Abstract

We demonstrate a means of increasing the signal-to-noise ratio in a Ramsey–Bordé interferometer with spatially separated oscillatory fields on a thermal atomic beam. The S01P13 intercombination line in neutral Ca40 is used as a frequency discriminator, with an extended cavity diode laser at 423nm probing the ground state population after a Ramsey–Bordé sequence of 657nm light–field interactions with the atoms. Evaluation of the instability of the Ca frequency reference is carried out by comparison with (i) a hydrogen-maser and (ii) a cryogenic sapphire oscillator. In the latter case the Ca reference exhibits a square-root Λ variance of 9.2×1014 at 1s and 2.0×1014 at 64s. This is an order-of-magnitude improvement for optical beam frequency references, to our knowledge. The shot noise of the readout fluorescence produces a limiting square-root Λ variance of 7×1014τ, highlighting the potential for improvement. This work demonstrates the feasibility of a portable frequency reference in the optical domain with 1014 range frequency instability.

© 2010 Optical Society of America

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  1. T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
    [CrossRef] [PubMed]
  2. S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
    [CrossRef] [PubMed]
  3. T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
    [CrossRef] [PubMed]
  4. P. Antonini, M. Okhapkin, E. Goklu, and S. Schiller, “Test of constancy of speed of light with rotating cryogenic optical resonators,” Phys. Rev. A 71, 050101 (2005).
    [CrossRef]
  5. H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
    [CrossRef] [PubMed]
  6. H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, “Optical cavity tests of Lorentz invariance for the electron,” Phys. Rev. D 68, 116006 (2003).
    [CrossRef]
  7. M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
    [CrossRef] [PubMed]
  8. N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
    [CrossRef]
  9. C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
    [CrossRef]
  10. M. Takamoto, F. L. Hong, R. Higashi, Y. Fujii, M. Imae, and H. Katori, “Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic Sr-87 isotope,” J. Phys. Soc. Jpn. 75, 104302 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
    [CrossRef] [PubMed]
  13. G. Wilpers, C. Oates, and L. Hollberg, “Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability Ca40 optical frequency standard,” Appl. Phys. B Lasers Opt. 85, 31-44 (2006).
    [CrossRef]
  14. J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
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    [CrossRef]
  16. K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
    [CrossRef]
  17. A. Makdissi and E. de Clercq, “Evaluation of the accuracy of the optically pumped caesium beam primary frequency standard of the BNM-LPTF,” Metrologia 38, 409-425 (2001).
    [CrossRef]
  18. L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
    [CrossRef]
  19. P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
    [CrossRef]
  20. C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
    [CrossRef]
  21. A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
    [CrossRef]
  22. F. Riehle, A. Witte, T. Kisters, and J. Helmcke, “Interferometry with Ca atoms,” Appl. Phys. B 54, 333-340 (1992).
    [CrossRef]
  23. A. Celikov, F. Riehle, V. Velichansky, and J. Helmcke, “Diode laser spectroscopy in a Ca atomic beam,” Opt. Commun. 107, 54-60 (1994).
    [CrossRef]
  24. W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: Observation of quantum jumps,” Phys. Rev. Lett. 56, 2797-2799 (1986).
    [CrossRef] [PubMed]
  25. J. J. McFerran, J. G. Hartnett, and A. N. Luiten, “An optical beam frequency reference with 10−14 range frequency instability,” Appl. Phys. Lett. 95, 031103 (2009).
    [CrossRef]
  26. J. Bergquist, S. Lee, and J. Hall, “Saturated absorption with spatially separated laser fields: observation of optical 'Ramsey' fringes,” Phys. Rev. Lett. 38, 159-162 (1977).
    [CrossRef]
  27. C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
    [CrossRef]
  28. C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).
  29. J. Helmcke, D. Zevgolis, and B. U. Yen, “Observation of high contrast, ultranarrow optical Ramsey fringes in saturated absorption utilizing 4 interaction zones of traveling waves,” Appl. Phys. B: Lasers Opt. 28, 83-84 (1982).
  30. S. T. Dawkins, “Sapphire room temperature optical frequency reference: design, construction and application,” Ph.D. thesis, University of Western Australia (2007).
  31. J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
    [CrossRef] [PubMed]
  32. R. L. Barger, J. C. Bergquist, T. C. English, and D. J. Glaze, “Resolution of photon-recoil structure of the 657.3 nm calcium line in an atomic beam with optical Ramsey fringes,” Appl. Phys. Lett. 34, 850-852 (1979).
    [CrossRef]
  33. N. Ramsey, Molecular Beams (Clarendon Press, 1956).
  34. P. E. Douglas, “The vapor pressure of calcium: I,” Proc. Phys. Soc. London Sect. B 67, 783-786 (1954).
    [CrossRef]
  35. H. J. Metcalf and P. van der Straten, “Laser cooling and trapping of atoms,” J. Opt. Soc. Am. B 20, 887-908 (2003).
    [CrossRef]
  36. A. Wallard, “Frequency stabilization of the helium-neon laser by saturated absorption in iodine vapour,” J. Phys. E 5, 926-930 (1972).
    [CrossRef]
  37. S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
    [CrossRef] [PubMed]
  38. C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
    [CrossRef] [PubMed]
  39. A. Joyet, G. Mileti, G. Dudle, and P. Thomann, “Theoretical study of the Dick effect in a continuously operated Ramsey resonator,” IEEE Trans. Instrum. Meas. 50, 150-156 (2001).
    [CrossRef]
  40. J. J. Snyder, J. Helmcke, and D. Zevgolis, “Longitudinal Ramsey-fringe spectroscopy in a calcium beam,” Appl. Phys. B: Lasers Opt. 32, 25-31 (1983).
    [CrossRef]
  41. D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
    [CrossRef]

