Abstract We report an improved absolute frequency measurement of a 176 Lu + ( 3 D 1 ) optical frequency standard, operated at the National University of Singapore (NUS), evaluated via a remote link to the NRC-FCs2 caesium fountain primary frequency standard. Operating a single ion clock with 94.2% uptime over 10 days, and using an ambiguity-resolved precise point positioning (PPP-AR) link over the Global Positioning System (GPS), we determine an absolute frequency of 353 638 794 073 800.332(91) Hz at a fractional uncertainty of 2.6×10 -16 . This agrees with our previous result, which underpins the CIPM recommended frequency value, and reduces the uncertainty by a factor of 3.6.

We report an improved absolute frequency measurement of the ^176Lu^+ (^3D_1) optical frequency standard, evaluated via a remote link to the NRC-FCs2 caesium fountain primary frequency standard. Operating a single ion clock with 94.2

New trapped-ion optical clocks with low systematic shift uncertainties are being developed at the National Research Council of Canada, with the goal of meeting the criteria for the redefinition of the SI second. The design of these new clocks addresses directly known limitations in the current laboratory system, to allow reaching 18-digits of accuracy. Besides the requirements of accuracy, another crucial criterion is continuity with the current definition of the SI second. We report progress on the development of the new ion optical clocks and a recent measurement of the absolute frequency of the 445 THz transition of the strontium ion with a fractional uncertainty of 1.0×10−16.

We have made improvements in the stability, accuracy, and performance of the NRC-FCs2 fountain clock. The dominant systematic effects have been re-evaluated. Optically-stabilized microwaves are used to improve the short-term stability, now reaching sigma y=3x10-14 tau-12. We have evaluated the distributed cavity phase shift using absorption imaging. This technique dramatically reduces the evaluation time and final uncertainty. We have re-evaluated biases due to microwave leakage and synchronous phase transients with higher accuracy. The total systematic uncertainty of NRC-FCs2 is now 1.1x10-16 in fractional frequency, a factor of 2 improvement over its most recent evaluation.

We report on a measurement of the absolute frequency of the 88Sr+ clock transition via a direct comparison to our cesium fountain clock, National Research Council Canada (NRC)-FCs2. The measurement yield a value of 444779044095485.404 +/- 0.045 Hz. The corresponding fractional uncertainty of 1.0x10-16 is, to our knowledge, the lowest so far reported for an absolute frequency measurement. The low uncertainty obtained is primarily a consequence of improvements to NRC-FCs2, specifically a systematic uncertainty of 9.3x10-17 and a stability of 6.3x10-14/tau. The measurement was made over a period of 37 days with 68% uptime, for a total measurement time of 2.16x106 s. The 88Sr+ frequency was also compared to terrestrial time via a global navigation satellite system (GNSS) link to Universal Coordinated Time, yielding a frequency value of 444779044095485.406 +/- 0.089 Hz, which is in agreement with the direct comparison with NRC-FCs2.

We describe a polarization maintaining erbium fibre optical frequency comb that was used to link NRC-FCs2 to an ultrastable laser, generating ultrastable microwaves (MW) that are shown to significantly shorten the fountain clock averaging time. A detailed experimental setup for our next measurement linking NRC Sr-88(+) clock to the NRC-FCs2 Cs fountain clock is also presented.

We make absolute frequency measurements of Cs Rydberg transitions, 6S1/2, F = 3) - nS1/2(n = 23-90)) and nD3/2,5/2(n = 21-90)), with an accuracy of less than 72 kHz. The quantum defect parameters for the measured Rydberg series are the most precise obtained to date. The quantum defect series is terminated at delta 4, showing that prior fits requiring higher order quantum defects reflect uncertainties in the observations. The precision of the measured quantum defects allow for the calculation of Rydberg electric-dipole transitions and fine-structure intervals extrapolated from high principal quantum numbers, to rival that of sophisticated many-body relativistic calculations carried out at low Rydberg principal quantum numbers. We quantitatively predict the contributions to the quantum defect parameters from core polarization and core penetration of Cs inner shell electrons. A new value for the ionization energy, consistent across the nS1/2 and nD3/2,5/2 Rydberg series, is reported at 31406.46775148(14) cm-1.

