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The comparison of distant atomic clocks is foundational to international timekeeping, global positioning and tests of fundamental physics. Optical-fibre links allow the most precise optical clocks to be compared, without degradation, over intracontinental distances up to thousands of kilometres, but intercontinental comparisons remain limited by the performance of satellite transfer techniques. Here we show that very long baseline interferometry (VLBI), although originally developed for radio astronomy and geodesy, can overcome this limit and compare remote clocks through the observation of extragalactic radio sources. We developed dedicated transportable VLBI stations that use broadband detection and demonstrate the comparison of two optical clocks located in Italy and Japan separated by 9,000 km. This system demonstrates performance beyond satellite techniques and can pave the way for future long-term stable international clock comparisons. Very long baseline interferometry is used to compare two optical clocks located in Japan and Italy through the observation of extragalactic radio sources. This approach overcomes limitations of the performance of satellite transfer techniques.

We have developed a broadband VLBI (very long baseline interferometry) system inspired by the concept of the VLBI Global Observing System (VGOS). The new broadband VLBI system was implemented in the Kashima 34 m antenna and in two transportable stations utilizing 2.4 m diameter antennas. The transportable stations have been developed as a tool for intercontinental frequency comparison but are equally useful for geodesy. To enable practical use of such small VLBI stations in intercontinental VLBI, we have developed the procedure of node-hub style VLBI: In joint observation with a large, high sensitivity ‘hub’ antenna, the closure delay relation provides a virtual delay observable between ‘node’ stations. This overcomes the limited sensitivity of the small diameter node antennas, while error sources associated with large diameter antennas, such as gravitational deformation and delay changes in necessarily long signal cables, are eliminated. We show that this scheme does not result in an increased sensitivity to radio source structure if one side of the baseline triangle is kept short. We have performed VLBI experiments utilizing this approach over both short range and intercontinental distance. This article describes the system components, signal processing procedure, experiment, and results in terms of baseline repeatability. Our measurements reveal signatures of structure effects in the correlation amplitude of several of the observed radio sources. We present a model of the frequency-dependent source size for 1928+738 derived from correlation amplitude data observed in four frequency bands.

The optical lattice clock NICT-Sr1 [1] regularly reports calibration data for the international atomic time TAI, obtained by intermittent measurements of a flywheel hydrogen maser. Continuous frequency measurements of this maser against the local UTC(NICT) and a GNSS satellite link then provide a traceable chain to UTC, which differs from TAI by the number of accumulated leap seconds, but shares its frequency. By using data publicly available from the International Bureau of Weights and Measures (BIPM), we extend the chain to eight individual primary frequency standards that reported calibration data for suitably similar intervals. For 63 such directly traced comparisons, we individually determine nine uncertainty contributions, including clock statistical and systematic uncertainties, the satellite link instability, and operating interval extrapolations that address measurement deadtime and mismatched evaluation periods. A covariance matrix constructed from these contributions addresses correlated and uncorrelated uncertainties. A suitable distribution of weights is found by a least-squares approach based on the Gauss-Markov theorem. Direct tracing to individual primary standards allows a flexible choice of evaluation intervals and provides results in terms of the nominal SI second even when the BIPM calculation of the TAI scale interval error includes contributions of secondary standards. From 776 hours of strontium clock data acquired over four years, we thus find the absolute frequency of the 87Sr clock transition to be f(Sr) = 429 228 004 229 873.08(8) Hz [2], with a fractional uncertainty of less than 1.8e-16, approaching the systematic limits of the best realizations of the SI second. The evaluation shows no statistical anomalies or significant variation over time. Our result is consistent with a recent measurement performed at PTB [3] against local primary standards, which determined the 87Sr clock transition frequency as f(Sr@PTB) = 429 228 004 229 873.00(7) Hz. A loop closure over the absolute frequencies of 87Sr, 171Yb [4,5] and direct optical measurements of their ratio [6] also finds excellent consistency. If this level of agreement between independent measurements is reflected in a revision of the recommended frequencies provided by the International Committee of Weights and Measures (CIPM), it will support optical lattice clocks operating as frequency standards with absolute uncertainties of 2e-16 or below, outperforming all but the best cesium clocks even before a redefinition of the SI second. References: [1] H. Hachisu et al. “SI-traceable measurement of an optical frequency at the low 10?16 level without a local primary standard“, Opt. Express 25 8511–23 (2017) DOI: 10.1364/OE.25.008511 [2] N. Nemitz et al. “Absolute frequency of 87Sr at 1.8 × 10?16 uncertainty by reference to remote primary frequency standards”, submitted to Metrologia arXiv:2008.00723 (2020); [3] R. Schwarz et al. “Long term measurement of the 87Sr clock frequency at the limit of primary Cs clocks”, Phys. Rev. Res. 2, 033242 (2020) DOI: 10.1103/PhysRevResearch.2.033242 [4] W. F. McGrew et al. “Towards the optical second: verifying optical clocks at the SI limit”, Optica 6 448-454 (2019) DOI: 10.1364/OPTICA.6.000448 [5] M. Pizzocaro et al. “Absolute frequency measurement of the 1S0–3P0 transition of 171Yb with a link to international atomic time”, Metrologia 57 035007 (2020) DOI: 10.1088/1681-7575/ab50e8 [6] Boulder Atomic Clock Optical Network, “Frequency ratio measurements with 18-digit accuracy using a network of optical clocks“ arXiv: 2005.14694 (2020)

