Abstract

We have developed a technique to measure the absolute frequencies of optical transitions by using an evacuated Rb-stabilized ring-cavity resonator as a transfer cavity. The absolute frequency of the Rb D2 line (at 780 nm) used to stabilize the cavity is known and allows us to determine the absolute value of the unknown frequency. We study wavelength-dependent errors due to dispersion at the cavity mirrors by measuring the frequency of the same transition in the Cs D2 line (at 852 nm) at three cavity lengths. The spread in the values shows that dispersion errors are below 30 kHz, corresponding to a relative precision of 1010. We give an explanation for reduced dispersion errors in the ring-cavity geometry by calculating errors due to the lateral shift and the phase shift at the mirrors, and show that they are roughly equal but occur with opposite signs. We have earlier shown that diffraction errors (due to Guoy phase) are negligible in the ring-cavity geometry compared to a linear cavity; the reduced dispersion error is another advantage. Our values are consistent with measurements of the same transition using the more expensive frequency-comb technique. Our simpler method is ideally suited for measuring hyperfine structure, fine structure, and isotope shifts, up to several hundreds of gigahertz.

© 2012 Optical Society of America

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References

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  1. J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
    [CrossRef]
  2. T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006), and the references therein.
    [CrossRef]
  3. T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
    [CrossRef]
  4. J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
    [CrossRef]
  5. A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator,” Opt. Lett. 28, 1579–1581 (2003).
    [CrossRef]
  6. A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
    [CrossRef]
  7. D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
    [CrossRef]
  8. J. Ye, S. Swartz, P. Jungner, and J. L. Hall, “Hyperfine structure and absolute frequency of the Rb875P3/2 state,” Opt. Lett. 21, 1280–1282 (1996).
    [CrossRef]
  9. A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
    [CrossRef]
  10. D. Das and V. Natarajan, “Absolute frequency measurement of the lithium D lines: precise determination of isotope shifts and fine-structure intervals,” Phys. Rev. A 75, 052508(2007).
    [CrossRef]
  11. K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
    [CrossRef]
  12. A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
    [CrossRef]
  13. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef]
  14. E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
    [CrossRef]
  15. T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
    [CrossRef]
  16. R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179–189 (1989).
    [CrossRef]
  17. G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
    [CrossRef]
  18. A. K. Singh and V. Natarajan, “Observation of the nuclear magnetic octupole moment of Yb173 from precise measurements of hyperfine structure in the P32 state,” arXiv:1206.1663v1 [physics.atom-ph] (2012).

2012 (1)

A. K. Singh and V. Natarajan, “Observation of the nuclear magnetic octupole moment of Yb173 from precise measurements of hyperfine structure in the P32 state,” arXiv:1206.1663v1 [physics.atom-ph] (2012).

2009 (1)

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

2007 (1)

D. Das and V. Natarajan, “Absolute frequency measurement of the lithium D lines: precise determination of isotope shifts and fine-structure intervals,” Phys. Rev. A 75, 052508(2007).
[CrossRef]

2006 (4)

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006), and the references therein.
[CrossRef]

2004 (1)

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
[CrossRef]

2003 (2)

A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator,” Opt. Lett. 28, 1579–1581 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

2001 (1)

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

2000 (1)

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

1996 (1)

1990 (1)

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

1989 (1)

R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179–189 (1989).
[CrossRef]

1977 (1)

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

1974 (1)

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

1966 (1)

Allegrini, M.

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

Arimondo, E.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Banerjee, A.

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator,” Opt. Lett. 28, 1579–1581 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

Barthwal, S.

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

Biraben, F.

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

Curry, S. M.

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Das, D.

D. Das and V. Natarajan, “Absolute frequency measurement of the lithium D lines: precise determination of isotope shifts and fine-structure intervals,” Phys. Rev. A 75, 052508(2007).
[CrossRef]

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator,” Opt. Lett. 28, 1579–1581 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

Garreau, J. C.

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

Grimm, R.

R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179–189 (1989).
[CrossRef]

Hall, J. L.

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[CrossRef]

J. Ye, S. Swartz, P. Jungner, and J. L. Hall, “Hyperfine structure and absolute frequency of the Rb875P3/2 state,” Opt. Lett. 21, 1280–1282 (1996).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006), and the references therein.
[CrossRef]

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Inguscio, M.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Julien, L.

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

Jungner, P.

Kogelnik, H.

Kourogi, M.

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

Krishna, A.

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

Kumar, P. V. K.

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

Lee, S. A.

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Li, T.

Ming, H.

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

Mlynek, J.

R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179–189 (1989).
[CrossRef]

Natarajan, V.

A. K. Singh and V. Natarajan, “Observation of the nuclear magnetic octupole moment of Yb173 from precise measurements of hyperfine structure in the P32 state,” arXiv:1206.1663v1 [physics.atom-ph] (2012).

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

D. Das and V. Natarajan, “Absolute frequency measurement of the lithium D lines: precise determination of isotope shifts and fine-structure intervals,” Phys. Rev. A 75, 052508(2007).
[CrossRef]

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
[CrossRef]

A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator,” Opt. Lett. 28, 1579–1581 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

Nayfeh, M. H.

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Noble, G. A.

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

Pandey, K.

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

Rapol, U. D.

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

Reichert, J.

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

Schultz, B. E.

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

Shahin, I. S.

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Singh, A. K.