2009

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

J. J. McFerran, J. G. Hartnett, and A. N. Luiten, “An optical beam frequency reference with 10−14 range frequency instability,” Appl. Phys. Lett. 95, 031103 (2009).
[CrossRef]

2008

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
[CrossRef] [PubMed]

N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

2007

H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

2006

M. Takamoto, F. L. Hong, R. Higashi, Y. Fujii, M. Imae, and H. Katori, “Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic Sr-87 isotope,” J. Phys. Soc. Jpn. 75, 104302 (2006).
[CrossRef]

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
[CrossRef] [PubMed]

G. Wilpers, C. Oates, and L. Hollberg, “Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability Ca40 optical frequency standard,” Appl. Phys. B Lasers Opt. 85, 31-44 (2006).
[CrossRef]

K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
[CrossRef]

J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
[CrossRef] [PubMed]

2005

P. Antonini, M. Okhapkin, E. Goklu, and S. Schiller, “Test of constancy of speed of light with rotating cryogenic optical resonators,” Phys. Rev. A 71, 050101 (2005).
[CrossRef]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
[CrossRef]

2003

H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, “Optical cavity tests of Lorentz invariance for the electron,” Phys. Rev. D 68, 116006 (2003).
[CrossRef]

F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

H. J. Metcalf and P. van der Straten, “Laser cooling and trapping of atoms,” J. Opt. Soc. Am. B 20, 887-908 (2003).
[CrossRef]

2001

A. Makdissi and E. de Clercq, “Evaluation of the accuracy of the optically pumped caesium beam primary frequency standard of the BNM-LPTF,” Metrologia 38, 409-425 (2001).
[CrossRef]

L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
[CrossRef]

A. Joyet, G. Mileti, G. Dudle, and P. Thomann, “Theoretical study of the Dick effect in a continuously operated Ramsey resonator,” IEEE Trans. Instrum. Meas. 50, 150-156 (2001).
[CrossRef]

1999

P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
[CrossRef]

1994

A. Celikov, F. Riehle, V. Velichansky, and J. Helmcke, “Diode laser spectroscopy in a Ca atomic beam,” Opt. Commun. 107, 54-60 (1994).
[CrossRef]

1992

F. Riehle, A. Witte, T. Kisters, and J. Helmcke, “Interferometry with Ca atoms,” Appl. Phys. B 54, 333-340 (1992).
[CrossRef]

1991

D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
[CrossRef]

1989

A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
[CrossRef]

1986

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: Observation of quantum jumps,” Phys. Rev. Lett. 56, 2797-2799 (1986).
[CrossRef] [PubMed]

1984

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

1983

J. J. Snyder, J. Helmcke, and D. Zevgolis, “Longitudinal Ramsey-fringe spectroscopy in a calcium beam,” Appl. Phys. B: Lasers Opt. 32, 25-31 (1983).
[CrossRef]

1982

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

J. Helmcke, D. Zevgolis, and B. U. Yen, “Observation of high contrast, ultranarrow optical Ramsey fringes in saturated absorption utilizing 4 interaction zones of traveling waves,” Appl. Phys. B: Lasers Opt. 28, 83-84 (1982).