The indium ion is one of the original candidates in the first proposal for single-ion clocks with systematic uncertainties at the 10-18 level [1]. In+ has an alkaline-earth-like electron configuration, with a 1S0 - 3P0 clock transition frequency that has a low sensitivity to magnetic fields. It has the highest clock frequency of all presently investigated optical clocks [2]. Such high transition energies give it a very small sensitivity to blackbody radiation (BBR), which causes problematic frequency shifts in most other clocks, including optical lattice clocks. Direct state detection and laser cooling on the 1S0 - 3P1 transition are a further advantage for an 115In+ clock. The electric quadrupole moments of the two clock states are orders of magnitude smaller than those for the 2S1/2 - 2D5/2 quadrupole transitions of alkaline-like ions (Ca+, Sr+, Yb+). This makes the transition frequency insensitive to the electric field gradients imposed by adjacent ions. With direct readout available, In+ is thus ideal for a multi-ion clock, which can overcome the inherent stability limitations of a single-ion system. Despite the appeal of the 115In+ ion for a high-performance optical clock, its adoption has been hampered by concerns about technical reliability. Only two groups previously measured the clock transition frequency with fractional uncertainties approaching 1e-14, reported 2000[3] and 2007[4]. In 2017, we measured the clock frequency with an uncertainty of 5e-15 [5], which prompted an update of the frequency value recommended by the International Committee for Weights and Measures (CIPM). This initial frequency determination was performed by averaging 36 measurements of the magnetically unresolved spectrum, and was limited by the systematic uncertainty of the first order Zeeman shift as well as the statistical uncertainty. We recently improved our In+ clock by direct laser stabilization to the clock transition and controlled magnetic field application to resolve Zeeman sublevels [6]. In this presentation, we report on the first frequency ratio measurement of an 115In+ single ion clock and a 87Sr optical lattice clock. The measurement employs two independent Er-doped fiber frequency combs which reference a common hydrogen maser that serves as a flywheel oscillator. From 89 000 s of measurement time, the frequency ratio is determined to be 2.952 748 749 874 863 3(23) with 7.7e-16 relative uncertainty. If we adopt the CIPM recommended value for the 87Sr clock frequency, we find 1 267 402 452 901 040.0(1.1) Hz for the absolute In+ clock frequency [7]. [1] H. G. Dehmelt, “Monoion oscillator as potential ultimate laser frequency standard,” IEEE Transactions on Instrumentation Meas. pp. 83–87 (1982). [2] F. Riehle, P. Gill, F. Arias, and L. Robertsson, “The CIPM list of recommended frequency standard values: guidelines and procedures,” Metrologia. 55, 188–200 (2018). [3] J. von Zanthier, T. Becker, M. Eichenseer, A. Y. Nevsky, C. Schwedes, E. Peik, H. Walther, R. Holzwarth, J. Reichert, T. Udem, T. W. Hansch, P. V. Pokasov, M. N. Skvortsov, and S. N. Bagayev, Opt. Lett. 25, 1729 (2000). [4] Y. Wang, R. Dumke, T. Liu, A. Stejskal, Y. Zhao, J. Zhang, Z. Lu, L. Wang, T. Becker, and H. Walther, Opt. Commun. 273, 526 (2007). [5] N. Ohtsubo, Y. Li, K. Matsubara, T. Ido, and K. Hayasaka, Opt. Express 25, 11725 (2017). [6] N. Ohtsubo, Y. Li, N. Nemitz, H. Hachisu, K. Matsubara, T. Ido, and K. Hayasaka, Hyperfine Interact. 240, 39 (2019). [7] N. Ohtsubo, Y. Li, N. Nemitz, H. Hachisu, K. Matsubara, T. Ido, and K. Hayasaka, Optics Letters, accepted

