Applied Physics B

, Volume 114, Issue 1–2, pp 189–201 | Cite as

Evaluation of the systematic shifts and absolute frequency measurement of a single Ca+ ion frequency standard

  • Yao Huang
  • Peiliang Liu
  • Wu Bian
  • Hua Guan
  • Kelin GaoEmail author


This paper provides a detailed description of the 40Ca+ optical frequency standard uncertainty evaluation and the absolute frequency measurement of the clock transition, as a summary and supplement for the published papers of Yao Huang et al. (Phys Rev A 84:053841, 1) and Huang et al. (Phys Rev A 85:030503, 2). The calculation of systematic frequency shifts, expected for a single trapped Ca+ ion optical frequency standard with a “clock” transition at 729 nm is described. There are several possible causes of systematic frequency shifts that need to be considered. In general, the frequency was measured with an uncertainty of 10−15 level, and the overall systematic shift uncertainty was reduced to below a part in 10−15. Several frequency shifts were calculated for the Ca+ ion optical frequency standard, including the trap design, optical and electromagnetic fields geometry and laboratory conditions, including the temperature condition and the altitude of the Ca+ ion. And we measured the absolute frequency of the 729-nm clock transition at the 10−15 level. An fs comb is referenced to a hydrogen maser, which is calibrated to the SI-second through the Global Positioning System (GPS). Using the GPS satellites as a link, we can calculate the frequency difference of the two hydrogen masers with a long distance, one in WIPM (Wuhan) and the other in National Institute of Metrology (NIM, Beijing). The frequency difference of the hydrogen maser in NIM (Beijing) and the SI-second calculated by BIPM is published on the BIPM web site every 1 month, with a time interval of every 5 days. By analyzing the experimental data obtained within 32 days of a total averaging time of >2 × 10s, the absolute frequency of the 40Ca+ 4 s 2 S 1/2–3d 2D5/2 clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 × 10−15.


Global Position System Probe Laser Stark Shift Clock Transition Optical Frequency Comb 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We acknowledge H. Shu, H. Fan, B. Guo, Q. Liu, W. Qu, B. Ou, J. Cao and X. Huang for the early works, thank G. Huang for his valuable suggestion, thank T. Li and K. Liang for the GPS comparison works, and thank J. Ye, F.-L. Hong, H. Klein, K. Matsubara, M. Kajita, Y. Li, P. Dubé, L. Ma, Z. Yan and C. Lee for their fruitful discussions. This work is supported by the National Basic Research Program of China (2005CB724502) and (2012CB821301), the National Natural Science Foundation of China (10874205, 10274093 and 11034009) and Chinese Academy of Sciences.