1979

R. L. Barger, J. C. Bergquist, T. C. English, and D. J. Glaze, “Resolution of photon-recoil structure of the 657.3 nm calcium line in an atomic beam with optical Ramsey fringes,” Appl. Phys. Lett. 34, 850-852 (1979).
[CrossRef]

1977

J. Bergquist, S. Lee, and J. Hall, “Saturated absorption with spatially separated laser fields: observation of optical 'Ramsey' fringes,” Phys. Rev. Lett. 38, 159-162 (1977).
[CrossRef]

1972

A. Wallard, “Frequency stabilization of the helium-neon laser by saturated absorption in iodine vapour,” J. Phys. E 5, 926-930 (1972).
[CrossRef]

1954

P. E. Douglas, “The vapor pressure of calcium: I,” Proc. Phys. Soc. London Sect. B 67, 783-786 (1954).
[CrossRef]

Abgrall, M.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Antonini, P.

P. Antonini, M. Okhapkin, E. Goklu, and S. Schiller, “Test of constancy of speed of light with rotating cryogenic optical resonators,” Phys. Rev. A 71, 050101 (2005).
[CrossRef]

Ashby, N.

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

Avrillier, S.

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

Baillard, X.

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
[CrossRef] [PubMed]

Barber, Z.

N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

Barger, R. L.

R. L. Barger, J. C. Bergquist, T. C. English, and D. J. Glaze, “Resolution of photon-recoil structure of the 657.3 nm calcium line in an atomic beam with optical Ramsey fringes,” Appl. Phys. Lett. 34, 850-852 (1979).
[CrossRef]

Bassi, D.

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

Benhelm, J.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Bergquist, J.

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

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R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
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L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
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D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
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K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
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S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
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F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
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J. Bergquist, S. Lee, and J. Hall, “Saturated absorption with spatially separated laser fields: observation of optical 'Ramsey' fringes,” Phys. Rev. Lett. 38, 159-162 (1977).
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L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
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T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

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D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
[CrossRef]

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K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
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F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
[CrossRef]

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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
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C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
[CrossRef] [PubMed]

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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

M. Takamoto, F. L. Hong, R. Higashi, Y. Fujii, M. Imae, and H. Katori, “Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic Sr-87 isotope,” J. Phys. Soc. Jpn. 75, 104302 (2006).
[CrossRef]

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P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
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T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
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H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
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H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, “Optical cavity tests of Lorentz invariance for the electron,” Phys. Rev. D 68, 116006 (2003).
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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
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S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
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R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
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S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
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R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
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T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
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D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
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C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
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C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
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C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

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S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
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A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
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J. J. McFerran, J. G. Hartnett, and A. N. Luiten, “An optical beam frequency reference with 10−14 range frequency instability,” Appl. Phys. Lett. 95, 031103 (2009).
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J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
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A. Makdissi and E. de Clercq, “Evaluation of the accuracy of the optically pumped caesium beam primary frequency standard of the BNM-LPTF,” Metrologia 38, 409-425 (2001).
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F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

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J. J. McFerran, J. G. Hartnett, and A. N. Luiten, “An optical beam frequency reference with 10−14 range frequency instability,” Appl. Phys. Lett. 95, 031103 (2009).
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S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
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J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
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P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
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Metcalf, H. J.

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A. Joyet, G. Mileti, G. Dudle, and P. Thomann, “Theoretical study of the Dick effect in a continuously operated Ramsey resonator,” IEEE Trans. Instrum. Meas. 50, 150-156 (2001).
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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
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A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
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H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
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A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
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F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

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T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

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C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

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H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, “Optical cavity tests of Lorentz invariance for the electron,” Phys. Rev. D 68, 116006 (2003).
[CrossRef]

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N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

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C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

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J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

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M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Riedmann, M.

J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

Riehle, F.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
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P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
[CrossRef]

A. Celikov, F. Riehle, V. Velichansky, and J. Helmcke, “Diode laser spectroscopy in a Ca atomic beam,” Opt. Commun. 107, 54-60 (1994).
[CrossRef]

F. Riehle, A. Witte, T. Kisters, and J. Helmcke, “Interferometry with Ca atoms,” Appl. Phys. B 54, 333-340 (1992).
[CrossRef]

A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
[CrossRef]

Roos, C. F.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Rosenband, T.

