Abstract

SI-traceable measurements of optical frequencies using International Atomic Time (TAI) do not require a local primary frequency reference, but suffer from an uncertainty in tracing to the SI second. For the measurement of the 87Sr lattice clock transition, we have reduced this uncertainty to the low 10−16 level by averaging three sets of ten-day intermittent measurements, in which we operated the lattice clock for 104 s on each day. Moreover, a combined oscillator of two hydrogen masers was employed as a local flywheel oscillator (LFO) in order to mitigate the impact of sporadic excursion of LFO frequency. The resultant absolute frequency with fractional uncertainty of 4.3 × 10−16 agrees with other measurements based on local state-of-the-art cesium fountains.

© 2017 Optical Society of America

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  26. K. Gibble, “Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions,” Phys. Rev. Lett. 110(18), 180802 (2013).
  27. B. Miyahara, T. Kodama, and Y. Kuroishi, “Development of new hybrid geoid model for Japan, GSIGEO2011,” Bull. GSI 62, 11 (2014).
  28. Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).
  29. J. Azoubib, M. Granveaud, and B. Guinot, “Estimation of the scale unit duration of time scales,” Metrologia 13(3), 87–93 (1977).
  30. 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).
  31. St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).
  32. Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).
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  34. J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).
  35. 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).

2017 (1)

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

2016 (4)

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

2015 (5)

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

F. Riehle, “Towards a re-definition of the second based on optical atomic clocks,” C. R. Phys. 16(5), 506–515 (2015).

H. Hachisu and T. Ido, “Intermittent optical frequency measurements to reduce the dead time uncertainty of frequency link,” Jpn. J. Appl. Phys. 54(11), 112401 (2015).

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(11), 115002 (2015).

2014 (4)

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(1), 012401 (2014).

B. Miyahara, T. Kodama, and Y. Kuroishi, “Development of new hybrid geoid model for Japan, GSIGEO2011,” Bull. GSI 62, 11 (2014).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

2013 (4)

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).

K. Gibble, “Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions,” Phys. Rev. Lett. 110(18), 180802 (2013).

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

2012 (5)

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(2), 022701 (2012).

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

G. Panfilo, A. Harmegnies, and L. Tisserand, “A new prediction algorithm for the generation of International Atomic Time,” Metrologia 49(1), 49–56 (2012).

J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, “Observation and cancellation of a perturbing dc stark shift in strontium optical lattice clocks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 411–415 (2012).

T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, “High accuracy correction of blackbody radiation shift in an optical lattice clock,” Phys. Rev. Lett. 109(26), 263004 (2012).

2011 (3)

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

2010 (1)

G. Panfilo and T. E. Parker, “A theoretical and experimental analysis of frequency transfer uncertainty, including frequency transfer into TAI,” Metrologia 47(5), 552–560 (2010).

2008 (2)

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

G. Panfilo and P. Tavella, “Atomic clock prediction based on stochastic differential equations,” Metrologia 45(6), S108–S116 (2008).

2007 (1)

D. Yu, M. Weiss, and T. E. Parker, “Uncertainty of a frequency comparison with distributed dead time and measurement interval offset,” Metrologia 44(1), 91–96 (2007).

2005 (1)

F. Nakagawa, M. Imae, Y. Hanado, and M. Aida, “Development of multichannel dual-mixer time difference system to generate UTC(NICT),” IEEE Trans. Instrum. Meas. 54(2), 829–832 (2005).

1987 (1)

D. W. Allan, ““Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators,” IEEE Trans. Ultrasonic,” Ferro. Freq. Control UFFC 34(6), 647–654 (1987).

1977 (1)

J. Azoubib, M. Granveaud, and B. Guinot, “Estimation of the scale unit duration of time scales,” Metrologia 13(3), 87–93 (1977).

Abgrall, M.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

Aida, M.

F. Nakagawa, M. Imae, Y. Hanado, and M. Aida, “Development of multichannel dual-mixer time difference system to generate UTC(NICT),” IEEE Trans. Instrum. Meas. 54(2), 829–832 (2005).

Akamatsu, D.

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(11), 115002 (2015).

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(1), 012401 (2014).

Allan, D. W.

D. W. Allan, ““Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators,” IEEE Trans. Ultrasonic,” Ferro. Freq. Control UFFC 34(6), 647–654 (1987).

