratios measured between standards based on different transitions. Such ratios between unperturbed atomic transitions are significant, because they are dimensionless quantities given by nature. As a result, two independent measurements of such ratios should coincide within the combined measurement uncertainties. Thus, comparisons between independent measurements of given ratios provide further means to validate stated uncertainties of OFS. We note that such measurements almost always rely on optical frequency combs to span the frequency gap between standards. Therefore, comparing independent measurements of a given optical frequency ratio tests not only the stated uncertainties of optical standards themselves, but those of the combs (and any other optical frequency metrology capabilities relevant to the use of OFS). To date, the most accurate measurement of an optical frequency ratio has a fractional uncertainty of 6 × 10⁻¹⁸ (between two labs about 2 km apart) [39, 40]. A few optical ratios have been measured multiple times by different institutes, thereby enabling first comparisons of such measurements at uncertainty levels ranging from 3 × 10⁻¹⁷ to 2 × 10⁻¹⁶.

We also emphasize that frequency ratio measurements between optical and microwave standards are common and serve to validate our capabilities to connect the optical domain with the microwave domain, as well as to link a potential future definition to the current one. The accuracies of such measurements are now at the limit of the primary standards based on Cs (∼10⁻¹⁶). In the last few years, many such absolute measurements of optical standards have been performed by comparison with TAI, whose rate with respect to the SI second is provided by BIPM publications, based on the currently available reports from primary and secondary frequency standards (www.bipm.org/en/time-ftp/circular-t). Several groups have performed extended measurement campaigns involving both optical and microwave clocks that have lasted from several months [40–44] to several years [45–47]. Although not continuous, these campaigns were realized by performing multiple measurements over a given time span.

Taken as a whole, the resulting ensemble of high accuracy measurements of atomic frequency ratios published after peer-review provides an overdetermined dataset from which one can determine the best values for these atomic frequency ratios, using an adjustment procedure. This task is done on a regular basis by the CCL-CCTF working group on frequency standards (CCL-CCTF WGFS). The resulting output of this calculation provides the basis for the recommended values and uncertainties of frequency standards shown in table 5 [9]. In addition, given the strongly overdetermined nature of the dataset, this adjustment provides a global validation of the status of high accuracy atomic frequency standards and of related measurement capabilities, as described in [3]. In the last implementation reported to the 22nd meeting of the CCTF on 19 March 2021, the adjustment took into account 105 measurements (69 in 2017), including 33 optical frequency ratios (11 in 2017) and 72 absolute frequency measurements (58 in 2017). We note that it is necessary to take into account correlations (483 for the latest adjustment) between these measurements to perform the calculation correctly [10].

Despite the considerable progress to date in optical clock performance, there remains much room for further improvements in terms of clock stability, uncertainty, and robustness. Reduced clock instability is not only useful in direct timing applications, but the extremely low uncertainty of optical clocks is only useful if the statistical uncertainty (Allan deviation) can be reduced to the evaluated uncertainty level at a practical averaging time for the measurement application. Improvements in the observed stability of optical lattice clocks and long-lived ion transitions (²⁷Al^{+, 171}Yb⁺ (E3)) are ongoing but are technically challenging, as they require ultra-stable lasers with coherence times of several seconds to minutes. In addition to continued advances in cavity performance mentioned earlier, there are efforts in parallel to develop novel measurement protocols that mitigate the limitations caused by reference cavity noise, such as zero-dead time interrogation [37], correlation spectroscopy [48, 49], and dynamic decoupling of laser phase noise in compound atomic clocks [50]. It is anticipated that the use of compound clocks could improve the stability of single ion clocks with long clock transition lifetimes to levels comparable to that of optical lattice clocks [50]. For ion species with shorter lifetimes, the stability can be improved directly by increasing the number of ions, but this approach requires special care in the selection of the atomic transition and the control of the systematic shifts to preserve accuracy [51, 52]. Entanglement in multi-ion or neutral atom clocks offers the potential for a stability beyond the standard quantum limit and thus could be a method to further improve the stability of optical clocks [53]. A new type of clock with high relative stability has been demonstrated recently, called a 'tweezer array optical clock' that balances the benefits of non-interacting particles as found in single-ion clocks with the large number of atoms as found in optical lattice clocks [54].

