Abstract

Optical frequency comparison of the 40Ca+ clock transition νCa (2S1/2-2D5/2, 729nm) against the 87Sr optical lattice clock transition νSr (1S0-3P0, 698nm) has resulted in a frequency ratio νCa / νSr = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio νCa / νSr to reach 1 × 10−15 in 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of νCa using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We note that the absolute frequency of 40Ca+ we measure deviates from other published values by more than three times our measurement uncertainty.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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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).
[CrossRef]

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

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. Cont. 59, 391–420 (2012).

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

K. Hayasaka, “Synthesis of two-species ion chains for a new optical frequency standard with an indium ion,” Appl. Phys. B 107(4), 965–970 (2012).
[CrossRef]

2011 (3)

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

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

2010 (1)

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

2009 (3)

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

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(5), 692–694 (2009).
[CrossRef] [PubMed]

2008 (6)

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

2007 (1)

B. Arora, M. S. Safronova, and C. W. Clark, “Blackbody-radiation shift in a 43Ca+ ion optical frequency standard,” Phys. Rev. A 76(6), 064501 (2007).
[CrossRef]

2005 (3)

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).
[CrossRef]

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005).
[CrossRef] [PubMed]

2004 (2)

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

1994 (1)

Abgrall, M.

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. Cont. 59, 391–420 (2012).

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

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).
[CrossRef]

Alnis, J.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Amemiya, M.

Arora, B.

B. Arora, M. S. Safronova, and C. W. Clark, “Blackbody-radiation shift in a 43Ca+ ion optical frequency standard,” Phys. Rev. A 76(6), 064501 (2007).
[CrossRef]

Baillard, X.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Barwood, G. P.

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

Benhelm, J.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Bergquist, J. C.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Bize, S.

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. Cont. 59, 391–420 (2012).

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Blatt, R.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Blatt, S.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Boyd, M. M.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Brusch, A.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Campbell, G. K.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Cao, J.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Chapelet, F.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Chou, C. W.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Chupin, B.

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. Cont. 59, 391–420 (2012).

Chwalla, M.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Clairon, A.

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. Cont. 59, 391–420 (2012).

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Clark, C. W.

B. Arora, M. S. Safronova, and C. W. Clark, “Blackbody-radiation shift in a 43Ca+ ion optical frequency standard,” Phys. Rev. A 76(6), 064501 (2007).
[CrossRef]

de Miranda, M. H. G.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Degenhardt, C.

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Diddams, S. A.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Droste, S.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Drullinger, R. E.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Falke, St.

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

Fortier, T. M.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Fouche, M.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Fujieda, M.

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

Fujii, Y.

Gao, K.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Gibble, K.

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. Cont. 59, 391–420 (2012).

Gill, P.

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

Grosche, G.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

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

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Guan, H.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Guéna, J.

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. Cont. 59, 391–420 (2012).

Hachisu, 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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

Hall, J. L.

Hanado, Y.

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).
[CrossRef]

Hänsch, T. W.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Hänsel, W.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Hayasaka, K.

K. Hayasaka, “Synthesis of two-species ion chains for a new optical frequency standard with an indium ion,” Appl. Phys. B 107(4), 965–970 (2012).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Heavner, T. P.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Higashi, R.

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Holzwarth, R.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Hong, F.-L.

Hosokawa, M.

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

Huang, G.

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

Huang, X.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Huang, Y.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Hume, D. B.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Ido, T.

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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

Ikegami, T.

Imae, M.

Inaba, H.

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).
[CrossRef]

Itano, W. M.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Ito, H.

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

Jefferts, S. R.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Jungner, P.

Kajita, M.

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Katori, H.

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

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(5), 692–694 (2009).
[CrossRef] [PubMed]

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Kim, K.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Kirchmair, G.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Klein, H. A.

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

Koelemeij, J. C. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

Laurent, P.

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. Cont. 59, 391–420 (2012).