Al-Masoudi, A.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

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(1), 012401 (2014).

Azoubib, J.

J. Azoubib, M. Granveaud, and B. Guinot, “Estimation of the scale unit duration of time scales,” Metrologia 13(3), 87–93 (1977).

Barber, Z. W.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Barrett, M. D.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Beck, K. M.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Bernard, J. E.

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

Bian, W.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Bilicki, S.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Bishof, M.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Bize, S.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

Blatt, S.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Bloom, B. J.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Bookjans, E.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Boyd, M. M.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Bromley, S. L.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Burt, E. A.

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Campbell, G. K.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Campbell, S. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Cho, J. W.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Clairon, A.

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).

Clark, C. W.

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

de Miranda, M. H. G.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Diddams, S. A.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Dörscher, S.

Dubé, P.

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

Falke, S.

T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, “High accuracy correction of blackbody radiation shift in an optical lattice clock,” Phys. Rev. Lett. 109(26), 263004 (2012).

Falke, St.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Fang, F.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Fang, Z.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Foreman, S. M.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Fortier, T. M.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Fukuzaki, Y.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Furuya, Y.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Gao, K.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Gartman, R.

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).

Gerginov, V.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Gertsvolf, M.

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

Gibble, K.

K. Gibble, “Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions,” Phys. Rev. Lett. 110(18), 180802 (2013).

Granveaud, M.

J. Azoubib, M. Granveaud, and B. Guinot, “Estimation of the scale unit duration of time scales,” Metrologia 13(3), 87–93 (1977).

Grebing, C.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Grosche, G.

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Guan, H.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Guena, J.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Guéna, J.

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).

Guinot, B.

J. Azoubib, M. Granveaud, and B. Guinot, “Estimation of the scale unit duration of time scales,” Metrologia 13(3), 87–93 (1977).

Gurov, M.

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).

J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, “Observation and cancellation of a perturbing dc stark shift in strontium optical lattice clocks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 411–415 (2012).

Hachisu, H.

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

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).

H. Hachisu and T. Ido, “Intermittent optical frequency measurements to reduce the dead time uncertainty of frequency link,” Jpn. J. Appl. Phys. 54(11), 112401 (2015).

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(2), 022701 (2012).

Hafner, S.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Häfner, S.

Hagemann, Ch.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Hanado, Y.

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).

F. Nakagawa, M. Imae, Y. Hanado, and M. Aida, “Development of multichannel dual-mixer time difference system to generate UTC(NICT),” IEEE Trans. Instrum. Meas. 54(2), 829–832 (2005).

Harmegnies, A.

G. Panfilo, A. Harmegnies, and L. Tisserand, “A new prediction algorithm for the generation of International Atomic Time,” Metrologia 49(1), 49–56 (2012).

Hiyama, Y.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Hong, F.-L.

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(11), 115002 (2015).

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(1), 012401 (2014).

Hosaka, K.

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(11), 115002 (2015).

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(1), 012401 (2014).

Huang, Y.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Huntemann, N.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Hutson, R. B.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Ido, T.

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

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).

H. Hachisu and T. Ido, “Intermittent optical frequency measurements to reduce the dead time uncertainty of frequency link,” Jpn. J. Appl. Phys. 54(11), 112401 (2015).

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(2), 022701 (2012).

Ikegami, T.

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(11), 115002 (2015).

Imae, M.

F. Nakagawa, M. Imae, Y. Hanado, and M. Aida, “Development of multichannel dual-mixer time difference system to generate UTC(NICT),” IEEE Trans. Instrum. Meas. 54(2), 829–832 (2005).

Inaba, H.

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(11), 115002 (2015).

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(1), 012401 (2014).

Inukai, T.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Ishijima, H.

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(2), 022701 (2012).

Iwata, M.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kageyama, I.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kawahara, T.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kawamoto, S.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kim, E. B.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Kimura, I.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kipphardt, B.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Kobayashi, T.

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(11), 115002 (2015).

Kodama, T.

B. Miyahara, T. Kodama, and Y. Kuroishi, “Development of new hybrid geoid model for Japan, GSIGEO2011,” Bull. GSI 62, 11 (2014).

Kokado, K.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kozlov, M. G.

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

Kumagai, M.

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(2), 022701 (2012).