Another critical aspect for the spread of optical clock performance throughout the clock community will be the demonstration of high duty cycle, high performance, robust optical systems. In this direction there has been considerable effort with many systems under development. Indeed, all major subsystems of an optical clock with laser cooled atoms or ions have already been developed as robust transportable devices for autonomous operation, which have been partially tested for operation in space. This includes vacuum systems and traps for atoms [55] and ions [56], tunable laser systems for cooling and interrogation, optical reference cavities for obtaining a narrow linewidth of the reference laser [57–59], and optical frequency combs for transfer of the optical stability to a microwave output signal [60]. However, the integration of an optical clock from the subsystems also requires the robust optical alignment of multiple laser beams and the monitoring, control and adjustment of a few dozen electrical and mechanical parameters. Fully integrated prototype systems that have been used as transportable optical clocks on the footprint of a small trailer have been demonstrated for a Sr optical lattice clock [61, 62] and for a clock with a single trapped Ca⁺ ion [63].

Some groups have demonstrated high clock operation uptimes, for example 80.3% for a duration of 6 months [42], 93.8% uptime for a period of 10 d [44]. More recently fully autonomous operation for 2 weeks with 99.8% uptime at 2 × 10⁻¹⁷ systematic uncertainty inside a laboratory has been demonstrated for the OptiClock based on the E2 transition of ¹⁷¹Yb⁺ [64, 65]. The system fits inside the volume of two 19 inch racks and has been developed by PTB jointly with industry [65]. Optical clocks with (nearly) 100% uptimes for one month of continuous operation or longer are expected to become common in the next few years. These results indicate that the development of a turn-key autonomous optical clock is technically feasible at a performance level that is superior to available microwave frequency standards and shows the way towards a commercial high-performance optical reference.

Finally, one of the most exciting directions in optical clock research today is the search for transitions that have still lower sensitivities to external fields than current optical clocks in an effort to further reduce clock uncertainties. Some of these include a nuclear transition in ^229mTh [66], and transitions in highly-charged ions [67, 68] and lutetium ions [52]. While all of these systems present their own technological challenges, they could well be among the main candidates for future optical clocks with performance at the 19th and 20th digits.

Remote comparison of time scales and frequency standards has been studied for nearly 50 y using space-based microwave techniques, including Global Navigation Satellite Systems (GNSS) and Two-way Satellite Time and Frequency Transfer (TWSTFT). Besides, another technique using Very Long Baseline Interferometry (VLBI) has been recently realized, although only limited number of laboratories, far from operational network, has demonstrated the capability. In the last decade, optical techniques using fibre optic links have offered greatly improved stability and accuracy. Innovative satellite transfer in the optical domain is also envisaged. Lastly, Transportable OFS or Clocks (TOCs) used as travelling standards can support a redefinition of the second that requires comparisons at an accuracy level of 10⁻¹⁸ and global geographical coverage.

GNSS time transfer is a one-way technique used since the 1980s, notably for the realization of UTC. A collaboration with the International GNSS Service (IGS) has led to the use of Precise Point Positioning (PPP) for time and frequency comparisons and development of the integer ambiguity PPP technique (IPPP), which to date offers the best long-term stability among the GNSS techniques. Figure 1 [69] shows that IPPP provides time transfer with a modified Allan deviation of 7 × 10⁻¹⁶/τ, where τ is the averaging time in days of continuous phase measurements. A twofold improvement is expected using satellites from all the GNSS, as opposed to just GPS as at present.

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TWSTFT, the second intercontinental-capable satellite-based microwave method, typically employs the code-phase of a signal modulated by a pseudorandom noise code sent and received by microwave link via a geostationary telecommunications satellite, at Ku-band frequencies [71]. Improved performance is achieved by the use of Two-Way Carrier-Phase (TWCP), which exploits carrier-phase measurements, with an instability of a few parts in 10¹⁶ at one day. Further results [72] indicate that TWCP performs at least as well as IPPP in terms of stability. Figure 2 shows the modified Allan deviation of Code Phase and Carrier Phase TWCP.

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In addition, a recently implemented software-defined receiver (SDR) successfully reduced the long-term instability by about a quarter [73]. Similar technology is expected to be applied to the transmitters for further improvement resulting in integrated digital modems that are an important step to improve TWSTFT beyond the current state of art. Moreover, in order to reach to the sub 1E-17 level it is essential to improve on modeling of all non-reciprocal error sources, such as signal propagation, atmospheric turbulence, and relativistic effects [74].

