Abstract

We demonstrate that optical pumping plays a significant role in determining the noise in certain types of laser-pumped vapor-cell microwave frequency standards by changing the way in which the laser’s FM noise is converted to AM noise by the optical-absorption profile. When this FM–AM conversion is the dominant noise source, the noise spectrum of the transmitted intensity can be dramatically altered by the optical-pumping process. FM noise at Fourier frequencies larger than the optical-pumping time is converted to AM noise differently from noise at lower Fourier frequencies. This effect can modify the optimum design of vapor-cell frequency references and adds an additional FM–AM-related noise source that cannot be eliminated with laser tuning.

© 2001 Optical Society of America

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References

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  1. A. Kastler, “Quelques suggestions concernant la production optique et la detection optique d’une inegalite de population des niveaux de quantification spatiale des atomes. Application a l’experiance de Stern et Gerlach et a la resonance magnetique,” J. Phys. Radium 11, 255–265 (1950).
    [CrossRef]
  2. W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972).
    [CrossRef]
  3. J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Adam Hilger, Bristol, UK, 1989).
  4. J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Frequency-dependent optical pumping effects in driven, three-level systems,” Opt. Lett. (to be published).
  5. A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
    [CrossRef]
  6. P. R. Hemmer, M. S. Shahriar, H. Lamela-Rivera, S. P. Smith, B. E. Bernacki, and S. Ezekiel, “Semiconductor laser excitation of Ramsey fringes by using a Raman transition in a cesium atomic beam,” J. Opt. Soc. Am. B 10, 1326–1329 (1993).
    [CrossRef]
  7. N. Cyr, M. Te⁁tu, and M. Breton, “All-optical microwave frequency standard: a proposal,” IEEE Trans. Instrum. Meas. 42, 640–649 (1993).
    [CrossRef]
  8. J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
    [CrossRef]
  9. G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
    [CrossRef]
  10. E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento 17, 333–338 (1976).
    [CrossRef]
  11. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257 (1996).
    [CrossRef]
  12. T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
    [CrossRef] [PubMed]
  13. Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
    [CrossRef] [PubMed]
  14. R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067–5077 (1994).
    [CrossRef] [PubMed]
  15. B. J. Dalton and P. L. Knight, “The effects of laser field fluctuations on coherent population trapping,” J. Phys. B 15, 3997–4015 (1982).
    [CrossRef]
  16. H. G. Robinson, V. V. Vasiliev, V. L. Velichansky, L. Hollberg, and A. S. Zibrov, “Diode laser noise conversion and reduction in atomic vapor,” presented at the International Conference on Atomic Physics, Boulder, Colo., July 31–Aug. 5, 1994.
  17. M. Bahoura, “Influence du bruit de phase d’une diode laser sur les performances ultimes de son asser vissement en frequence sur une resonance optique,” Ph.D. dissertation (University of Paris XI, Paris, 1998).
  18. J. C. Camparo, “Conversion of laser phase noise to amplitude noise in an optically thick vapor,” J. Opt. Soc. Am. B 15, 1177–1186 (1998).
    [CrossRef]
  19. J. C. Camparo and J. G. Coffer, “Conversion of laser phase noise to amplitude noise in a resonant atomic vapor: the role of laser linewidth,” Phys. Rev. A 59, 728–735 (1999).
    [CrossRef]
  20. J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
    [CrossRef]
  21. S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B (to be published).
  22. C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
    [CrossRef]
  23. M. Arditi and J.-L. Picque, “Precision measurement of light shifts induced by a narrow band GaAs laser in the 0–0 133Cs hyperfine transition,” J. Phys. B 8, L331–L335 (1975).
    [CrossRef]
  24. J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
    [CrossRef]
  25. A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
    [CrossRef]

2000 (2)

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

1999 (2)

J. C. Camparo and J. G. Coffer, “Conversion of laser phase noise to amplitude noise in a resonant atomic vapor: the role of laser linewidth,” Phys. Rev. A 59, 728–735 (1999).
[CrossRef]

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

1998 (2)

J. C. Camparo, “Conversion of laser phase noise to amplitude noise in an optically thick vapor,” J. Opt. Soc. Am. B 15, 1177–1186 (1998).
[CrossRef]

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
[CrossRef]

1996 (1)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257 (1996).
[CrossRef]

1994 (1)

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067–5077 (1994).
[CrossRef] [PubMed]

1993 (2)

1991 (2)

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef] [PubMed]