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

Rovera, G. D.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
[CrossRef] [PubMed]

Saenz, A.

H. Müller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, “Optical cavity tests of Lorentz invariance for the electron,” Phys. Rev. D 68, 116006 (2003).
[CrossRef]

Salomon, C.

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

Sandberg, J.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: Observation of quantum jumps,” Phys. Rev. Lett. 56, 2797-2799 (1986).
[CrossRef] [PubMed]

Santarelli, G.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Schiller, S.

P. Antonini, M. Okhapkin, E. Goklu, and S. Schiller, “Test of constancy of speed of light with rotating cryogenic optical resonators,” Phys. Rev. A 71, 050101 (2005).
[CrossRef]

Schindler, P.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Schmidt, P.

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

Schnatz, H.

J. Friebe, A. Pape, M. Riedmann, K. Moldenhauer, T. Mehlstaubler, N. Rehbein, C. Lisdat, E. Rasel, W. Ertmer, H. Schnatz, B. Lipphardt, and G. Grosche, “Absolute frequency measurement of the magnesium intercombination transition S01-->P13,” Phys. Rev. A 78, 033830 (2008).
[CrossRef]

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
[CrossRef]

Schneider, T.

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

Scoles, G.

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

Senger, A.

H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

Shirley, J.

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

Snyder, J. J.

J. J. Snyder, J. Helmcke, and D. Zevgolis, “Longitudinal Ramsey-fringe spectroscopy in a calcium beam,” Appl. Phys. B: Lasers Opt. 32, 25-31 (1983).
[CrossRef]

Stalnaker, J.

N. Poli, Z. Barber, N. Lemke, C. Oates, L. Ma, J. Stalnaker, T. Fortier, S. Diddams, L. Hollberg, J. Bergquist, A. Brusch, S. Jefferts, T. Heavner, and T. Parker, “Frequency evaluation of the doubly forbidden S01-->P03 transition in bosonic Yb174,” Phys. Rev. A 77, 050501 (2008).
[CrossRef]

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

T. Fortier, N. Ashby, J. Bergquist, M. Delaney, S. Diddams, T. Heavner, L. Hollberg, W. Itano, S. Jefferts, K. Kim, F. Levi, L. Lorini, W. Oskay, T. Parker, J. Shirley, and J. Stalnaker, “Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance,” Phys. Rev. Lett. 98, 070801 (2007).
[CrossRef] [PubMed]

Stanwix, P. L.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
[CrossRef] [PubMed]

H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
[CrossRef] [PubMed]

Sterr, U.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
[CrossRef]

P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
[CrossRef]

Stoehr, H.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
[CrossRef]

Sugiyama, K.

F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

Swann, W.

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

Takamoto, M.

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

M. Takamoto, F. L. Hong, R. Higashi, Y. Fujii, M. Imae, and H. Katori, “Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic Sr-87 isotope,” J. Phys. Soc. Jpn. 75, 104302 (2006).
[CrossRef]

Tamm, C.

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

Tcherbakoff, O.

R. Le Targat, X. Baillard, M. Fouche, A. Brusch, O. Tcherbakoff, G. D. Rovera, and P. Lemonde, “Accurate optical lattice clock with Sr87 atoms,” Phys. Rev. Lett. 97, 130801 (2006).
[CrossRef] [PubMed]

Theobald, G.

L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
[CrossRef]

Thomann, P.

A. Joyet, G. Mileti, G. Dudle, and P. Thomann, “Theoretical study of the Dick effect in a continuously operated Ramsey resonator,” IEEE Trans. Instrum. Meas. 50, 150-156 (2001).
[CrossRef]

Thomsen, J. W.

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

Tobar, M. E.

C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79, 051301 (2008).
[CrossRef] [PubMed]

H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

J. J. McFerran, S. T. Dawkins, P. L. Stanwix, M. E. Tobar, and A. N. Luiten, “Optical frequency synthesis from a cryogenic microwave sapphire oscillator,” Opt. Express 14, 4316-4327 (2006).
[CrossRef] [PubMed]

van der Straten, P.

van Lerberghe, A.

C. J. Bordé, C. Salomon, S. Avrillier, A. van Lerberghe, C. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836-1848 (1984).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

Velichansky, V.