VLBI utilizes the reception of radio signals from extragalactic radio sources, with the time difference between the arrivals of the signals measured at two antennas equipped with local atomic clocks. Using VLBI, the frequency of an Yb and a Sr optical standard has been compared [75], with a statistical uncertainty from the VLBI link of 9 × 10⁻¹⁷ over 300 h of measurements.

Using optical communication, satellite-based comparisons were demonstrated with the Time Transfer by Laser Link (T2L2), onboard the Jason-2 satellite [76]. Three T2L2 links were compared with IPPP links [77], with the standard deviation of the time difference well below 100 ps. Promising results have also been obtained using terrestrial free-space optical time and frequency transfer, using CW or coherent pulsed lasers. For both, uncertainties of parts in 10¹⁶ in a few minutes have been achieved over distances up to tens of kilometers. The synchronization of two clocks 28 km apart below 1 fs within 100 s, even at high Doppler velocities of up to ±24 m s⁻¹, and under stable weather conditions has been shown [78]. A comparison at 113 km with modified Allan deviation of 10⁻¹⁹ at 10⁴ s was also reported [79], the first evidence of the method compatibility with Low Earth Orbit satellites. Figure 3 indicates both results.

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Optical fibres offer several key advantages compared to free-space techniques: high isolation from external interference; high bandwidth; and low propagation losses, when compensated by optical amplifiers and regeneration devices, at distances more than 1000 km. For time and frequency comparisons, three main methods are used: CW light from an ultra-stable laser, without modulation; modulated laser light (amplitude, frequency, or phase modulation); and protocol-based signals, based on digital data transfer.

Propagation of optical signals in optical fibres for frequency comparisons offers two main choices: bi-directional fibre links, providing the best performance, and unidirectional fibre links, which are easier to implement on common telecommunication networks. Submarine links are less noisy than terrestrial links [80], as shown in figure 4.

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Optical frequency transfer over fully bi-directional links [81] exhibits typical Allan deviations of ∼10⁻¹⁵ at 1 s and <10⁻¹⁸ for greater than 100 s, over (100–1000) km long links. There is no systematic frequency shift reported so far at the level of 10⁻¹⁸. Conversely, optical frequency transfer over unidirectional links has demonstrated an Allan deviation of ∼10⁻¹⁵ at 1 s integration time, unidirectional links have demonstrated an Allan deviation of 7 × 10⁻¹⁷ for averaging times between 30 s and 200 s [82]. There is no systematic frequency shift reported so far in the range of 10⁻¹⁶ [83]. Modulation of the optical carrier frequency enables a frequency reference in the radio and microwave domain (10 MHz−10 GHz) to be transmitted, with typical uncertainty less than 10⁻¹⁷ at 10⁴ s. Latest synchronization experiments report 300 km free space link and demonstrate a sub ps capability [84].

Time transfer over fibre can be in the radio/microwave domain (10 MHz–10 GHz) or in the optical domain. In either case, the technique requires the modulation (amplitude, phase or frequency) to be tied to a time scale. The time uncertainty is less than 1 ns, approaching tens of picoseconds, in particular with White Rabbit (WR) Precise Time Protocol [70] and the ELSTAB technique [85].

Transportable optical clocks offer the best immediate prospects to meet the criteria for the redefinition of the SI second in regard to the required accuracy level and geographical coverage. As described above, space microwave techniques need to significantly improve their uncertainty levels. Fibre techniques meet the required uncertainty, but obtaining global coverage requires a large effort and investment. Satellite-based optical comparisons have not yet been demonstrated on a full metrological and operational basis. On the other hand, several TOCs have already reported the performance results that meet the redefinition requirements. An accuracy ranging from 10⁻¹⁵ down to parts in 10¹⁸ has been reported for several ⁸⁷Sr TOCs [86–88]. A bosonic ⁸⁸Sr TOC achieved 2 × 10⁻¹⁷ uncertainty [89]. TOCs based on ions have also been reported: a Ca⁺ TOC with a systematic uncertainty of 1.3 × 10⁻¹⁷ [90]; an Al⁺ standard, with four main biases evaluated at the 10⁻¹⁸ level [91]; and a Yb⁺ standard demonstrated with 10⁻¹⁷ accuracy [65]. In addition to their role in the redefinition, the TOCs are essential tools for chronometric levelling and some have already been used for this purpose [62, 87, 90].