Kurihara, S.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Kuroishi, Y.

B. Miyahara, T. Kodama, and Y. Kuroishi, “Development of new hybrid geoid model for Japan, GSIGEO2011,” Bull. GSI 62, 11 (2014).

Kwon, T. Y.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Laurent, P.

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).

Le Coq, Y.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Le Targat, R.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

Lecallier, A.

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Lee, S.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Lee, S. K.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Lee, W.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Lemke, N.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Lemke, N. D.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Lemonde, P.

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).

J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, “Observation and cancellation of a perturbing dc stark shift in strontium optical lattice clocks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 411–415 (2012).

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Li, T.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Li, Y.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

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(2), 022701 (2012).

Liang, K.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Lin, B.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Lin, Y.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Lipphardt, B.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Lisdat, C.

T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, “High accuracy correction of blackbody radiation shift in an optical lattice clock,” Phys. Rev. Lett. 109(26), 263004 (2012).

Lisdat, Ch.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Liu, P.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Lodewyck, J.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, “Observation and cancellation of a perturbing dc stark shift in strontium optical lattice clocks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 411–415 (2012).

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Lorini, L.

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).

J. Lodewyck, M. Zawada, L. Lorini, M. Gurov, and P. Lemonde, “Observation and cancellation of a perturbing dc stark shift in strontium optical lattice clocks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 411–415 (2012).

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Lours, M.

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).

Ludlow, A. D.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Ma, L.

Y. Huang, H. Guan, P. Liu, W. Bian, L. Ma, K. Liang, T. Li, and K. Gao, “Frequency comparison of two 40Ca+ optical clocks with an uncertainty at the 10−17 level,” Phys. Rev. Lett. 116(1), 013001 (2016).

Madej, A. A.

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

Marti, G. E.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Martin, M. J.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Matsumura, S.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

McNally, R. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Meng, F.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Middelmann, T.

T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, “High accuracy correction of blackbody radiation shift in an optical lattice clock,” Phys. Rev. Lett. 109(26), 263004 (2012).

Middelmann, Th.

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Millo, J.

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Miyahara, B.

B. Miyahara, T. Kodama, and Y. Kuroishi, “Development of new hybrid geoid model for Japan, GSIGEO2011,” Bull. GSI 62, 11 (2014).

Mun, J.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Nagano, S.

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(2), 022701 (2012).

Nagórny, B.

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).

Nakagawa, F.

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).

F. Nakagawa, M. Imae, Y. Hanado, and M. Aida, “Development of multichannel dual-mixer time difference system to generate UTC(NICT),” IEEE Trans. Instrum. Meas. 54(2), 829–832 (2005).

Nicholson, T. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Nicolodi, D.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Oates, C. W.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Ohtaki, M.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Okubo, S.

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(11), 115002 (2015).

Onae, A.

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(11), 115002 (2015).

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(1), 012401 (2014).

Panfilo, G.

G. Panfilo, A. Harmegnies, and L. Tisserand, “A new prediction algorithm for the generation of International Atomic Time,” Metrologia 49(1), 49–56 (2012).

G. Panfilo and T. E. Parker, “A theoretical and experimental analysis of frequency transfer uncertainty, including frequency transfer into TAI,” Metrologia 47(5), 552–560 (2010).

G. Panfilo and P. Tavella, “Atomic clock prediction based on stochastic differential equations,” Metrologia 45(6), S108–S116 (2008).

Park, C. Y.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Park, S. E.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Park, S. J.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

Parker, T. E.

G. Panfilo and T. E. Parker, “A theoretical and experimental analysis of frequency transfer uncertainty, including frequency transfer into TAI,” Metrologia 47(5), 552–560 (2010).

D. Yu, M. Weiss, and T. E. Parker, “Uncertainty of a frequency comparison with distributed dead time and measurement interval offset,” Metrologia 44(1), 91–96 (2007).

Petit, G.

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

Poli, N.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Porsev, S. G.

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

Riehle, F.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

F. Riehle, “Towards a re-definition of the second based on optical atomic clocks,” C. R. Phys. 16(5), 506–515 (2015).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Robyr, J.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Rosenbusch, P.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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).

Rovera, D. G.

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).

Safronova, M. S.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

Safronova, U. I.

