Abstract

The pursuit of ever more precise measures of time and frequency motivates redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on the microwave hyperfine transition in Cs133, it is necessary to measure the absolute frequency of candidate optical standards relative to primary cesium references. Armed with independent measurements, a stringent test of optical clocks can be made by comparing ratios of absolute frequency measurements against optical frequency ratios measured via direct optical comparison. Here we measure the S01P03 transition of Yb171 using satellite time and frequency transfer to compare the clock frequency to an international collection of national primary and secondary frequency standards. Our measurements consist of 79 runs spanning eight months, yielding the absolute frequency to be 518 295 836 590 863.71(11) Hz and corresponding to a fractional uncertainty of 2.1×1016. This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty <3×1016, limited for the first time by the current realization of the second in the International System of Units (SI). Doing so represents a key step towards an optical definition of the SI second, as well as future optical time scales and applications. Furthermore, these high accuracy measurements distributed over eight months are analyzed to tighten the constraints on variation of the electron-to-proton mass ratio, μ=me/mp. Taken together with past Yb and Sr absolute frequency measurements, we infer new bounds on the coupling coefficient to gravitational potential of kμ=(1.9±9.4)×107 and a drift with respect to time of μ˙μ=(5.3±6.5)×1017/yr.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (10)

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564, 87–90 (2018).
[Crossref]

H. Hachisu, F. Nakagawa, Y. Hanado, and T. Ido, “Months-long real-time generation of a time scale based on an optical clock,” Sci. Rep. 8, 4243 (2018).
[Crossref]

J. Yao, T. E. Parker, N. Ashby, and J. Levine, “Incorporating an optical clock into a time scale,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 127–134 (2018).
[Crossref]

J. Yao, J. Sherman, T. Fortier, H. Leopardi, T. Parker, J. Levine, J. Savory, S. Romisch, W. McGrew, X. Zhang, D. Nicolodi, R. Fasano, S. Schaeffer, K. Beloy, and A. Ludlow, “Progress on optical-clock-based time scale at NIST: simulations and preliminary real-data analysis,” Navigation 65, 601–608 (2018).
[Crossref]

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).
[Crossref]

S. Weyers, V. Gerginov, M. Kazda, J. Rahm, B. Lipphardt, G. Dobrev, and K. Gibble, “Advances in the accuracy, stability, and reliability of the PTB primary fountain clocks,” Metrologia 55, 789–805 (2018).
[Crossref]

J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
[Crossref]

D. Akamatsu, T. Kobayashi, Y. Hisai, T. Tanabe, K. Hosaka, M. Yasuda, and F.-L. Hong, “Dual-mode operation of an optical lattice clock using strontium and ytterbium atoms,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1069–1075 (2018).
[Crossref]

M. Fujieda, S. Yang, T. Gotoh, S. Hwang, H. Hachisu, H. Kim, Y. Lee, R. Tabuchi, T. Ido, W. Lee, M. Heo, C. Y. Park, D. Yu, and G. Petit, “Advanced satellite-based frequency transfer at the 10−16 level,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 973–978 (2018).
[Crossref]

N. Ashby, T. E. Parker, and B. R. Patla, “A null test of general relativity based on a long-term comparison of atomic transition frequencies,” Nat. Phys. 14, 822–826 (2018).
[Crossref]

2017 (7)

V. A. Dzuba and V. V. Flambaum, “Limits on gravitational Einstein equivalence principle violation from monitoring atomic clock frequencies during a year,” Phys. Rev. D 95, 015019 (2017).
[Crossref]

M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, “Search for new physics with atoms and molecules,” Rev. Mod. Phys. 90, 025008 (2017).
[Crossref]

H. Kim, M.-S. Heo, W.-K. Lee, C. Y. Park, S.-W. Hwang, and D.-H. Yu, “Improved absolute frequency measurement of the 171Yb optical lattice clock at KRISS relative to the SI second,” Jpn. J. Appl. Phys. 56, 050302 (2017).
[Crossref]