The time and frequency transfer techniques described above allow to compare timescales and their scale intervals around the world. We can also compare the scale intervals by evaluating them with respect to locally available accurate frequency standards. However, this assumes that we have knowledge of the geopotential at the clocks location, since the atomic clocks generate their proper time and the tick rate is affected by the relativistic frequency shift. We should also note that International Atomic Time (TAI) is defined in Resolution 2 of the 26th CGPM (2018) as a realization of Terrestrial Time, which has a reference potential of W₀. Thus, the local geopotential needs to be obtained with respect to W₀ particularly for the calibration of the TAI scale interval. For the modelling of the geopotential, satellite data only provides information valid at a spatial resolution of 200 km or worse. Combining regional information from gravity measurements with the global model as well as the results of the levelling from the nearest reference to the trapped atoms, the gravity shifts of optical clocks in some metrological laboratories are now evaluated with uncertainty at the mid 10⁻¹⁸ level or better [92–94].

Resolution 2 of the 26th CGPM (2018) states that Coordinated Universal Time (UTC), based on TAI, is the only recommended international time reference and provides the basis of civil time in most countries. Thus, the scale interval of TAI needs to be maintained with respect to OFS for the redefinition of the second. The future TAI should have at least a similar or better performance than the current realization of TAI, which is nowadays calibrated mainly by microwave-based primary frequency standards. To this end, more than 10 d of regular operation of optical clocks or a local timescale steered by an optical clock is required, in each Circular T reporting period, since the frequency link of local clocks to TAI is made by GNSS or TWSTFT. For the determination of TAI, the BIPM employs an uncertainty of ∼10⁻¹⁵/(t/5), where t is the signal integration time in days [95].

The capabilities for TAI calibration of several specific OFS have been examined by the CCTF Working Group on Primary and Secondary Frequency Standards (CCTF-WGPSFS), and as a result, eight OFSs, recognized at present as Secondary Frequency Standards (SFS), have contributed to TAI.

The first data for TAI calibration with an OFS was obtained in 2014 by an optical ⁸⁷Sr lattice clock from SYRTE [44], applied for TAI calibration in 2017, and since mid-2021, at least one SFS has calibrated TAI every month. The BIPM incorporates the data from SFS into the TAI steering with additional uncertainty u_srep, which is determined by the uncertainty in the CIPM recommended frequency of the SFS (table 5). The recent update of CIPM recommended frequencies has reduced u_srep, leading to an increased total weight of typically more than 10% for all SRS for the determination of the TAI scale interval. The stated uncertainties from the laboratories, ignoring the recommended uncertainty (u_srep) of the SRS, range from 1.9 × 10⁻¹⁶–3.3 × 10⁻¹⁵, limited primarily by dead time and link uncertainties. Until now, the lowest uncertainty in the SFS data submitted to TAI was reached by the NICT-Sr1 in Circular T 408, and IT-Yb1 in Circular T 411.

The calibrations provided from all OFSs [31, 42, 44, 96–99] are so far consistent with those provided by primary frequency standards (see also https://webtai.bipm.org/database/d_plot.html). The development of OFSs with high uptimes over the typical reporting intervals of (15–30) d, the development of better local oscillators, and advances in frequency transfer are crucial goals to obtain significant improvements in the stability of TAI.

UTC is a post-processed timescale determined by the BIPM. For civil time, time and frequency metrology laboratories generate and provide real-time signals equivalent to UTC. These real time signals are called UTC(k), denoting a real-time UTC generated at the laboratory 'k'. In general, such a UTC(k) is often employed as a national standard time with the addition of a time offset appropriate to the respective time zone. For the future redefinition of the second, UTC(k) generated or at least steered by an optical clock is one ancillary condition. UTC(k) time scales must be continuous, whereas it is unrealistic at this point to operate optical clocks completely without dead time. The operation of multiple optical clocks for redundancy is not yet realized since maintaining multiple optical clocks is a difficult task and the procedure to switch between optical clocks has not yet been studied. On the other hand, intermittent operation of an optical clock enables generation of a real-time timescale steered by the optical clock [100–104]. Here, the source oscillator is still a microwave oscillator (hydrogen maser), but the scale interval is tuned with respect to an optical clock. In some metrology institutes, a similar generation of UTC(k) has already been successfully implemented for some time utilizing caesium fountain frequency standards [105–108]. In future, an all-optical timescale is expected [109], particularly for improvement of the short-term stability. Here, a CW laser, stabilized to a stable optical cavity, would play the role of the source oscillator. Considerable progress in mode-hop free operation of CW lasers has been made in the last decade.