A. Celikov, F. Riehle, V. Velichansky, and J. Helmcke, “Diode laser spectroscopy in a Ca atomic beam,” Opt. Commun. 107, 54-60 (1994).
[CrossRef]

Villar, A. S.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. S. Villar, W. Hansel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, and P. Laurent, “Absolute frequency measurement of the Ca+404sS3/22-3dD5/22 clock transition,” Phys. Rev. Lett. 102, 023002 (2009).
[CrossRef] [PubMed]

Wallard, A.

A. Wallard, “Frequency stabilization of the helium-neon laser by saturated absorption in iodine vapour,” J. Phys. E 5, 926-930 (1972).
[CrossRef]

Wang, Y.-Q.

D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
[CrossRef]

Weyers, S.

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

Wilpers, G.

G. Wilpers, C. Oates, and L. Hollberg, “Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability Ca40 optical frequency standard,” Appl. Phys. B Lasers Opt. 85, 31-44 (2006).
[CrossRef]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: approaching 10−15 relative uncertainty,” Phys. Rev. A 72, 062111 (2005).
[CrossRef]

Wineland, D.

T. Rosenband, D. Hume, P. Schmidt, C. Chou, A. Brusch, L. Lorini, W. Oskay, R. Drullinger, T. Fortier, J. Stalnaker, S. Diddams, W. Swann, N. Newbury, W. Itano, D. Wineland, and J. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319, 1808-1812 (2008).
[CrossRef] [PubMed]

Witte, A.

F. Riehle, A. Witte, T. Kisters, and J. Helmcke, “Interferometry with Ca atoms,” Appl. Phys. B 54, 333-340 (1992).
[CrossRef]

Wolf, P.

H. Müller, P. L. Stanwix, M. E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, and A. Peters, “Tests of relativity by complementary rotating Michelson-Morley experiments,” Phys. Rev. Lett. 99, 050401 (2007).
[CrossRef] [PubMed]

Wynands, R.

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

Yang, D.-H.

D.-H. Yang, E.-X. Li, L.-M. Chen, B.-Y. Huang, and Y.-Q. Wang, “Experiment on optically pumped cesium beam frequency standard with sharp angle incidence probing laser beam,” Opt. Commun. 84, 275-278 (1991).
[CrossRef]

Ye, J.

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

Yen, B. U.

J. Helmcke, D. Zevgolis, and B. U. Yen, “Observation of high contrast, ultranarrow optical Ramsey fringes in saturated absorption utilizing 4 interaction zones of traveling waves,” Appl. Phys. B: Lasers Opt. 28, 83-84 (1982).

Yu, D.-S.

K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
[CrossRef]

Zelevinsky, T.

S. Blatt, A. D. Ludlow, G. K. Campbell, J. W. Thomsen, T. Zelevinsky, M. M. Boyd, J. Ye, X. Baillard, M. Fouche, R. Le Targat, A. Brusch, P. Lemonde, M. Takamoto, F. L. Hong, H. Katori, and V. V. Flambaum, “New limits on coupling of fundamental constants to gravity using Sr87 optical lattice clocks,” Phys. Rev. Lett. 100, 140801 (2008).
[CrossRef] [PubMed]

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, “Systematic study of the Sr87 clock transition in an optical lattice,” Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Zevgolis, D.

J. J. Snyder, J. Helmcke, and D. Zevgolis, “Longitudinal Ramsey-fringe spectroscopy in a calcium beam,” Appl. Phys. B: Lasers Opt. 32, 25-31 (1983).
[CrossRef]

J. Helmcke, D. Zevgolis, and B. U. Yen, “Observation of high contrast, ultranarrow optical Ramsey fringes in saturated absorption utilizing 4 interaction zones of traveling waves,” Appl. Phys. B: Lasers Opt. 28, 83-84 (1982).

Zhang, J.-W.

K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
[CrossRef]

Zhuan, W.

K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
[CrossRef]

Appl. Phys. B

F. Riehle, A. Witte, T. Kisters, and J. Helmcke, “Interferometry with Ca atoms,” Appl. Phys. B 54, 333-340 (1992).
[CrossRef]

Appl. Phys. B Lasers Opt.

G. Wilpers, C. Oates, and L. Hollberg, “Improved uncertainty budget for optical frequency measurements with microkelvin neutral atoms: results for a high-stability Ca40 optical frequency standard,” Appl. Phys. B Lasers Opt. 85, 31-44 (2006).
[CrossRef]

Appl. Phys. B: Lasers Opt.