For the aim to enable precise frequency transfer over earth radius scale distance, NICT developed a broadband VLBI system observing 3-14 GHz radio frequency range, and that was implemented in a pair of transportable 2.4m diameter VLBI stations and Kashima 34m diameter VLBI station. The small diameter VLBI stations installed in Medicina observatory of INAF (Italy) and NICT headquarters in Koganei (Japan) were used compare the atomic frequency standards. The poor sensitivity of VLBI observation with the small antenna pair was compensated by participation of the large diameter antenna for boosting the signal to noise ratio (SNR) of the VLBI observation. Owing to the broad observing frequency range, a few pico seconds precision of group delay is achieved on intercontinental baseline even with small diameter antenna. Advanced digital data acquisition with highspeed 16 GHz sampling enabled stable group delay measurement. A series of frequency transfer experiments was conducted during Oct. 2018 – Feb. 2019 by using the broadband VLBI system between ytterbium (Yb) optical lattice clock of INRiM (Italy) and strontium (Sr) lattice clock of NICT(Japan) separated by 9000km. The deviation of fractional frequency ratio between Yb and Sr was obtained by VLBI observation as y(Yb/Sr)=2.5(2.8)x10-16. The uncertainty in this experiment is evaluated not to be limited by the VLBI link itself, and further improvement is expected. Prospect of VLBI frequency link and uncertainty budget in VLBI observation is discussed in this report.

We report on the first, to the best of our knowledge, frequency ratio measurement of an

We report on the first, to the best of our knowledge, frequency ratio measurement of an single-ion clock and a optical lattice clock. A hydrogen maser serves as a flywheel oscillator to measure the ratio by independent optical combs. From 89,000 s of measurement time, the frequency ratio is determined to be 2.952 748 749 874 863 3(23) with relative uncertainty. The measurement creates a new connection in the network of frequency ratios of optical clocks.

We report on the progress of an optical clock based on an indium ion (115In+) sympathetically cooled with a calcium ion (40Ca+) in a linear trap. In our previous work, we have measured the clock transition frequency with an uncertainty of 5× 10− 15, prompting an update of the Comite International des Poids et Mesures (CIPM) recommended value. The uncertainty was mainly limited by the evaluation of the Zeeman shift which was complicated by unresolved sublevel components. In contrast to the previous measurement, Zeeman sublevels are now separated by application of a magnetic field. Combined with optical pumping to specific Zeeman substates, the magnetic field application method successfully reduces the observed linewidth of the clock transition spectrum down to about 80 Hz full width at half maximum (FWHM). Frequency locking of the clock laser to the transition is demonstrated for the first time. The clock reaches a relative instability of 1.5× 10− 15 for an integration time of 4000 seconds.