M. Pizzocaro, P. Thoumany, B. Rauf, F. Bregolin, G. Milani, C. Clivati, G. A. Costanzo, F. Levi, and D. Calonico, “Absolute frequency measurement of the 1S0–3P0 transition of 171Yb,” Metrologia 54, 102–112 (2017).
[Crossref]

H. Hachisu, G. Petit, F. Nakagawa, Y. Hanado, and T. Ido, “SI-traceable measurement of an optical frequency at the low 10−16 level without a local primary standard,” Opt. Express 25, 8511–8523 (2017).
[Crossref]

H. Hachisu, G. Petit, and T. Ido, “Absolute frequency measurement with uncertainty below 1 × 10−15 using International Atomic Time,” Appl. Phys. B 123, 34 (2017).
[Crossref]

H. Leopardi, J. Davila-Rodriguez, F. Quinlan, J. Olson, J. A. Sherman, S. A. Diddams, and T. M. Fortier, “Single-branch Er:fiber frequency comb for precision optical metrology with 10−18 fractional instability,” Optica 4, 879–885 (2017).
[Crossref]

2016 (6)

J. A. Sherman and R. Jördens, “Oscillator metrology with software defined radio,” Rev. Sci. Instrum. 87, 054711 (2016).
[Crossref]

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).
[Crossref]

T. Ido, H. Hachisu, F. Nakagawa, and Y. Hanado, “Rapid evaluation of time scale using an optical clock,” J. Phys. Conf. Ser. 723, 012041 (2016).
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C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and C. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563–569 (2016).
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J. Lodewyck, S. Bilicki, E. Bookjans, J. L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53, 1123–1130 (2016).
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N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, “Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time,” Nat. Photonics 10, 258–261 (2016).
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2015 (6)

M. Takamoto, I. Ushijima, M. Das, N. Nemitz, T. Ohkubo, K. Yamanaka, N. Ohmae, T. Takano, T. Akatsuka, A. Yamaguchi, and H. Katori, “Frequency ratios of Sr, Yb, and Hg based optical lattice clocks and their applications,” C. R. Physique 16, 489–498 (2015).
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T. Tanabe, D. Akamatsu, T. Kobayashi, A. Takamizawa, S. Yanagimachi, T. Ikegami, T. Suzuyama, H. Inaba, S. Okubo, M. Yasuda, F. L. Hong, A. Onae, and K. Hosaka, “Improved frequency measurement of the 1S0-3P0 clock transition in 87Sr using a Cs fountain clock as a transfer oscillator,” J. Phys. Soc. Jpn. 84, 115002 (2015).
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Y.-G. Lin, Q. Wang, Y. Li, F. Meng, B.-K. Lin, E.-J. Zang, Z. Sun, F. Fang, T.-C. Li, and Z.-J. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32, 090601 (2015).
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H. S. Margolis and P. Gill, “Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values,” Metrologia 52, 628–634 (2015).
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A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
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F. Fang, M. Li, P. Lin, W. Chen, N. Liu, Y. Lin, P. Wang, K. Liu, R. Suo, and T. Li, “NIM5 Cs fountain clock and its evaluation,” Metrologia 52, 454–468 (2015).
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2014 (6)

F. Levi, D. Calonico, C. E. Calosso, A. Godone, S. Micalizio, and G. A. Costanzo, “Accuracy evaluation of ITCsF2: a nitrogen cooled caesium fountain,” Metrologia 51, 270–284 (2014).
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J. Guéna, M. Abgrall, A. Clairon, and S. Bize, “Contributing to TAI with a secondary representation of the SI second,” Metrologia 51, 108–120 (2014).
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T. P. Heavner, E. A. Donley, F. Levi, G. Costanzo, T. E. Parker, J. H. Shirley, N. Ashby, S. Barlow, and S. R. Jefferts, “First accuracy evaluation of NIST-F2,” Metrologia 51, 174–182 (2014).
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D. Akamatsu, M. Yasuda, H. Inaba, K. Hosaka, T. Tanabe, A. Onae, and F.-L. Hong, “Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks,” Opt. Express 22, 7898–7905 (2014).
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D. Akamatsu, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, “Spectroscopy and frequency measurement of the 87Sr clock transition by laser linewidth transfer using an optical frequency comb,” Appl. Phys. Express 7, 012401 (2014).
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S. Falke, N. Lemke, C. Grebing, B. Lipphardt, S. Weyers, V. Gerginov, N. Huntemann, C. Hagemann, A. Al-Masoudi, S. Häfner, S. Vogt, U. Sterr, and C. Lisdat, “A strontium lattice clock with 3 × 10−17 inaccuracy and its frequency,” New J. Phys. 16, 073023 (2014).
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2013 (5)