M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, “Blackbody-radiation shift in the Sr optical atomic clock,” Phys. Rev. A 87(1), 012509 (2013).

Santarelli, G.

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).

Sasaki, T.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Sato, Y.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Schnatz, H.

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Shi, C.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Shiga, N.

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(2), 022701 (2012).

Shigematsu, H.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Shouji, Y.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Stalnaker, J. E.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Sterr, U.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

T. Middelmann, S. Falke, C. Lisdat, and U. Sterr, “High accuracy correction of blackbody radiation shift in an optical lattice clock,” Phys. Rev. Lett. 109(26), 263004 (2012).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Strouse, G. F.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Sun, Z.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Suzuyama, T.

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(11), 115002 (2015).

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(1), 012401 (2014).

Takamizawa, A.

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(11), 115002 (2015).

Tanabe, T.

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(11), 115002 (2015).

Tavella, P.

G. Panfilo and P. Tavella, “Atomic clock prediction based on stochastic differential equations,” Metrologia 45(6), S108–S116 (2008).

Tew, W. L.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

Thomsen, J. W.

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Tisserand, L.

G. Panfilo, A. Harmegnies, and L. Tisserand, “A new prediction algorithm for the generation of International Atomic Time,” Metrologia 49(1), 49–56 (2012).

Tobar, M. E.

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).

Tsuji, H.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Tsutsumi, T.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Vallet, G.

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

Vogt, S.

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

Vogt, St.

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Wang, Q.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

Weiss, M.

D. Yu, M. Weiss, and T. E. Parker, “Uncertainty of a frequency comparison with distributed dead time and measurement interval offset,” Metrologia 44(1), 91–96 (2007).

Westergaard, P. G.

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).

P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

Weyers, S.

C. Grebing, A. Al-Masoudi, S. Dörscher, S. Häfner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, and Ch. Lisdat, “Realization of a timescale with an accurate optical lattice clock,” Optica 3, 563 (2016).

St. Falke, N. Lemke, C. Grebing, B. Kipphardt, S. Weyers, V. Gerginov, N. Huntemann, Ch. Hagemann, A. Al-Masoudi, S. Hafner, S. Vogt, U. Sterr, and Ch. Lisdat, “A strontium lattice clock with 3×10−17 inaccuracy and its frequency,” New J. Phys. 16(7), 073023 (2014).

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Williams, J. R.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Winfred, J. S. R. V.

St. Falke, H. Schnatz, J. S. R. V. Winfred, Th. Middelmann, St. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and Ch. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011).

Yahagi, T.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Yamagiwa, A.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Yamaguchi, A.

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(2), 022701 (2012).

Yamaguchi, K.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Yamao, H.

Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

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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(11), 115002 (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(11), 115002 (2015).

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(1), 012401 (2014).

Ye, J.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Yoon, T. H.

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Yu, D.

C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

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Y. Hiyama, A. Yamagiwa, T. Kawahara, M. Iwata, Y. Fukuzaki, Y. Shouji, Y. Sato, T. Yutsudo, T. Sasaki, H. Shigematsu, H. Yamao, T. Inukai, M. Ohtaki, K. Kokado, S. Kurihara, I. Kimura, T. Tsutsumi, T. Yahagi, Y. Furuya, I. Kageyama, S. Kawamoto, K. Yamaguchi, H. Tsuji, and S. Matsumura, “Revision of Survey Results of Control Points after the 2011 off the Pacific Coast of Tohoku Earthquake,” Bulletin of the GSI 59, 31 (2011).

Zang, E.

Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (2015).

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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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P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

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A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, and C. W. Oates, “Sr lattice clock at 1 × 10-16 fractional uncertainty by remote optical evaluation with a Ca clock,” Science 319(5871), 1805–1808 (2008).

Zhang, W.

T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Zhang, X.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

Zhou, Z.

A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

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

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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(2), 022701 (2012).

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(1), 012401 (2014).

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F. Riehle, “Towards a re-definition of the second based on optical atomic clocks,” C. R. Phys. 16(5), 506–515 (2015).

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Y. Lin, Q. Wang, Y. Li, F. Meng, B. Lin, E. Zang, Z. Sun, F. Fang, T. Li, and Z. Fang, “First evaluation and frequency measurement of the strontium optical lattice clock at NIM,” Chin. Phys. Lett. 32(9), 090601 (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(11), 115002 (2015).