We present an extended model for the lattice-induced light shifts of the clock frequency in optical lattice clocks, applicable to a wide range of operating conditions. The model extensions cover radial motional states with sufficient energies to invalidate the harmonic approximation of the confining potential. We reevaluate lattice-induced light shifts in our Yb optical lattice clock with an uncertainty of 6.1E-18 under typical clock operating conditions., Comment: 12 pages, 10 figures

We performed a frequency comparison of lattice clocks in Tokyo and Torino for the first time using broadband VLBI technique. Two portable antennas with 2.4 m diameters were installed at NICT Koganei headquarters and INAF Medicina Radio Observatory, close to Bologna, Italy, realizing a VLBI network together with Kashima large-aperture antenna of 34 m diameter. The clock signal at INAF was evaluated by INRIM using an optical fiber link between Medicina and Torino. The fractional frequency difference that VLBI evaluated was consistent with the difference between two HM frequencies which were separately calibrated by a Sr lattice clock at NICT and a Yb lattice clock at INRIM.

The optical lattice clock NICT-Sr1 regularly reports calibration measurements of the international timescale TAI. By comparing measurement results to the reports of eight primary frequency standards, we find the absolute frequency of the 87Sr clock transition to be f S r = 429 228 004 229 873.082 76 H z , with a fractional uncertainty of less than 1.8 × 10−16 approaching the systematic limits of the best realization of the SI second. Our result is consistent with other recent measurements and further supported by the loop closure over the absolute frequencies of 87Sr, 171Yb and direct optical measurements of their ratio.

UTokyo Research掲載「異なる原子の光格子時計の短時間精密比較に成功」 URI: http://www.u-tokyo.ac.jp/ja/utokyo-research/research-news/rapid-comparison-of-optical-lattice-clocks.html, UTokyo Research "Rapid comparison of optical lattice clocks" URI: http://www.u-tokyo.ac.jp/en/utokyo-research/research-news/rapid-comparison-of-optical-lattice-clocks.html

We performed the first direct measurement of the frequency ratio between a mercury (199Hg) and an ytterbium (171Yb) optical lattice clock to find νHg/νYb = 2.177 473 194 134 565 07(19) with the fractional uncertainty of 8.8 × 10−17. The ratio is in excellent agreement with expectations from the ratios νHg/νSr and νYb/νSr obtained previously in comparisons against a strontium (87Sr) optical lattice clock. The completed closure (νHg/νYb)(νYb/νSr)(νSr/νHg) − 1 = 0.4(1.3) × 10−16 tests the frequency reproducibility of the optical lattice clocks beyond what is achievable in comparison against the current realization of the second in the International System of Units (SI).

We introduce a description of Ramsey spectra under atomic interactions as a sum of decomposed components with differing dependence on interaction parameters. This description enables intuitive understanding of the loss of contrast and asymmetry of Ramsey spectra. We derive a quantitative relationship between the asymmetry and atomic interaction parameters, which enables their characterization without changing atom density. The model is confirmed through experiments with a Yb optical lattice clock.

We explore the method of rapid adiabatic passage for collisional frequency shift measurements in the primary caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt (PTB). This method can be used to vary the local density distribution of the atom cloud by exactly a factor of 2. We investigate the performance of the method for different parameter ranges and obtained agreement between experimental and Monte-Carlo simulation results. When used for collisional frequency shift measurements, the rapid adiabatic passage method results in a systematic uncertainty contribution of less than 1% of the collisional shift value. Implications of this method for the systematic uncertainty of CSF2 are discussed.