R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, “Experimental realization of an optical second with strontium lattice clocks,” Nat. Commun. 4, 2109 (2013).
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S. Peil, S. Crane, J. L. Hanssen, T. B. Swanson, and C. R. Ekstrom, “Tests of local position invariance using continuously running atomic clocks,” Phys. Rev. A 87, 010102 (2013).
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P. Delva and J. Lodewyck, “Atomic clocks: new prospects in metrology and geodesy,” Acta Futura 7, 67–78 (2013).

Y. S. Domnin, V. N. Baryshev, A. I. Boyko, G. A. Elkin, A. V. Novoselov, L. N. Kopylov, and D. S. Kupalov, “The MTsR-F2 fountain-type cesium frequency standard,” Meas. Tech. 55, 1155–1162 (2013).
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C. Y. Park, D.-H. Yu, W.-K. Lee, S. E. Park, E. B. Kim, S. K. Lee, J. W. Cho, T. H. Yoon, J. Mun, S. J. Park, T. Y. Kwon, and S.-B. Lee, “Absolute frequency measurement of 1S0(F = 1/2)-3P0(F = 1/2) transition of 171Yb atoms in a one-dimensional optical lattice at KRISS,” Metrologia 50, 119–128 (2013).
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2012 (3)

M. Yasuda, H. Inaba, T. Kohno, T. Tanabe, Y. Nakajima, and K. Hosaka, “Improved absolute frequency measurement of the 171Yb optical lattice clock towards the redefinition of the second,” Appl. Phys. Express 5, 102401 (2012).
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J. Guéna, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, R. Li, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
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A. Yamaguchi, N. Shiga, S. Nagano, Y. Li, H. Ishijima, H. Hachisu, M. Kumagai, and T. Ido, “Stability transfer between two clock lasers operating at different wavelengths for absolute frequency measurement of clock transition in 87Sr,” Appl. Phys. Express 5, 022701 (2012).
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2011 (1)

S. T. Falke, H. Schnatz, J. S. R. V. Winfred, T. H. Middelmann, S. T. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and C. H. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48, 399–407 (2011).
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2009 (6)

F.-L. Hong, M. Musha, M. Takamoto, H. Inaba, S. Yanagimachi, A. Takamizawa, K. Watabe, T. Ikegami, M. Imae, Y. Fujii, M. Amemiya, K. Nakagawa, K. Ueda, and H. Katori, “Measuring the frequency of a Sr optical lattice clock using a 120  km coherent optical transfer,” Opt. Lett. 34, 692–694 (2009).
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V. V. Flambaum and V. A. Dzuba, “Search for variation of the fundamental constants in atomic, molecular, and nuclear spectra,” Can. J. Phys. 87, 25–33 (2009).
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T. H. Dinh, A. Dunning, V. A. Dzuba, and V. V. Flambaum, “Sensitivity of hyperfine structure to nuclear radius and quark mass variation,” Phys. Rev. A 79, 054102 (2009).
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N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates, “Spin-1/2 optical lattice clock,” Phys. Rev. Lett. 103, 063001 (2009).
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Z. Jiang and G. Petit, “Combination of TWSTFT and GNSS for accurate UTC time transfer,” Metrologia 46, 305–314 (2009).
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T. Kohno, M. Yasuda, K. Hosaka, H. Inaba, Y. Nakajima, and F. L. Hong, “One-dimensional optical lattice clock with a fermionic 171Yb isotope,” Appl. Phys. Express 2, 072501 (2009).
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2008 (3)