This section contains a detailed description of the criteria and the estimation of their fulfilment level in 2022.

Mandatory criterion I.1—Accuracy budgets of OFS

I.1.a—At least three OFS based on the same reference transition, in different institutes, have demonstrated evaluated relative frequency uncertainties ≲2 × 10⁻¹⁸ based on comprehensive, comparable and published accuracy budgets.

Fulfilment level: 20%–40% [30–32].

I.1.b—At least three frequency evaluations of OFS based on different reference transitions, either in the same institute or different institutes, have demonstrated evaluated uncertainties ≲2 × 10⁻¹⁸ based on comprehensive, comparable and published accuracy budgets.

Fulfilment level: 80%–100% [30–32].

→ Overall Fulfilment level of criterion I.1: 30%–50%.

Mandatory criterion I.2—Validation of optical frequency standard accuracy budgets—Frequency ratios

I.2.a—Unit ratios (frequency comparison between standards with same clock transition): at least three measurements between OFS in different institutes in agreement with an overall uncertainty of the comparison Δν/ν ≲5 × 10⁻¹⁸ (either by transportable clocks or advanced links). Applicable to at least one radiation of I.1.

Fulfilment level: 0%–20% [31, 34, 62].

Strictly speaking the reported measurements of unit ratios are not between different institutes and should not count in this fulfilment level. Nevertheless, a fulfilment level at 0%–20% has been assigned based on these in house comparisons with uncertainties significantly lower than 5 × 10⁻¹⁸ that can be considered as the first step in the right direction.

I.2.b—Non unit ratios (frequency comparison between standards with different clock transitions): at least five measurements between standards among I.1 or other, each ratio measured at least twice by different institutes in agreement with an overall uncertainty of the comparison Δν/ν <5 × 10⁻¹⁸ (either by direct comparisons, transportable clocks or advanced links).

Fulfilment level: 0%–20% [40].

Again, this measurement alone is not valid in terms of the criterion which demands ratio measurements «twice by independent» institutes. However, it is the first measurement at about the required uncertainty level, and it is considered the first step towards the fulfilment of this index.

→ Overall Fulfilment level for Criterion I.2: <30%.

Mandatory criterion I.3—Continuity with the definition based on Cs

There are at least three independent frequency evaluations of the optical frequency transitions utilized by the standards in I.1) with TAI or with three independent Cs primary frequency standards (in different or the same institutes), possibly via optical frequency ratio measurements, where the measurements are limited essentially by TAI or by the uncertainty of these Cs frequency standards (Δν/ν <3 × 10⁻¹⁶).

→ Fulfilment level: 90%–100% [44–47, 97, 98, 104, 110, 111].

Mandatory criterion I.4—Regular contributions of OFS to TAI (as secondary representations of the second)

At least three state-of-art calibrations of TAI (uncertainty ≲2 × 10⁻¹⁶ without counting the recommended uncertainty of the secondary representation of the second u_srep) each month from a set of at least five OFS for at least 1 y. Check that there is no degradation of TAI if its calibrations were done by OFS considered as primary standards and Cs frequency standards considered as secondary standards.

Fulfilment level: 30%–50% [see www.bipm.org/en/time-ftp/circular-t, and https://webtai.bipm.org/database/show_psfs.htm, https://webtai.bipm.org/database/d_plot.html].

Ancillary condition I.5—High reliability of OFS

Reliable continuous operation capability of OFS, in a laboratory environment, with the appropriate level of uncertainty.

Progress status: Typical uptimes of OFS over measurement durations >10 d currently cover a wide range from a few percent to 90% [44, 111, 112], and www.bipm.org/en/time-ftp/circular-t.

Ancillary condition I.6—Regular contributions of OFS to UTC(k)

Progress status: Preliminary tests of UTC(k) steered by an OFS [100–103, 109].