The uncertainty evaluation of CSF2, the second caesium fountain primary frequency standard at PTB, is presented. The fountain uses optical molasses to cool atoms down to 0.6 µK. The atoms are launched vertically in a moving optical molasses, and state selected in the |F = 3, mF = 0 hyperfine ground state. During their ballistic flight, the atoms interact twice with a microwave field, thus completing the Ramsey interaction. With a launch height of 36.5 cm above the cavity centre, the central Ramsey fringe has a width of 0.9 Hz. About 3 × 104 atoms, 30% of the initial number in the |F = 3, mF = 0 state, are detected after their second interaction with the microwave field. Stabilizing the microwave frequency to the centre of the central Ramsey fringe, a typical relative frequency instability of 2.5 × 10−13(τ/s)−1/2 is obtained. The CSF2 systematic uncertainty for realizing the SI second is estimated as 0.80 × 10−15. First comparisons with the fountain CSF1 at the Physikalisch-Technische Bundesanstalt and other fountain frequency standards worldwide demonstrate agreement within the stated uncertainties.

This article describes the recent progress of optical lattice clocks with neutral strontium ($^{87}$Sr), ytterbium ($^{171}$Yb) and mercury ($^{199}$Hg) atoms. In particular, we present frequency comparison between the clocks locally via an optical frequency comb and between two Sr clocks at remote sites using a phase-stabilized fibre link. We first review cryogenic Sr optical lattice clocks that reduce the room-temperature blackbody radiation shift by two orders of magnitude and serve as a reference in the following clock comparisons. Similar physical properties of Sr and Yb atoms, such as transition wavelengths and vapour pressure, have allowed our development of a compatible clock for both species. A cryogenic Yb clock is evaluated by referencing a Sr clock. We also report on a Hg clock, which shows one order of magnitude less sensitivity to blackbody radiation, while its large nuclear charge makes the clock sensitive to the variation of fine-structure constant. Connecting all three types of clocks by an optical frequency comb, the ratios of the clock frequencies are determined with uncertainties smaller than possible through absolute frequency measurements. Finally, we describe a synchronous frequency comparison between two Sr-based remote clocks over a distance of 15 km between RIKEN and the University of Tokyo, as a step towards relativistic geodesy., 11 pages, 5 figures, invited review article in Comptes Rendus de Physique 2015

We report recent progress of optical lattice clocks with strontium, ytterbium and mercury atoms with an emphasis on their synchronous frequency comparison inside a laboratory and inter-laboratories connected by a phase-stabilized fiber link.

In the uncertainty budget of primary atomic cesium fountain clocks, evaluations of frequency-pulling shifts of the hyperfine clock transition caused by unintentional excitation of its nearby transitions (Rabi and Ramsey pulling) have been based so far on an approach developed for cesium beam clocks. We re-evaluate this type of frequency pulling in fountain clocks and pay particular attention to the effect of initial coherent atomic states. We find significantly enhanced frequency shifts caused by Ramsey pulling due to sublevel population imbalance and corresponding coherences within the state-selected hyperfine component of the initial atom ground state. Such shifts are experimentally investigated in an atomic fountain clock and quantitative agreement with the predictions of the model is demonstrated.

We describe a measurement of the frequency of the 2S1/2(F = 0) - 2D3/2(F' = 2) transition of 171Yb+ at the wavelength 436 nm (frequency 688 THz), using a single Yb+ ion confined in a Paul trap and two caesium fountains as references. In one of the fountains, the frequency of the microwave oscillator that interrogates the caesium atoms is stabilized by the laser that excites the Yb+ reference transition with a linewidth in the hertz range. The stability is transferred to the microwave oscillator with the use of a fiber laser based optical frequency comb generator that also provides the frequency conversion for the absolute frequency measurement. The frequency comb generator is configured as a transfer oscillator so that fluctuations of the pulse repetition rate and of the carrier offset frequency do not degrade the stability of the frequency conversion. The phase noise level of the generated ultrastable microwave signal is comparable to that of a cryogenic sapphire oscillator. For fountain operation with optical molasses loaded from a laser cooled atomic beam source, we obtain a stability corresponding to a fractional Allan deviation of $4.1\times 10^{-14}\ (\tau/\text{s})^{-1/2}$. With the molasses loaded from thermal vapor and an averaging time of 65 h, we measure the frequency of the Yb+ transition with a relative statistical uncertainty of $2.8\times10^{-16}$ and a systematic uncertainty of $5.9\times10^{-16}$. The frequency was also simultaneously measured with the second fountain that uses a quartz-based interrogation oscillator. The unperturbed frequency of the Yb+ transition is realized with an uncertainty of $1.1\times10^{-16}$ that mainly results from the uncertainty of the blackbody shift at the operating temperature near 300 K. The transition frequency of 688 358 979 309 307.82(36) Hz, measured with the two fountains, is in good agreement with previous results., Comment: 25 pages, 4 figures. Submitted to Phys. Rev. A