We make absolute frequency measurements of Cs Rydberg transitions, | 6S_1/2, F=3 ⟩→| nS_1/2 (n=23-90)⟩ and | nD_3/2,5/2 (n=21-90)⟩, with an accuracy of less than 72 kHz. The quantum defect parameters for the measured Rydberg series are the most precise obtained to date. The quantum defect series is terminated at δ_4, showing that prior fits requiring higher order quantum defects reflect uncertainties in the observations. The precision of the measured quantum defects allow for the calculation of Rydberg electric-dipole transitions and fine-structure intervals extrapolated from high principal quantum numbers, to rival that of sophisticated many-body relativistic calculations carried out at low Rydberg principal quantum numbers. We quantitatively predict the contributions to the quantum defect parameters from core polarization and core penetration of Cs inner shell electrons. A new value for the ionization energy, consistent across the nS_1/2 and nD_3/2,5/2 Rydberg series, is reported at 31406.467 751 48 (14) cm^-1.

The NRC-FCs2 fountain clock was first evaluated in 2020 [1]. Since that time, it has demonstrated both accuracy and robustness and has contributed regularly to the steering of International Atomic Time (TAI) through monthly submissions to the BIPM. It is also currently used to steer UTC(NRC), Canada's official timescale. We have recently undertaken a reevaluation of several prominent systematic effects in NRC-FCs2. Thus far, this has resulted in a reduction of the overall uncertainty from similar to 3 x 10(-1)6 to 1.7 x 10(-16). Here, we will describe the details of the re-evaluation.

We report on the first characterization of the frequency transfer performance of the GPS precise point positioning with carrier-phase integer ambiguity resolution (PPP-AR) implemented by the Natural Resources Canada (NRCan) online service CSRS-PPP. We show that continuous PPP-AR links of multiple days can be formed by carefully fixing the day boundary phase discontinuity. The stability of the links can reach 7 × 10 − 16 and 1 × 10 − 16 (Allan deviation) at 1 d and 7 d averaging times, respectively, and mid to low 10 −17 at 20 d–30 d. We compared the atomic fountain primary frequency standards (PFS) between NRC in Ottawa, Canada and PTB in Braunschweig, Germany for 135 d via GPS PPP-AR and precise point positioning links. The NRC and PTB PFS agree within a few parts in 10 16 , which is well below the combined systematic uncertainty. It is expected that with uncertainty at 10 −17 , the PPP-AR links will become a powerful tool for remote comparisons of atomic optical clocks, essential for the future redefinition of the SI second.

The collisional frequency shift is a dominant contribution to the uncertainty of many caesium fountain clocks. Minimizing the effect can be difficult, as lowering the atomic density comes at the cost of a reduced signal-to-noise ratio. Also, it is typically not atomic density, but total atom number that is measured in the experiment, which can lead to a potential measurement bias. In this paper, we describe a direct measurement of the atomic density using absorption imaging of the atomic cloud. For the caesium fountain clock, NRC-FCs2, at the National Research Council Canada, these measurements have led to a reduction in the uncertainty due to the collisional shift by a factor of 10.

Atomic clocks form the foundation of international timekeeping and synchronization. At the National Research Council Canada, the NRC-FCs2 fountain clock has been run nearly continuously with minimal interruption since 2020, participating in the steering of International Atomic Time through regular submissions of data to the International Bureau of Weights and Measures. We describe the design and performance of NRC-FCs2, a caesium fountain clock serving as a primary frequency standard for Canada, and its role in global timekeeping.