  1. 1.
    Y. Huang, Q. Liu, J. Cao, B. Ou, P. Liu, H. Guan, X. Huang, K. Gao, Phys. Rev. A 84, 053841 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Huang, J. Cao, P. Liu, K. Liang, B. Ou, H. Guan, X. Huang, T. Li, K. Gao, Phys. Rev. A 85, 030503 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    T. Udem, T.W. Hänsch, Nature 416, 233 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    S.T. Cundiff, J. Ye, Rev. Mod. Phys. 75, 325 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    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, S.R. Jefferts, Metrologia 45, 539 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    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, C.W. Oates, Science 319, 1805 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    N.D. Lemke, A.D. Ludlow, Z.W. Barber, T.M. Fortier, S.A. Diddams, Y. Jiang, S.R. Jefferts, T.P. Heavner, T.E. Parker, C.W. Oates, Phys. Rev. Lett. 103, 063001 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    C.W. Chou, D.B. Hume, J.C.J. Koelemeij, D.J. Wineland, T. Rosenband, Phys. Rev. Lett. 104, 070802 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    H.S. Margolis, G.P. Barwood, G. Huang, H.A. Klein, S.N. Lea, K. Szymaniec, P. Gill, Science 306, 1355 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    T. Schneider, E. Peik, C. Tamm, Phys. Rev. Lett. 94, 230801 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    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, Ph Laurent, Phys. Rev. Lett. 102, 023002 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    T. Akatsuka, M. Takamoto, H. Katori, Nat. Phys. 4, 954 (2008)CrossRefGoogle Scholar
  13. 13.
    N. Poli, Z.W. Barber, N.D. Lemke, C.W. Oates, L.S. Ma, J.E. Stalnaker, T.M. Fortier, S.A. Diddams, L. Hollberg, J.C. Bergquist, A. Brusch, S. Jefferts, T. Heavner, T. Parker, Phys. Rev. A 77, 050501 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    N. Huntemann, M. Okhapkin, B. Lipphardt, S. Weyers, C. Tamm, E. Peik, Phys. Rev. Lett. 108, 090801 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    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, J.C. Bergquist, Science 319, 1808 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    J.E. Stalnaker, S.A. Diddams, T.M. Fortier, K. Kim, L. Hollberg, J.C. Bergquist, W.M. Itano, M.J. Delany, L. Lorini, W.H. Oskay, T.P. Heavner, S.R. Jefferts, F. Levi, T.E. Parker, J. Shirley et al., Appl. Phys. B 89, 167 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    F.-L. Hong, M. Takamoto, R. Higashi, Y. Fukuyama, J. Jiang, H. Katori, Opt. Express 13, 5253 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    M. Takamoto, F.-L. Hong, R. Higashi, H. Katori, Nature 435, 321 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    S.A. King, R.M. Godun, S.A. Webster, H.S. Margolis, L.A.M. Johnson, K. Szymaniec, P.E.G. Baird, P. Gill, New J. Phys. 14, 013045 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Alan A. Madej, Pierre Dube, Zichao Zhou, John E. Bernard, Marina Gertsvolf, Phys. Rev. Lett. 109, 203002 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    Recommendation 2(c2-2009)-(CIPM)Google Scholar
  22. 22.
    K. Matsubara et al., Appl. Phys. Express 1, 067011 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    K. Matsubara et al., Joint meeting of the European frequency and time forum and the IEEE international frequency control symposium, 1 &2, 751 (2009)Google Scholar
  24. 24.
    K. Matsubara et al., Opt. Express 20, 22034 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    C. Champenois, M. Houssin, C. Lisowski, M. Knoop, G. Hagel, M. Vedel, F. Vedel, Phy. Lett. A 331, 298 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    S. Gulde, D. Rotter, P. Barton, F. Schmidt-Kaler, R. Blatt, W. Hogervorst, Appl. Phys. B 73, 861 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    H. Dehmelt, IEEE Trans. Instrum. Meas. 31, 83 (1982)ADSCrossRefGoogle Scholar
  28. 28.
    G. Barwood, K. Gao, P. Gill, G. Huang, H.A. Klein, IEEE Trans. Instrum. Meas. 50, 543 (2001)CrossRefGoogle Scholar
  29. 29.
    J.E. Bernard, A.A. Madej, L. Marmet, B.G. Whitford, K.J. Siemsen, S. Cundy, Phys. Rev. Lett. 82, 3228 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    D.J. Berkeland, J.D. Miller, J.C. Bergquist, W.M. Itano, D.J. Wineland, J. Appl. Phys. 83, 5025 (1998)ADSCrossRefGoogle Scholar
  31. 31.
    A.A. Madej, J.E. Bernard, P. Dube, L. Marmet, R.S. Windeler, Phys. Rev. A 70, 012507 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    M. Itano, J. Res. NIST 105, 829 (2000)CrossRefGoogle Scholar
  33. 33.
    M.S. Safronova, U.I. Safronova, Phys. Rev. A 83, 012503 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    B. Arora, M.S. Safronova, C.W. Clark, Phys. Rev. A 76, 064501 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    J. Mitroy, J.Y. Zhang, Eur. Phys. J. D 46, 415 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    J. Mitroy, M.S. Safronova, C.W. Clark, J. Phys. B 43, 202001 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    C.W. Chou, D.B. Hume, T. Rosenband, D.J. Wineland, Science 329, 1630 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    W. Lewandowski, W.J. Azoubib, W.J. Klepczynski, Proc. IEEE 87, 163 (1999)ADSCrossRefGoogle Scholar
  39. 39.
    Bureau International des Poids et Mesures (BIPM), Circular T, May&June (2011)
  40. 40.
    P. Dubé, A.A. Madej, Z. Zhou, J.E. Bernard, Phys. Rev. A 87, 023806 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yao Huang
    • 1
    • 2
  • Peiliang Liu
    • 1
    • 2
    • 3
  • Wu Bian
    • 1
    • 2
    • 3
  • Hua Guan
    • 1
    • 2
  • Kelin Gao
    • 1
    • 2
    Email author
  1. 1.State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhanChina
  2. 2.Center for Cold Atom PhysicsChinese Academy of SciencesWuhanChina
  3. 3.Graduate SchoolChinese Academy of SciencesBeijingChina

Personalised recommendations