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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X. Baillard, M. Fouché, R. Le Targat, P. G. Westergaard, A. Lecallier, F. Chapelet, M. Abgrall, G. D. Rovera, P. Laurent, P. Rosenbusch, S. Bize, G. Santarelli, A. Clairon, P. Lemonde, G. Grosche, B. Lipphardt, and H. Schnatz, “An optical lattice clock with spin-polarized 87Sr atoms,” Eur. Phys. J. D 48, 11–17 (2008).
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G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. De Miranda, T. Zelevinsky, M. M. Boyd, and J. Ye, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45, 539–548 (2008).
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2007 (3)

M. M. Boyd, A. D. Ludlow, S. Blatt, S. M. Foreman, T. Ido, T. Zelevinsky, and J. Ye, “87Sr lattice clock with inaccuracy below 10−15,” Phys. Rev. Lett. 98, 083002 (2007).
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J. E. Stalnaker, S. A. Diddams, T. M. Fortier, K. Kim, L. Hollberg, J. C. Bergquist, W. M. Itano, M. J. Delany, L. Lorini, W. H. Oskay, T. P. Heavner, S. R. Jefferts, F. Levi, T. E. Parker, and J. Shirley, “Optical-to-microwave frequency comparison with fractional uncertainty of 10−15,” Appl. Phys. B 89, 167–176 (2007).
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D.-H. Yu, M. Weiss, and T. E. Parker, “Uncertainty of a frequency comparison with distributed dead time and measurement interval offset,” Metrologia 44, 91–96 (2007).
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2006 (5)

T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate >1  GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
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J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
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A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the 87Sr clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
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R. Le Targat, X. Baillard, M. Fouché, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with 87Sr atoms,” Phys. Rev. Lett. 97, 130801 (2006).
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V. V. Flambaum and A. F. Tedesco, “Dependence of nuclear magnetic moments on quark masses and limits on temporal variation of fundamental constants from atomic clock experiments,” Phys. Rev. C 73, 055501 (2006).
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2003 (1)

H. Katori, M. Takamoto, V. G. Pal’chikov, and V. D. Ovsiannikov, “Ultrastable optical clock with neutral atoms in an engineered light shift trap,” Phys. Rev. Lett. 91, 173005 (2003).
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2002 (1)

N. Ashby, “Relativity and the global positioning system,” Phys. Today 55(5), 41–47 (2002).
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1968 (1)

J. Terrien, “News from the International Bureau of Weights and Measures,” Metrologia 4, 41–45 (1968).
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1952 (1)

H. Lyons, “Spectral lines as frequency standards,” Ann. N.Y. Acad. Sci. 55, 831–871 (1952).
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Abgrall, M.

J. Lodewyck, S. Bilicki, E. Bookjans, J. L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53, 1123–1130 (2016).
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J. Guéna, M. Abgrall, A. Clairon, and S. Bize, “Contributing to TAI with a secondary representation of the SI second,” Metrologia 51, 108–120 (2014).
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R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, “Experimental realization of an optical second with strontium lattice clocks,” Nat. Commun. 4, 2109 (2013).
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J. Guéna, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, R. Li, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
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X. Baillard, M. Fouché, R. Le Targat, P. G. Westergaard, A. Lecallier, F. Chapelet, M. Abgrall, G. D. Rovera, P. Laurent, P. Rosenbusch, S. Bize, G. Santarelli, A. Clairon, P. Lemonde, G. Grosche, B. Lipphardt, and H. Schnatz, “An optical lattice clock with spin-polarized 87Sr atoms,” Eur. Phys. J. D 48, 11–17 (2008).
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Akamatsu, D.