Recently, several changes were applied to UTC(NRC) generation and dissemination to improve its accuracy and reliability. First, the source clock that is used for UTC(NRC) generation was switched from a caesium thermal beam commercial clock to a commercial hydrogen maser, steered by an external frequency offset generator. The introduction of an automatic steering of UTC(NRC) to match the frequency of NRC caesium fountain primary frequency standard, NRC-FCs2 [1] was implemented next. The redundancy of the UTC(NRC) dissemination for NRC time services including telephone talking clocks, NTP servers, and NRC TimeLink™ system has been improved by a complete rerouting of RF, 1 PPS and DC power to provide stacks of fully independent systems. NRC-FCs2 has an overall systematic uncertainty of 2.3 × 10^-16 in fractional frequency and its typical stability, 1.95 × 10^-13 at 1 sec averaging time, is limited by the short term stability of the local oscillator. NRC-FCs2 has been reporting to the BIPM for the steering of International Atomic Time (TAI) / UTC since October 2019 with a typical uptime of more than 95% every month. This nearly continuous operation of FCs2 makes it ideal as a frequency reference for the automated steering of UTC(NRC). The new UTC(NRC) uses an active hydrogen maser (Vremya-CH, VCH-1003ML), VM1, as its source oscillator and an Auxiliary Output Generator (AOG) to generate UTC(NRC) 5 MHz signals. The frequency of the AOG output signal is steered to NRC-FCs2 daily and is used to generate the 1 PPS UTC(NRC) signal using a frequency divider. In order to select the steering algorithm time constants and thresholds, and to optimize the UTC(NRC) stability and accuracy, we performed a numerical study based on noise modeling of VM1 and FCs2. The modeling shows that UTC(NRC) remains within 2 ns of the reference with daily frequency adjustments. In the laboratory implementation, the AOG is steered daily with the predictive frequency correction calculated from a linear fit to several days of the measurement results between NRC-FCs2 and the VM1 maser. In the absence of FCs2 data, e.g. due to maintenance, the algorithm uses rapid UTC (UTCr) reports to steer UTC(NRC). We started the UTC(NRC) steering based on NRC-FCs2 on August 26, 2021 (MJD 59452). The upgraded UTC(NRC) has been aligned with the UTCr on the same day. From UTCr – UTC(NRC) reports we find that UTC(NRC) has not deviated from UTCr by more than 2 ns in one month. In addition to the upgrades to UTC(NRC) generation, we have been enhancing the NRC TimeLink™ (TL) dissemination system [2]. We implemented predictive frequency corrections to its rubidium frequency standard local oscillator that significantly improved its performance over 48 hours of holdover. We are also preparing the installation of the TL system in Inuvik Canada and will present the system performance over twice the baseline of more than 4,000 km from Ottawa to Inuvik and back. References: [1] S. Beattie, B. Jian, J. Alcock, M. Gertsvolf, R. Hendricks, K. Szymaniec, and K. Gibble, Metrologia 57 035010, 2020 [2] R. Douglas, A. Charbonneau and M. Gertsvolf, Metrologia, 58 055003, 2021.

SummaryWe describe the portable fiber combs that were recently set up at the NRC. We also describe two of their intended applications: the frequency measurement of a strontium-88 ion clock against the primary standard NRC-FCs2 and ultra-stable radio frequency synthesis.

We report the first accuracy evaluation of NRC-FCs2, an atomic fountain clock developed at the National Research Council Canada. The short term stability at high atomic density is 1.1 x 10(-13) at 1 second of averaging time. The typical overall fractional type B uncertainty is 2.3 x 10(-16). GNSS-based frequency comparisons of NRC-FCs2 with the SI second, as reported by the BIPM over fourteen months, give a fractional frequency difference of -2.4(3.7) x 10(-16).

Distributed cavity phase (DCP) frequency shifts are a leading systematic effect in atomic fountain frequency standards. They originate from the phase variations of the field in the microwave cavity combined with different positions of the atoms in the cavity on the ascent and descent. Here we demonstrate techniques to precisely determine the position of the cloud of atoms in the microwave cavity, using either the approximately linear variation of the transverse components of the microwave field or the quadratic variation of the longitudinal microwave field amplitude in the cavity. We also show that shifting the initial position of the atoms gives a significantly higher sensitivity to DCP variations than the often-used tilting of fountains. A demonstrated centring precision of order 50 mu m will enable DCP frequency shift uncertainties to be reduced to less than 10(-17)and thereby contribute insignificantly to the accuracy budget of a standard. These techniques to vertically align a fountain are straightforward to automate for routine operation and require a negligible fraction of the standard's averaging time.

Frequency shifts due to the microwave distributed cavity phase (DCP) have been evaluated for the NRC-FCs2 atomic fountain primary frequency standard of the National Research Council Canada. NRC-FCs2 utilizes a Ramsey microwave cavity designed to minimize the DCP frequency shifts. We present the evaluation of the contributing azimuthal components of the DCP shifts of NRC-FCs2.

At the National Research Council Canada we are currently performing the first accuracy evaluation of our newly developed caesium fountain clock, NRC-FCs2. This primary frequency standard operates with a short term stability of σy(τ)=1.1 x 10 -13 τ -1/2 and, upon full evaluation, we expect to achieve a type B uncertainty in fractional frequency below 5 x 10 -16 . We will discuss the current status of the evaluation, including several evaluated shifts, as well as the outstanding systematics yet to be fully characterized.

Following a refined NPL design, we have constructed several Cs fountain primary frequency standards for use in different metrology laboratories. In this paper we describe the design of these new systems and present measurements of their performance.

The National Research Council of Canada is finalizing the first evaluation of a new primary frequency standard, the NRC-FCs2 cesium fountain clock. The physics package for NRC-FCs2 was designed and built in collaboration with the National Physical Laboratory (NPL) in the UK, based on the design of NPL fountains CsF2 and CsF3 [1]. The physics package has been successfully integrated with the optical, microwave, and electronics subsystems developed at the NRC [2].