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C. Y. Park, D. Yu, W. 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. 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(2), 119–128 (2013).

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G. Panfilo and T. E. Parker, “A theoretical and experimental analysis of frequency transfer uncertainty, including frequency transfer into TAI,” Metrologia 47(5), 552–560 (2010).

D. Yu, M. Weiss, and T. E. Parker, “Uncertainty of a frequency comparison with distributed dead time and measurement interval offset,” Metrologia 44(1), 91–96 (2007).

J. Lodewyck, S. Bilicki, E. Bookjans, J. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Guena, M. Abgrall, P. Rosenbusch, and S. Bize, “Optical to microwave clock frequency ratios with a nearly continuous strontium optical lattice clock,” Metrologia 53(4), 1123–1130 (2016).

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T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty,” Nat. Commun. 6, 6896 (2015).

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).

Nature (1)

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506(7486), 71–75 (2014).

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P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, “Lattice-induced frequency shifts in Sr optical lattice clocks at the 10-17 level,” Phys. Rev. Lett. 106(21), 210801 (2011).

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A. A. Madej, P. Dubé, Z. Zhou, J. E. Bernard, and M. Gertsvolf, “88Sr+ 445-THz single-ion reference at the 10-17 level via control and cancellation of systematic uncertainties and its measurement against the SI second,” Phys. Rev. Lett. 109(20), 203002 (2012).

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Figures (5)

Fig. 1
Fig. 1

(a) Allan deviations of the HMs used in this work. (b) Overlapping Hadamard deviations of the two HMs and the combined oscillator. Over the averaging time of up to 10 days, the deviations between the two HMs are shown as empty squares, whereas those over longer times are shown as deviations versus UTC.

Fig. 2
Fig. 2

Schematic diagram of the local measurement to obtain f(Sr)/f(UTC(NICT);10d).

Fig. 3
Fig. 3

(a) Evaluation of HMa frequency based on Sr in a 10-day intermittent operation (Campaign #2, MJD 57539 ̶ 57549). Most of the points are the results of 103 s evaluations. The error bars are the Allan deviation of the HMa in the corresponding evaluation interval. Linear fitting provides mean frequency of 10 days. (b) Fractional frequency of the optical clock signal against two HMs and a combined oscillator. The linear frequency drift of the HMs is clearly observed. The offset is removed so that the three linear fitting lines intersect at the midpoint of the campaign. The fluctuation of the data points is mitigated when we take the average of the two values, which is a benefit of employing the combined LFO.

Fig. 4
Fig. 4

Absolute frequency of the 87Sr clock transition evaluated with the LFO of two HMs and the combined oscillator.

Fig. 5
Fig. 5

Comparison of 87Sr clock transition frequencies recently reported by various institutes [6,11‒13, 30, 34]. The last five points reported in 2016 or later show good agreement, indicating the validity of reducing the uncertainty in the 87Sr standard frequency.

Tables (2)

Tables Icon

Table 1 Systematic shifts and uncertainties of the 87Sr lattice clock

Tables Icon

Table 2 Uncertainties of the absolute frequency measurement

Equations (5)

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ν 0 ( Sr ) f 0 ( SIs ) = ν 0 ( Sr ) f ( LFO ) f ( LFO ) f ( UTC(k) ) f ( UTC(k) ) f ( TAI ) f ( TAI ) f 0 ( SIs ) ,
ν 0 ( Sr ) f 0 ( SIs ) = ν 0 ( Sr ) f ( LFO ; 10 4 s ) f ( LFO;5d ) f ( UTC(k);5d ) f ( UTC(k);5d ) f ( TAI;5d ) f ( TAI;1m ) f 0 ( SIs ) .
f ( HMb ; Δ t ) f ( HMa ; Δ t ) = 1 + Φ 2 ( t f ) Φ 2 ( t i ) t f t i .
ν 0 ( Sr ) f ( HMb ; Δ t ) = [ 1 + Φ 2 ( t f ) Φ 2 ( t i ) t f t i ] 1 ν 0 ( Sr ) f ( HMa ; Δ t ) .
1 2 ( ν 0 ( Sr ) f ( HMa ; Δ t ) + ν 0 ( Sr ) f ( HMb; Δ t ) )

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