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
[CrossRef]

1988 (1)

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

1983 (1)

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[CrossRef]

1982 (1)

B. J. Dalton and P. L. Knight, “The effects of laser field fluctuations on coherent population trapping,” J. Phys. B 15, 3997–4015 (1982).
[CrossRef]

1976 (2)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento 17, 333–338 (1976).
[CrossRef]

1975 (1)

M. Arditi and J.-L. Picque, “Precision measurement of light shifts induced by a narrow band GaAs laser in the 0–0 133Cs hyperfine transition,” J. Phys. B 8, L331–L335 (1975).
[CrossRef]

1972 (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972).
[CrossRef]

1950 (1)

A. Kastler, “Quelques suggestions concernant la production optique et la detection optique d’une inegalite de population des niveaux de quantification spatiale des atomes. Application a l’experiance de Stern et Gerlach et a la resonance magnetique,” J. Phys. Radium 11, 255–265 (1950).
[CrossRef]

Affolderbach, C.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Akulshin, A. M.

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
[CrossRef]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

Arditi, M.

M. Arditi and J.-L. Picque, “Precision measurement of light shifts induced by a narrow band GaAs laser in the 0–0 133Cs hyperfine transition,” J. Phys. B 8, L331–L335 (1975).
[CrossRef]

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257 (1996).
[CrossRef]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento 17, 333–338 (1976).
[CrossRef]

Bernacki, B. E.

Brandt, S.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

Breton, M.

N. Cyr, M. Te⁁tu, and M. Breton, “All-optical microwave frequency standard: a proposal,” IEEE Trans. Instrum. Meas. 42, 640–649 (1993).
[CrossRef]

Camparo, J. C.

J. C. Camparo and J. G. Coffer, “Conversion of laser phase noise to amplitude noise in a resonant atomic vapor: the role of laser linewidth,” Phys. Rev. A 59, 728–735 (1999).
[CrossRef]

J. C. Camparo, “Conversion of laser phase noise to amplitude noise in an optically thick vapor,” J. Opt. Soc. Am. B 15, 1177–1186 (1998).
[CrossRef]

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[CrossRef]

Celikov, A. A.

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
[CrossRef]

Coffer, J. G.

J. C. Camparo and J. G. Coffer, “Conversion of laser phase noise to amplitude noise in a resonant atomic vapor: the role of laser linewidth,” Phys. Rev. A 59, 728–735 (1999).
[CrossRef]

Cooper, J.

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

Cyr, N.

N. Cyr, M. Te⁁tu, and M. Breton, “All-optical microwave frequency standard: a proposal,” IEEE Trans. Instrum. Meas. 42, 640–649 (1993).
[CrossRef]

Dalton, B. J.

B. J. Dalton and P. L. Knight, “The effects of laser field fluctuations on coherent population trapping,” J. Phys. B 15, 3997–4015 (1982).
[CrossRef]

Ezekiel, S.

Frueholz, R. P.

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[CrossRef]

Godone, A.

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

Happer, W.

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972).
[CrossRef]

Haslwanter, Th.

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

Hemmer, P. R.

Hollberg, L.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Jung, C.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Kastler, A.

A. Kastler, “Quelques suggestions concernant la production optique et la detection optique d’une inegalite de population des niveaux de quantification spatiale des atomes. Application a l’experiance de Stern et Gerlach et a la resonance magnetique,” J. Phys. Radium 11, 255–265 (1950).
[CrossRef]

Kitching, J.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Knappe, S.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Knight, P. L.

B. J. Dalton and P. L. Knight, “The effects of laser field fluctuations on coherent population trapping,” J. Phys. B 15, 3997–4015 (1982).
[CrossRef]

Lamela-Rivera, H.

Levi, F.

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
[CrossRef]

Meschede, D.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

Mitsui, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef] [PubMed]

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

Nagel, A.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento 17, 333–338 (1976).
[CrossRef]

Picque, J.-L.

M. Arditi and J.-L. Picque, “Precision measurement of light shifts induced by a narrow band GaAs laser in the 0–0 133Cs hyperfine transition,” J. Phys. B 8, L331–L335 (1975).
[CrossRef]

Ritsch, H.

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

Shahriar, M. S.

Smith, S. P.

Tanaka, U.

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef] [PubMed]

Te?tu, M.

N. Cyr, M. Te⁁tu, and M. Breton, “All-optical microwave frequency standard: a proposal,” IEEE Trans. Instrum. Meas. 42, 640–649 (1993).
[CrossRef]

Vanier, J.