D. Akamatsu, T. Kobayashi, Y. Hisai, T. Tanabe, K. Hosaka, M. Yasuda, and F.-L. Hong, “Dual-mode operation of an optical lattice clock using strontium and ytterbium atoms,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 1069–1075 (2018).
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T. Tanabe, D. Akamatsu, T. Kobayashi, A. Takamizawa, S. Yanagimachi, T. Ikegami, T. Suzuyama, H. Inaba, S. Okubo, M. Yasuda, F. L. Hong, A. Onae, and K. Hosaka, “Improved frequency measurement of the 1S0-3P0 clock transition in 87Sr using a Cs fountain clock as a transfer oscillator,” J. Phys. Soc. Jpn. 84, 115002 (2015).
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D. Akamatsu, M. Yasuda, H. Inaba, K. Hosaka, T. Tanabe, A. Onae, and F.-L. Hong, “Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks,” Opt. Express 22, 7898–7905 (2014).
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D. Akamatsu, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, “Spectroscopy and frequency measurement of the 87Sr clock transition by laser linewidth transfer using an optical frequency comb,” Appl. Phys. Express 7, 012401 (2014).
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Akatsuka, T.

M. Takamoto, I. Ushijima, M. Das, N. Nemitz, T. Ohkubo, K. Yamanaka, N. Ohmae, T. Takano, T. Akatsuka, A. Yamaguchi, and H. Katori, “Frequency ratios of Sr, Yb, and Hg based optical lattice clocks and their applications,” C. R. Physique 16, 489–498 (2015).
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Al-Masoudi, A.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and C. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563–569 (2016).
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S. Falke, N. Lemke, C. Grebing, B. Lipphardt, S. Weyers, V. Gerginov, N. Huntemann, C. Hagemann, A. Al-Masoudi, S. Häfner, S. Vogt, U. Sterr, and C. Lisdat, “A strontium lattice clock with 3 × 10−17 inaccuracy and its frequency,” New J. Phys. 16, 073023 (2014).
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Amemiya, M.

D. Akamatsu, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, “Spectroscopy and frequency measurement of the 87Sr clock transition by laser linewidth transfer using an optical frequency comb,” Appl. Phys. Express 7, 012401 (2014).
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F.-L. Hong, M. Musha, M. Takamoto, H. Inaba, S. Yanagimachi, A. Takamizawa, K. Watabe, T. Ikegami, M. Imae, Y. Fujii, M. Amemiya, K. Nakagawa, K. Ueda, and H. Katori, “Measuring the frequency of a Sr optical lattice clock using a 120  km coherent optical transfer,” Opt. Lett. 34, 692–694 (2009).
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Arias, F.

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).
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Ashby, N.

J. Yao, T. E. Parker, N. Ashby, and J. Levine, “Incorporating an optical clock into a time scale,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65, 127–134 (2018).
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N. Ashby, T. E. Parker, and B. R. Patla, “A null test of general relativity based on a long-term comparison of atomic transition frequencies,” Nat. Phys. 14, 822–826 (2018).
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T. P. Heavner, E. A. Donley, F. Levi, G. Costanzo, T. E. Parker, J. H. Shirley, N. Ashby, S. Barlow, and S. R. Jefferts, “First accuracy evaluation of NIST-F2,” Metrologia 51, 174–182 (2014).
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N. Ashby, “Relativity and the global positioning system,” Phys. Today 55(5), 41–47 (2002).
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X. Baillard, M. Fouché, R. Le Targat, P. G. Westergaard, A. Lecallier, F. Chapelet, M. Abgrall, G. D. Rovera, P. Laurent, P. Rosenbusch, S. Bize, G. Santarelli, A. Clairon, P. Lemonde, G. Grosche, B. Lipphardt, and H. Schnatz, “An optical lattice clock with spin-polarized 87Sr atoms,” Eur. Phys. J. D 48, 11–17 (2008).
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R. Le Targat, X. Baillard, M. Fouché, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with 87Sr atoms,” Phys. Rev. Lett. 97, 130801 (2006).
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N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates, “Spin-1/2 optical lattice clock,” Phys. Rev. Lett. 103, 063001 (2009).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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T. P. Heavner, E. A. Donley, F. Levi, G. Costanzo, T. E. Parker, J. H. Shirley, N. Ashby, S. Barlow, and S. R. Jefferts, “First accuracy evaluation of NIST-F2,” Metrologia 51, 174–182 (2014).
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Baryshev, V. N.