P. Kersten, F. Mensing, U. Sterr, and F. Riehle, “A transportable optical calcium frequency standard,” Appl. Phys. B: Lasers Opt. 68, 27-38 (1999).
[CrossRef]

A. Morinaga, F. Riehle, J. Ishikawa, and J. Helmcke, “A ca optical frequency standard: Frequency stabilization by means of nonlinear ramsey resonances,” Appl. Phys. B: Lasers Opt. 48, 165-171 (1989).
[CrossRef]

C. J. Bordé, S. Avrillier, A. van Lerberghe, C. Salomon, C. Breant, D. Bassi, and G. Scoles, “Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6,” Appl. Phys. B: Lasers Opt. 28, 82-83 (1982).

J. Helmcke, D. Zevgolis, and B. U. Yen, “Observation of high contrast, ultranarrow optical Ramsey fringes in saturated absorption utilizing 4 interaction zones of traveling waves,” Appl. Phys. B: Lasers Opt. 28, 83-84 (1982).

J. J. Snyder, J. Helmcke, and D. Zevgolis, “Longitudinal Ramsey-fringe spectroscopy in a calcium beam,” Appl. Phys. B: Lasers Opt. 32, 25-31 (1983).
[CrossRef]

Appl. Phys. Lett.

R. L. Barger, J. C. Bergquist, T. C. English, and D. J. Glaze, “Resolution of photon-recoil structure of the 657.3 nm calcium line in an atomic beam with optical Ramsey fringes,” Appl. Phys. Lett. 34, 850-852 (1979).
[CrossRef]

J. J. McFerran, J. G. Hartnett, and A. N. Luiten, “An optical beam frequency reference with 10−14 range frequency instability,” Appl. Phys. Lett. 95, 031103 (2009).
[CrossRef]

Chin. Phys. Lett.

K.-K. Huang, J.-W. Zhang, D.-S. Yu, Z.-H. Chen, W. Zhuan, and J.-B. Chen, “Application of electron-shelving detection via 423 nm transition in calcium-beam optical frequency standard,” Chin. Phys. Lett. 23, 3198-3201 (2006).
[CrossRef]

IEEE Trans. Instrum. Meas.

C. Tamm, B. Lipphardt, H. Schnatz, R. Wynands, S. Weyers, T. Schneider, and E. Peik, “Yb+171 single-ion optical frequency standard at 688 THz,” IEEE Trans. Instrum. Meas. 56, 601-604 (2007).
[CrossRef]

F.-L. Hong, J. Ishikawa, K. Sugiyama, A. Onae, H. Matsumoto, J. Ye, and J. Hall, “Comparison of independent optical frequency measurements using a portable iodine-stabilized nd:yag laser,” IEEE Trans. Instrum. Meas. 52, 240-244 (2003).
[CrossRef]

A. Joyet, G. Mileti, G. Dudle, and P. Thomann, “Theoretical study of the Dick effect in a continuously operated Ramsey resonator,” IEEE Trans. Instrum. Meas. 50, 150-156 (2001).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

L. Chassagne, R. Hamouda, G. Theobald, and P. Crez, “Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48, 1513-1516 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. E

A. Wallard, “Frequency stabilization of the helium-neon laser by saturated absorption in iodine vapour,” J. Phys. E 5, 926-930 (1972).
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J. Phys. Soc. Jpn.

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Figures (10)

Fig. 1
Fig. 1

Relevant energy levels for the Ca atom probing and readout. For the thermal beam system employed here the resolution of the clock feature is determined by the temporal length of the dipole precessing regions, rather than the natural linewidth of the transition.

Fig. 2
Fig. 2

Illustrating the principal components of the S 0 1 P 1 3 probing and P 1 1 S 0 3 readout. The sequence of probe beams form the Ramsey–Bordé interferometer. Third-harmonic detection of the fringe signal is produced at the output of the lock-in amplifier, which is used to lock the 657 nm laser to the clock transition. ECDL, extended cavity diode laser; M, mirror; L, lens; PD photodetector; PDH, Pound–Drever–Hall; PMT, photomultiplier tube; D, beam separation affecting the fringe resolution. Omitted is the vacuum chamber housing the Ca oven and thermal beam. Reprinted with permission from [25]. Copyright 2009, American Institute of Physics.