Using resonant two-step laser excitation of trapped 232Th+ ions, we observe 43 previously unknown energy levels within the energy range from 7.3 to 8.3 eV. The high density of states promises a strongly enhanced electronic bridge excitation of the 229mTh nuclear state that is expected in this energy range. From the observation of resonantly enhanced three-photon ionization of Th+, the second ionization potential of thorium can be inferred to lie within the range between 11.9 and 12.3 eV. Pulsed laser radiation in a wide wavelength range from 237 to 289 nm is found to provide efficient photodissociation of molecular ions that are formed in reactions of Th+ with impurities in the buffer gas, leading to a significantly increased storage time for Th+ in the ion trap., Comment: 7 pages, 6 figures

We describe a new method to determine the position of the atomic cloud during its interaction with the microwave field in the cavity of a fountain clock. The positional information is extracted from the spectrum of the F=3,mF=0 to F=4,mF=-1 hyperfine transition, which shows a position dependent asymmetry when the magnetic C-field is tilted by a few degrees with respect to the cavity axis. Analysis of this spectral asymmetry provides the horizontal center-of-mass position for the ensemble of atoms contributing to frequency measurements. With an uncertainty on the order of 0.1 mm, the obtained information is useful for putting limits on the systematic uncertainty due to distributed cavity phase gradients. The validity of the new method is demonstrated through experimental evidence., Comment: 6 figures, submitted to PRA

We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3E-16, with a frequency bias of 0.4E-16. The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wavepackets. We report a total PTB-CSF2 systematic uncertainty of 4.1E-16., Comment: 15 pages, 5 figures, to be published in Metrologia

We have experimentally realized a hybrid trap for ultracold paramagnetic rubidium and diamagnetic ytterbium atoms by combining a bichromatic optical dipole trap for ytterbium with a Ioffe-Pritchard-type magnetic trap for rubidium. In this hybrid trap, sympathetic cooling of five different ytterbium isotopes through elastic collisions with rubidium was achieved. A strong dependence of the interspecies collisional cross section on the mass of the ytterbium isotope was observed., Comment: 4 pages, 4 figures

Theoretical calculations of atomic structure are constantly being refined and are now reaching a degree of accuracy where the final discrepancies to tabulated measurements (see e.g. [1]) might be due to the experimental values [2,3]. This uncertainty also exists for caesium, where the difference in the measured nuclear magnetic moments for free caesium atoms [4], free caesium ions [5] and ions in solution [6] do not agree with calculated shielding factors [7]. The best known ratio of the nuclear and electronic g-factors in free caesium atoms is given in [4] as gi/gj= -1.9917400(26) ×10-4. We aim to remeasure this ratio by investigating a set of hyperfine transition frequencies using the two available caesium fountains CSF1 and CSF2 at PTB. In this report we describe the results of the first tests and the challenges they show for a precision measurement.

We have produced ultracold heteronuclear ${\text{YbRb}}^{\ensuremath{\ast}}$ molecules in a combined magneto-optical trap by photoassociation. The formation of electronically excited molecules close to the dissociation limit was observed by the trap loss spectroscopy in mixtures of $^{87}\text{R}\text{b}$ with $^{174}\text{Y}\text{b}$ and $^{176}\text{Y}\text{b}$. The molecules could be prepared in well-defined rovibrational levels, allowing for an experimental determination of the long-range potential in the electronically excited state.