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
[CrossRef]

Velichansky, V. L.

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
[CrossRef]

Volk, C. H.

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[CrossRef]

Vukicevic, N.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Walser, R.

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067–5077 (1994).
[CrossRef] [PubMed]

Weidemann, W.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Wiedenmann, D.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Wynands, R.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

Yabuzaki, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef] [PubMed]

Zoller, P.

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067–5077 (1994).
[CrossRef] [PubMed]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

Appl. Phys. B (1)

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Non-linear spectroscopy using a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Europhys. Lett. (1)

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, “Light shift of coherent population trapping resonances,” Europhys. Lett. 48, 385–389 (1999).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on dark-line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

N. Cyr, M. Te⁁tu, and M. Breton, “All-optical microwave frequency standard: a proposal,” IEEE Trans. Instrum. Meas. 42, 640–649 (1993).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (2)

M. Arditi and J.-L. Picque, “Precision measurement of light shifts induced by a narrow band GaAs laser in the 0–0 133Cs hyperfine transition,” J. Phys. B 8, L331–L335 (1975).
[CrossRef]

B. J. Dalton and P. L. Knight, “The effects of laser field fluctuations on coherent population trapping,” J. Phys. B 15, 3997–4015 (1982).
[CrossRef]

J. Phys. Radium (1)

A. Kastler, “Quelques suggestions concernant la production optique et la detection optique d’une inegalite de population des niveaux de quantification spatiale des atomes. Application a l’experiance de Stern et Gerlach et a la resonance magnetique,” J. Phys. Radium 11, 255–265 (1950).
[CrossRef]

Lett. Nuovo Cimento (1)

E. Arimondo and G. Orriols, “Nonabsorbing atomic coherences by coherent two-photon transitions in a three-level optical pumping,” Lett. Nuovo Cimento 17, 333–338 (1976).
[CrossRef]

Nuovo Cimento B (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

Opt. Commun. (1)

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Subnatural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
[CrossRef]

Phys. Rev. A (5)

J. Vanier, A. Godone, and F. Levi, “Coherent population trapping in cesium: dark lines and coherent microwave emission,” Phys. Rev. A 58, 2345–2358 (1998).
[CrossRef]

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38, 5652–5659 (1988).
[CrossRef] [PubMed]

R. Walser and P. Zoller, “Laser-noise-induced polarization fluctuations as a spectroscopic tool,” Phys. Rev. A 49, 5067–5077 (1994).
[CrossRef] [PubMed]

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[CrossRef]

J. C. Camparo and J. G. Coffer, “Conversion of laser phase noise to amplitude noise in a resonant atomic vapor: the role of laser linewidth,” Phys. Rev. A 59, 728–735 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

T. Yabuzaki, T. Mitsui, and U. Tanaka, “New type of high-resolution spectroscopy with a diode laser,” Phys. Rev. Lett. 67, 2453–2456 (1991).
[CrossRef] [PubMed]

Prog. Opt. (1)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972).
[CrossRef]

Other (5)

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Adam Hilger, Bristol, UK, 1989).

J. Kitching, L. Hollberg, S. Knappe, and R. Wynands, “Frequency-dependent optical pumping effects in driven, three-level systems,” Opt. Lett. (to be published).

H. G. Robinson, V. V. Vasiliev, V. L. Velichansky, L. Hollberg, and A. S. Zibrov, “Diode laser noise conversion and reduction in atomic vapor,” presented at the International Conference on Atomic Physics, Boulder, Colo., July 31–Aug. 5, 1994.

M. Bahoura, “Influence du bruit de phase d’une diode laser sur les performances ultimes de son asser vissement en frequence sur une resonance optique,” Ph.D. dissertation (University of Paris XI, Paris, 1998).

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, “Characterization of coherent population trapping resonances as atomic frequency references,” J. Opt. Soc. Am. B (to be published).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup. The inset shows the tunings of the relevant laser fields with respect to the atomic energy levels.

Fig. 2
Fig. 2

Tuning of the laser with respect to the atomic transitions. The first-order sidebands on the optical field are resonant with the two atomic transitions from the F=3 and F=4 ground states.

Fig. 3
Fig. 3

Fraction of total optical power transmitted through the cell as the RF-modulated laser is scanned over the Cs D2 line. The largest peak occurs when the two first-order laser sidebands are resonant with the two hyperfine absorption lines, as in Fig. 2. The remaining peaks occur when the carrier or higher-order sidebands are resonant.