Y. S. Domnin, V. N. Baryshev, A. I. Boyko, G. A. Elkin, A. V. Novoselov, L. N. Kopylov, and D. S. Kupalov, “The MTsR-F2 fountain-type cesium frequency standard,” Meas. Tech. 55, 1155–1162 (2013).
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J. Grotti, S. Koller, S. Vogt, S. Häfner, U. Sterr, C. Lisdat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Barbieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, “Geodesy and metrology with a transportable optical clock,” Nat. Phys. 14, 437–441 (2018).
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W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schäffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564, 87–90 (2018).
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T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808–1812 (2008).
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Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).
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J. Lodewyck, S. Bilicki, E. Bookjans, J. L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53, 1123–1130 (2016).
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J. Lodewyck, S. Bilicki, E. Bookjans, J. L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guéna, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53, 1123–1130 (2016).
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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. Experimental setup of the Yb optical lattice standard. A counter or SDR measures the beat note between f rep and the nominal 1 GHz reference derived from hydrogen maser ST15. The frequency of ST15 is compared by the NIST TSMS to that of two maser time scales—AT1E (blue) and AT1 (orange); see Supplement 1. These time scales utilize the same masers (approximately eight, including ST15) but differ in the statistical weight given to each maser [21]. The frequency of AT1 is sent to a central hub (the “star topology” used in TAI computations) via the TWGPPP protocol [22]. The measurements are then sent from the hub to the BIPM by an internet connection, and the BIPM publishes data allowing a comparison of AT1 against PSFS, composed of k separate clocks in different National Metrological Institutes (NMIs), where k varies from five to eight during the measurements.
Fig. 2.
Fig. 2. Absolute frequency measurements of the S 0 1 P 0 3 transition frequency measured by four different laboratories: NIST (blue) [18], National Metrological Institute of Japan (red) [34,35], the Korea Research Institute of Standards and Science (green) [36,37], and the Istituto Nazionale di Ricerca Metrologica (purple) [38]. The light-blue points in the inset represent the eight monthly values reported in this work, y m ( Yb - PSFS ) , and the final dark blue point represents y T ( Yb - PSFS ) . The yellow shaded region represents the 2017 CIPM recommended frequency and uncertainty. The inset shows a sinusoidal fit of the coupling parameter to gravitational potential for measurements of the frequency ratio between Yb and Cs between November 2017 and June 2018. The red shaded region in the inset represents 1 σ uncertainty in the fit function.
Fig. 3.
Fig. 3. Graphical representation of the agreement between frequency ratios derived from absolute frequency measurements of Yb 171 and Sr 87 and direct optical measurements. (a) Schematic of the Cs-Yb-Sr-Cs loop that is examined. The central number is the misclosure, as parts in 10 16 . (b) Average Yb and Sr frequency, offset from the CIPM 2017 recommended values, parametrically plotted against each other. The error bars are the 1 σ uncertainty in the averaged absolute frequency measurements. The optical ratio measurement (dark green) appears as a line in this parameter-space, with the shaded region representing the uncertainty of the ratio. Frequency ratios derived from absolute frequencies agree well with ratios measured optically.

Tables (2)

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Table 1. Uncertainty Budget of the Eight-Month Campaign for the Absolute Frequency Measurement of the Yb 171 Clock Transition

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Table 2. Measurements of Coupling of Dimensionless Constants to Gravitational Potential, with Sensitivity Coefficients, Δ K , from [6264]

Equations (1)

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y ( A B ) y A ( t ) y B ( t ) = ν A act ν A nom ν B act ν B nom ν A act / ν B act ν A nom / ν B nom 1 ,

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