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Laurent, Ph.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Le Targat, R.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Lea, S. N.

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

Lecallier, A.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Legero, Th.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Lemonde, P.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Li, R.

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. Cont. 59, 391–420 (2012).

Li, T.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Li, Y.

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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

Liang, K.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Lipphardt, B.

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

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Lisdat, C.

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

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Liu, P.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Lorini, L.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Lours, M.

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. Cont. 59, 391–420 (2012).

Ludlow, A. D.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Ma, L.-S.

Margolis, H. S.

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

Martin, M. J.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Matsubara, K.

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

Middelmann, T.

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

Monz, T.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Musha, M.

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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Nakagawa, F.

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).
[CrossRef]

Nakagawa, K.

Nazarova, T.

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Newbury, N. R.

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
[CrossRef]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Oskay, W. H.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Ou, B.

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

Parker, T. E.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Predehl, K.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Raupach, S. M. F.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Riebe, M.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Riehle, F.

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

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Roos, C. F.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Rosenband, T.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Rosenbusch, P.

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. Cont. 59, 391–420 (2012).

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Rovera, D.

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. Cont. 59, 391–420 (2012).

Rovera, G. D.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Safronova, M. S.

B. Arora, M. S. Safronova, and C. W. Clark, “Blackbody-radiation shift in a 43Ca+ ion optical frequency standard,” Phys. Rev. A 76(6), 064501 (2007).
[CrossRef]

Santarelli, G.

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. Cont. 59, 391–420 (2012).

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Schindler, P.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Schmidt, P. O.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Schnatz, H.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

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

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

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).
[CrossRef]

Stalnaker, J. E.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Sterr, U.

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

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Stoehr, H.

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

Swann, W. C.

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
[CrossRef]

Szymaniec, K.

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

Takamizawa, A.

Takamoto, M.

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

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(5), 692–694 (2009).
[CrossRef] [PubMed]

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Takano, T.

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

Terra, O.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Thomsen, J. W.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Tobar, M. E.

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. Cont. 59, 391–420 (2012).

Udem, Th.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

Ueda, K.

Villar, A. S.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Vogt, S.

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

Watabe, K.

Westergaard, P. G.

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

Weyers, S.

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

Williams, P. A.

Wineland, D. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

Winfred, J. S. R. V.

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

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).
[CrossRef]

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19(17), 16498–16507 (2011).
[CrossRef] [PubMed]

Yanagimachi, S.

Ye, J.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19(21), 1777–1779 (1994).
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Zelevinsky, T.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Appl. Phys. B (1)

K. Hayasaka, “Synthesis of two-species ion chains for a new optical frequency standard with an indium ion,” Appl. Phys. B 107(4), 965–970 (2012).
[CrossRef]

Appl. Phys. Express (3)

A. Yamaguchi, M. Fujieda, M. Kumagai, H. Hachisu, S. Nagano, Y. Li, T. Ido, T. Takano, M. Takamoto, and H. Katori, “Direct comparison of distant optical lattice clocks at the 10−16 uncertainty,” Appl. Phys. Express 4(8), 082203 (2011).
[CrossRef]

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).
[CrossRef]

K. Matsubara, K. Hayasaka, Y. Li, H. Ito, S. Nagano, M. Kajita, and M. Hosokawa, “Frequency measurement of the optical clock transition of 40Ca+ ions with an uncertainty of 10−14 level,” Appl. Phys. Express 1, 067011 (2008).
[CrossRef]

Eur. Phys. J. D (1)

X. Baillard, M. Fouche, 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(1), 11–17 (2008).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

C. Degenhardt, T. Nazarova, C. Lisdat, H. Stoehr, U. Sterr, and F. Riehle, “Influence of chirped excitation pulses in an optical clock with ultracold calcium atoms,” IEEE Trans. Instrum. Meas. 54(2), 771–775 (2005).
[CrossRef]

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).
[CrossRef]

IEEE Trans. Ultrason., Ferroelectr., Freq. Cont. (1)

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. Cont. 59, 391–420 (2012).