Fig. 4
Fig. 4

(a) Laser FM noise spectrum measured by use of an etalon fringe. (b) Comparison of the AM noise measured at the output of the Cs cell with the laser detuned by -217 MHz from the peak of the dc atomic absorption line (trace A) with the projected AM noise calculated from the laser FM noise spectrum and the slope of the atomic absorption line (trace B). (c) AM noise at the cell output with the laser detuned by -217 MHz (trace A), -9.5 MHz (trace B), and +17 MHz (trace C). The noise floor (trace D), determined by the intrinsic AM noise of the laser and measured with the laser tuned away from the absorption lines, is also shown. Strong peaks related to the 60-Hz line frequency have been removed from all spectra for clarity of presentation.

Fig. 5
Fig. 5

Noise at the detector output at 530 Hz, normalized to the dc level, measured as a function of the detuning of the laser from the peak of the dc optical-absorption spectrum. The points are the experimental data, and the solid curve is the prediction of the linear FM–AM conversion model. The 40-MHz shift of the noise minimum from the line peak can be explained with the optical-pumping process.

Fig. 6
Fig. 6

Theoretical model including optical pumping and excited-state hyperfine structure.

Fig. 7
Fig. 7

Detunings from the optical-absorption line at which the data in Fig. 4(c) were taken. At detuning A the high-frequency noise slope is larger than the slope of the low-frequency noise. At detuning B the high-frequency slope is near zero, and the low-frequency slope is nonzero but small. At detuning C the low-frequency slope is near zero but the high-frequency slope is nonzero.

Fig. 8
Fig. 8

(a) Optical frequency difference between the FM–AM conversion minima ωdiff=ωδSmin(2πf1)-ωδ Smin(2πf2) and (b) minimum FM–AM conversion at frequency f2, normalized to the light intensity, as a function of modulation frequency f2. The average optical intensity in each of the first-order sidebands was 170 µW/cm2 (circles), 47 µW/cm2 (triangles), and 15 µW/cm2 (squares). The solid curves are fits to Eq. (16) with ωdiffmax=69.4 MHz and ϕc=2.6 Hz/(µW/cm2).

Equations (18)

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N˙1=-R1(ω)(N1-N3)+γ2N3-(N1-N2)-(N1(0)-N2(0))2τ,
N˙2=-R2(ω)(N2-N3)+γ2N3-(N2-N1)-(N2(0)-N1(0))2τ,
N˙3=R1(ω)(N1-N3)+R2(ω)(N2-N3)-γN3.
S=2τ (β1N1(0)+β2N2(0))+2β1β21+β1+β2,
δS˜(Ω)=2τ β2+N1(0)1+β1+β2 1+iΩτ+2β21+iΩτ+β1+β2δβ˜1(Ω)+β1+N2(0)1+β2+β1 1+iΩτ+2β11+iΩτ+β2+β1δβ˜2(Ω).
α1,2(ω)=α0 Γ2(ω±Δ)2+Γ2,
I1,2(ω)=I10,20ω1,2(ω)L{1-exp[-α1,2(ω)L]}I10,201-α1,2(ω)L2,
β1,2(ω)=R1,2(ω) τ2=γ2 I1,2Isat τ2 Γ2(ω±Δ)2+Γ2
=γτ4 I10,20Isat 1-α0L2×Γ2(ω±Δ)2+Γ2×Γ2(ω±Δ)2+Γ2,
δβ1,2=γτ2 I10,20Isat(1-α0L) ω±ΔΓ2δω,
δS˜(Ω)=-2γΓ2(1-α0L) I10 I20(I10+I20)Isat×ω-β10-β20(β10+β20+iΩτ)Δδω˜
=-2γΓ2(1-α0L) I10 I20(I10+I20)Isat×ω-β102-β202(β10+β20)2+(Ωτ)2Δ+i Ωτ(β10-β20)(β10+β20)2+(Ωτ)2Δδω˜.
ωδSmin(Ω)=β102-β202Ω2τ2+(β10+β20)2Δ.
SδP(Ω)
=2ΔΓ22(α0L)2P02Ωτ(β10-β20)(β10+β20)2+(Ωτ)22Sδω(Ω),
ωdiff(max)=β10-β20β10+β20Δ.
ωdiff(f)=ωdiff(max)1+fϕcIopt2,
Rf2(2πf)=Mmax fϕcIopt1+fϕcIopt2,

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