A. K. Singh and V. Natarajan, “Observation of the nuclear magnetic octupole moment of Yb173 from precise measurements of hyperfine structure in the P32 state,” arXiv:1206.1663v1 [physics.atom-ph] (2012).

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

Suryanarayana, M. V.

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

Swartz, S.

Udem, T.

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

van Wijngaarden, W. A.

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

Violino, P.

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Wasan, A.

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

Ye, J.

Appl. Opt. (1)

Appl. Phys. B (1)

R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179–189 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

A. Banerjee, U. D. Rapol, A. Wasan, and V. Natarajan, “High-accuracy wavemeter based on a stabilized diode laser,” Appl. Phys. Lett. 79, 2139–2141 (2001).
[CrossRef]

Eur. Phys. J. D (1)

D. Das, A. Banerjee, S. Barthwal, and V. Natarajan, “A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in Cs133,” Eur. Phys. J. D 38, 545–552 (2006).
[CrossRef]

Europhys. Lett. (2)

A. Banerjee, D. Das, and V. Natarajan, “Absolute frequency measurements of the D1 lines in K39, Rb85, and Rb87 with ∼0.1  ppb uncertainty,” Europhys. Lett. 65, 172–178 (2004).
[CrossRef]

A. Banerjee, U. D. Rapol, D. Das, A. Krishna, and V. Natarajan, “Precise measurements of UV atomic lines: Hhyperfine structure and isotope shifts in the 398.8 nm line of Yb,” Europhys. Lett. 63, 340–346 (2003).
[CrossRef]

J. Phys. (1)

J. C. Garreau, M. Allegrini, L. Julien, and F. Biraben, “High resolution spectroscopy of the hydrogen atom—III. Wavelength comparison and Rydberg constant determination,” J. Phys. 51, 2293–2306 (1990).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

T. Udem, J. Reichert, T. W. Hänsch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A 62, 031801 (2000).
[CrossRef]

G. A. Noble, B. E. Schultz, H. Ming, and W. A. van Wijngaarden, “Isotope shifts and fine structures of Li6,7 D lines and determination of the relative nuclear charge radius,” Phys. Rev. A 74, 012502 (2006).
[CrossRef]

D. Das and V. Natarajan, “Absolute frequency measurement of the lithium D lines: precise determination of isotope shifts and fine-structure intervals,” Phys. Rev. A 75, 052508(2007).
[CrossRef]

K. Pandey, A. K. Singh, P. V. K. Kumar, M. V. Suryanarayana, and V. Natarajan, “Isotope shifts and hyperfine structure in the 555.8 nm S10→P31 line of Yb,” Phys. Rev. A 80, 022518(2009).
[CrossRef]

Phys. Rev. Lett. (1)

T. W. Hänsch, M. H. Nayfeh, S. A. Lee, S. M. Curry, and I. S. Shahin, “Precision measurement of the Rydberg constant by laser saturation spectroscopy of the Balmer α line in hydrogen and deuterium,” Phys. Rev. Lett. 32, 1336–1340(1974).
[CrossRef]

Rev. Mod. Phys. (3)

J. L. Hall, “Nobel lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006), and the references therein.
[CrossRef]

E. Arimondo, M. Inguscio, and P. Violino, “Experimental determinations of the hyperfine structures in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Other (1)

A. K. Singh and V. Natarajan, “Observation of the nuclear magnetic octupole moment of Yb173 from precise measurements of hyperfine structure in the P32 state,” arXiv:1206.1663v1 [physics.atom-ph] (2012).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the experiment. Figure key: λ / 2 , halfwave retardation plate; PBS, polarizing beam splitter; AOM, acousto-optic modulator; M, mirror; PD, photodiode; PZT, piezoelectric transducer.

Fig. 2.
Fig. 2.

Measured frequencies of the 4 3 transition versus the cavity length. The solid circles are measurements with an F = 1 F transition, and the open circles are with an F = 2 F transition. The line represents the weighted average yielding a value of 241(12) kHz.

Fig. 3.
Fig. 3.

Calculated reflectance and phase shift versus frequency at a multilayer dielectric mirror, for both TE and TM polarizations. The ends of the graph correspond to 852 nm and 780 nm, respectively.

Fig. 4.
Fig. 4.

(a) Lateral shift between the incident ray and the reflected ray after reflection from one set of layers at a multilayer dielectric mirror. (b) The free-space length traversed inside the ring cavity depends on the amount of shift, and is smaller for the ray that experiences the larger shift (red compared to blue).

Fig. 5.
Fig. 5.

Calculated deviation in lateral shift as a function of frequency (for TE polarization).

Fig. 6.
Fig. 6.

(a) Multilayer dielectric mirror structure with m dielectric layers. (b) and (c) Vectors E , H , and k for TE z and TM z forward wave propagation in layer j .

Tables (3)

Tables Icon

Table 1. Transition Frequencies Measured at Three Cavity Lengthsa

Tables Icon

Table 3. Comparison to Previous Frequency-Comb Measurementsa

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

L = n λ ,
ν unk ν ref + ν AOM = n unk n ref .
2 n π = 2 π λ L + ϕ .
ν ( L ) = ν 0 + c ϕ 2 π L ,
n ( λ ) = A + B λ 2 + ,
2 n π = 2 π ν c L + A ν = 2 π c ( L + A c ) ν .
k j = n j k 0 ,
k z , j = k j cos θ j = n j k 0 cos θ j .
n j sin θ j = n 0 sin θ 0 .
Z j , TE = η 0 n cos θ j and Z j , TM = η 0 cos θ j n ,

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