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (2)

Y. Li, S. Nagano, K. Matsubara, H. Ito, M. Kajita, and M. Hosokawa, “Narrow-line and frequency tunable diode laser system for S–D transition of Ca+ ions,” Jpn. J. Appl. Phys. 47(8), 6327–6332 (2008).
[CrossRef]

S. Nagano, H. Ito, Y. Li, K. Matsubara, and M. Hosokawa, “Stable operation of femtosecond laser frequency combs with uncertainty at the 10−17 level toward optical frequency standards,” Jpn. J. Appl. Phys. 48(4), 042301 (2009).
[CrossRef]

Metrologia (2)

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

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008).
[CrossRef]

Nature (1)

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, and K. Gao, “Hertz-level measurement of the 40Ca+ 4s2S1/2–3d2D5/2 clock transition frequency with respect to the SI second through the Global Positioning System,” Phys. Rev. A 85(3), 030503 (2012).
[CrossRef]

B. Arora, M. S. Safronova, and C. W. Clark, “Blackbody-radiation shift in a 43Ca+ ion optical frequency standard,” Phys. Rev. A 76(6), 064501 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

G. P. Barwood, H. S. Margolis, G. Huang, P. Gill, and H. A. Klein, “Measurement of the electric quadrupole moment of the 4d2D5/2 level in 88Sr+.,” Phys. Rev. Lett. 93(13), 133001 (2004).
[CrossRef] [PubMed]

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010).
[CrossRef] [PubMed]

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and Ph. Laurent, “Absolute frequency measurement of the 40Ca+ 4s2S1/2-3d2D5/2 clock transition,” Phys. Rev. Lett. 102(2), 023002 (2009).
[CrossRef] [PubMed]

Science (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(5871), 1808–1812 (2008).
[CrossRef] [PubMed]

H. S. Margolis, G. P. Barwood, G. Huang, H. A. Klein, S. N. Lea, K. Szymaniec, and P. Gill, “Hertz-level measurement of the optical clock frequency in a single 88Sr+ ion,” Science 306(5700), 1355–1358 (2004).
[CrossRef] [PubMed]

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Spectra of 40Ca+ clock transition. Each point of the excitation probability resulted from 40 measurements of 40 ms duration interrogation of the clock laser. The FWHM of the clock transition is 30 Hz.

Fig. 2
Fig. 2

Instability of the frequency ratio νCa / νSr (red) determined by the instability of Ca+ clock. An interleaved measurement of the Sr lattice clock has resulted in lower instability as shown in black.

Fig. 3
Fig. 3

Frequency ratio νCa / νS obtained for half a year. The reproducibility of less than 10−15 is consistent with the systematic uncertainties of two clocks. The thick and thin lines indicate the weighted average and the uncertainty, respectively.

Fig. 4
Fig. 4

One year record of absolute frequency measurements of 40Ca+ clock frequency. The corrections due to systematic shifts are included. Error bars, however, include only statistical errors. The hydrogen-maser frequency used for the frequency-comb stabilization was calibrated using the TAI link. Calibrations of UTC(NICT) of two data at MJD = 55704 and 55707 as well as three data at MJD = 56009-56011 are based on same Circular T. The weighted average frequency and statistical uncertainty is 411 042 129 776 398.4 (0.2) Hz.

Tables (1)

Tables Icon

Table 1 Systematic shifts and their uncertainties of the 40Ca+ clock

Equations (3)

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f rep = ν Sr f ceo f PLL N 1 ,
ν Ca = f ceo + N 2 f rep + f b .
ν Ca ν Sr = N 2 N 1 + ( 1 N 2 / N 1 ) f ceo ( N 2 / N 1 ) f PLL + f b ν Sr .

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