Mandatory criterion II.1—Availability of sustainable techniques for optical frequency standard comparisons

Availability and sustainability of transportable clocks or TF links with uncertainties <5 × 10⁻¹⁸ for frequency comparisons between at least NMIs operating OFS of I.1), on a national/intracontinental basis (baseline up to about 1000 km). Capability of repeated uncertainty estimations of these links.

→ Fulfilment level: 50%–70% [62, 113, 114].

Mandatory criterion II.2—Knowledge of the local geopotential with an adequate uncertainty level

Knowledge of geopotential differences for NMIs operating OFS of I.2) to be consistent with the uncertainty budget of a frequency comparison between OFS using advanced links, i.e. including the uncertainty budget of the two OFS and of the link. Knowledge of local geopotential for NMIs operating OFS of I.4) with an uncertainty corresponding to a frequency uncertainty ≲10⁻¹⁷, for the calibration of TAI.

→ Fulfilment level: 70%–90% [39, 87, 92–94] and www.bipm.org/en/time-ftp/data.

Ancillary condition II.3—High reliability of ultra high stability TF links

On-demand continuous operation capability of TF links over sufficient durations that do not limit OFS comparisons and their regular contributions to TAI.

Progress Status: a few months continuous operation of fibre links for intracontinental comparisons [113, 115] but no existing link allowing OFS intercontinental comparisons without degradation.

Mandatory criterion III.1—Definition allowing future more accurate realizations

The new definition must be long lasting. On the short term (just after the redefinition), it must ensure an improvement by 10/100 of its realization with OFS, i.e. reaching 10⁻¹⁷/10⁻¹⁸ relative frequency uncertainty. On the longer term, it must have the potential for further improvement of the realization of 10⁻¹⁸ and beyond in order to avoid any early obsolescence of the definition.

→ Fulfilment level: 100% (To be confirmed, based on the chosen option for the redefinition, but no identified fundamental effect limiting OFS accuracy at 10⁻¹⁸ level for all species in I.1, and some newer systems have the potential to go beyond 10⁻¹⁸)

Mandatory criterion III.2—Access to the realization of the new definition

III.2.a Realization/'mise en pratique' of the new definition must be easily understandable with a clear uncertainty evaluation process;

Fulfilment level: 0% (No existing document; pending the choice of the redefinition option)

III.2.b—Access for NMIs and high accuracy users to primary or secondary realizations of the new definition;

Fulfilment level: 100% (To be confirmed, based on the chosen option for the redefinition, but primary or secondary representations of the SI second will continue to be accessible via metrology institutes or TAI)

III.2.c—Cs frequency standards ensure a secondary realization of the new definition.

Fulfilment level: 100% (existing TAI architecture will be maintained at current level or better and Cs will be a secondary representation of the second)

→ Overall Fulfilment level for Criterion III.2: 70%–90%.

Ancillary condition III.3—Continuous improvement of the realization and of time scales after redefinition

Commitment of NMIs to make the best effort to:

• improve and operate OFS that provide primary or secondary realizations of the new definition (reliable/continuous operation, regular contributions to TAI, ...);Progress status: Several OFS are already in operation and used by the CCL-CCTF Working Group on Frequency Standards (CCL-CCTF-WGFS) to calculate the Recommended values of standard frequencies 2021 [10]
• maintain the operation of Cs fountain standards over the appropriate duration;Progress status: 12 Cs fountains in operation [116–124]
• development of new OFS;Progress status: Several other atomic species are being investigated as potential candidates for the next generation, for example ²²⁹Th⁺, Lu⁺, Cd, and several highly charged ions. The most recent references can be found for example in [Proceedings of the annual IEEE IFCS https://ieee-uffc.org/symposia/ifcs, and EFTF conferences www.eftf.org/].

Ancillary condition III.4—Availability of commercial OFS

Progress status: No available commercial OFS.

Ancillary condition III.5—Improved quality of the dissemination towards users

Progress status of TF links (GNSS, TWSTFT, Fibre/Internet) for the dissemination of the definition towards users:

• Frequency stability: 10⁻¹⁷–10⁻¹⁶ for satellite microwave techniques (GNSS, TWSTFT); 10⁻²⁰ level for fibre links [125]
• Time accuracy: 1 ns for satellite microwave techniques (GNSS, TWSTFT); 50 ps for fibre links [126].