Fig. 3
Fig. 3

Ca atom interrogation method. L1 and M1 represent the lens and mirror of cat’s eye 1; L2 ad M2, that of cat’s eye 2. CL, cylindrical lens; PMT, photomultiplier tube. The magnetic field and 423 nm beam are perpendicular to both the light paths and the atomic beam.

Fig. 4
Fig. 4

Oven schematic. Ca granules are placed in the central crucible. A second aperture of dimensions 150 μ m × 2.0 mm is located 100 mm above the oven outlet. Apart from the stainless steel (S.S.) support and tungsten filament, all the oven components are made of Macor. The drawing is approximately to scale with the outer diameter equal to 20 mm .

Fig. 5
Fig. 5

Integrated time-of-flight measurement of the atoms between the 657 nm and 423 nm light interactions, as measured by recording the increase in 423 nm fluorescence when the 657 nm field is halted at time = 0 s . The thick solid curve is a line fit based on Eq. (5). Inset, the corresponding velocity distribution. (b) The most probable velocity versus temperature generated from Eq. (5).

Fig. 6
Fig. 6

Line shapes for two different beam arrangements. The frequency on the abscissa is offset by the clock transition’s optical frequency. (a) A Doppler profile of the S 0 1 P 1 3 transition containing the saturation dip measured with orthogonal probe and readout beams. Here two opposing 657 nm beams interact with the atom flux. The saturation dip depth is 30 % of the Doppler profile. The curve corresponding to the left axis shows the dc change in fluorescence from the PMT. The lower curve (right axis) shows the same trace with an expanded frequency scale along with a Lorentzian fit to the saturation dip (solid curve). (b) The derivative of the Ramsey–Bordé fringe profile measured with first-harmonic detection and two pairs of counterpropagating 657 nm beams. The averaging time on the lock-in amplifier is 300 ms (and the scan time across the central discriminator is 2 s ).

Fig. 7
Fig. 7

(a) Schematic of the Ca clock versus cryogenic microwave sapphire oscillator (CSO) comparison. PD, photodetector; f R , repetition rate; MSF, microstructured fiber; BS, beam splitter (fiber). The CSO, with a carrier frequency of 11.2 GHz , is the input of a synthesis chain that produces a low-noise 10.0 GHz signal. The tenth harmonic of f R ( = 9.96 GHz ) , generated by a high-speed photodetector, is phase-locked to this signal. A commercial synthesizer is used to bridge the 40 MHz frequency difference. Reprinted with permission from [25]. Copyright 2009, American Institute of Physics

Fig. 8
Fig. 8

Fractional frequency instability measurements. (a) Filled circles, Ca optical frequency reference versus a hydrogen maser. Diamonds, Ca reference versus a cryogenic sapphire oscillator. Asterisks, the SR Λ V predicted when the Ca reference is limited by 423 nm light shot-noise. (b) The SR Λ V at 1 s measured for a range of atom flow rates ( N at ̱ det ) , as detected by the fluorescence levels on the photomultiplier tube. Each Λ deviation is produced from time traces of more than 500 s . Traces (i) and (iii) reprinted with permission from [25]. Copyright 2009, American Institute of Physics

Fig. 9
Fig. 9

Time trace of the frequency of the beat signal produced by heterodyning the Ca atom stabilized 657 nm laser and the neighboring tooth of a frequency comb stabilized by a microwave source referenced a hydrogen maser corresponding to trace (ii) in the above SR Λ V plot.

Fig. 10
Fig. 10

Ramsey–Bordé fringes generated through third-harmonic detection with the readout laser angled at 73° with respect to the atom beam (compared to 90° previously).

Equations (8)

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Q i z = 2 r l v ¯ 3 ( P k B T ) ( a b d 2 ) ,
N ph ̱ det = V fl K ν 423 h ,
γ P = γ 2 ( I 423 I S ) ( 1 + I 423 I S ) ,
N at ̱ det = v ¯ V fl K ν 423 h η ω b γ P .
F ( v , v o ) = v 2 e ( v v o ) 2 e ( v o v ) ,
σ ( τ ) = Δ ν π ν 0 1 τ [ ( N at + N eph N at ) 2 + 1 η N at n ph ] 1 2 .
σ ( τ ) = Δ ν π ν 0 1 τ N eph N at .
Δ v = c Δ ν ν 0 cos θ ,

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