Abstract

We present analytic solutions for saturated absorption spectra. The analytic forms of all the ground- and excited-state populations were obtained, and the absorption of a counterpropagating probe beam was calculated by solving the rate equations in the presence of a pump laser beam. The analytic solutions were compared with the numerical, experimental results, and Nakayama’s model and good agreement was found between them. We found that the analytic theory could provide accurate spectra at an arbitrary pump beam intensity and diameter.

© 2008 Optical Society of America

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  1. W. Demtröder, Laser Spectroscopy (Springer, 1998).
  2. M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, 1988).
  3. K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
    [CrossRef]
  4. P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
    [CrossRef]
  5. H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
    [CrossRef]
  6. R. Grimm and J. Mlynek, “The effect of resonant light pressure in saturation spectroscopy,” Appl. Phys. B 49, 179-189 (1989).
    [CrossRef]
  7. O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
    [CrossRef]
  8. H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).
  9. K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
    [CrossRef]
  10. A. Banerjee and V. Natarajan, “Saturated-absorption spectroscopy: eliminating crossover resonances by use of copropagating beams,” Opt. Lett. 28, 1912-1914 (2003).
    [CrossRef] [PubMed]
  11. S. Nakayama, “Theoretical analysis of Rb and Cs D2 lines in Doppler-free spectrosopic techniques with optical pumping,” Jpn. J. Appl. Phys., Part 1 24, 1-7 (1985).
    [CrossRef]
  12. S. Nakayama, “Optical pumping effects in high resolution laser spectroscopy,” Phys. Scr. T70, 64-74 (1997).
    [CrossRef]
  13. L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
    [CrossRef]
  14. D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631-637 (2004).
    [CrossRef]
  15. M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
    [CrossRef]
  16. W. Gawlik, “Nonstationary effects in velocity-selective optical pumping,” Phys. Rev. A 34, 3760-3769 (1986).
    [CrossRef] [PubMed]
  17. R. Grimm and J. Mlynek, “Light-pressure-induced nonlinear dispersion in a Doppler-broadened medium: theory and experimental proposal,” J. Opt. Soc. Am. B 5, 1655-1660 (1988).
    [CrossRef]
  18. R. Grimm and J. Mlynek, “Light-pressure-induced line-shape asymmetry of the saturation dip in an atomic gas,” Phys. Rev. Lett. 63, 232-235 (1989).
    [CrossRef] [PubMed]
  19. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Basic Processes and Applications (Wiley, 1992).
  20. P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
    [CrossRef]
  21. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1960).
  22. G. Moon and H. R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294-298 (2008).
    [CrossRef]
  23. G. Moon and H. R. Noh, “Theoretical calculation of the saturated absorption spectrum for a multilevel atom,” J. Korean Phys. Soc. 50, 1037-1043 (2007).
    [CrossRef]
  24. J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
    [CrossRef]

2008 (1)

G. Moon and H. R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294-298 (2008).
[CrossRef]

2007 (1)

G. Moon and H. R. Noh, “Theoretical calculation of the saturated absorption spectrum for a multilevel atom,” J. Korean Phys. Soc. 50, 1037-1043 (2007).
[CrossRef]

2006 (2)

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

2004 (1)

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631-637 (2004).
[CrossRef]

2003 (1)

2001 (1)

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

1998 (1)

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

1997 (1)

S. Nakayama, “Optical pumping effects in high resolution laser spectroscopy,” Phys. Scr. T70, 64-74 (1997).
[CrossRef]

1996 (1)

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
[CrossRef]

1994 (1)

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

1992 (1)

K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
[CrossRef]

1989 (2)

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

R. Grimm and J. Mlynek, “Light-pressure-induced line-shape asymmetry of the saturation dip in an atomic gas,” Phys. Rev. Lett. 63, 232-235 (1989).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

W. Gawlik, “Nonstationary effects in velocity-selective optical pumping,” Phys. Rev. A 34, 3760-3769 (1986).
[CrossRef] [PubMed]

1985 (1)

S. Nakayama, “Theoretical analysis of Rb and Cs D2 lines in Doppler-free spectrosopic techniques with optical pumping,” Jpn. J. Appl. Phys., Part 1 24, 1-7 (1985).
[CrossRef]

1980 (2)

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

Adams, C. S.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Banerjee, A.

Burns, M. M.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Basic Processes and Applications (Wiley, 1992).

Cornish, S. L.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Demtröder, W.

W. Demtröder, Laser Spectroscopy (Springer, 1998).

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Basic Processes and Applications (Wiley, 1992).

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1960).

Feld, M. S.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Gawlik, W.

W. Gawlik, “Nonstationary effects in velocity-selective optical pumping,” Phys. Rev. A 34, 3760-3769 (1986).
[CrossRef] [PubMed]

Grimm, R.

R. Grimm and J. Mlynek, “Light-pressure-induced line-shape asymmetry of the saturation dip in an atomic gas,” Phys. Rev. Lett. 63, 232-235 (1989).
[CrossRef] [PubMed]

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

R. Grimm and J. Mlynek, “Light-pressure-induced nonlinear dispersion in a Doppler-broadened medium: theory and experimental proposal,” J. Opt. Soc. Am. B 5, 1655-1660 (1988).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Basic Processes and Applications (Wiley, 1992).

Harris, M. L.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Hinshelwood, D. D.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Huennekens, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
[CrossRef]

Hughes, I. G.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631-637 (2004).
[CrossRef]

Huhle, T.

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

Im, K. B.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Jung, H. Y.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Kano, S. S.

M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, 1988).

Kim, P. S.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Knaak, K. M.

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

Lee, H. S.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Levenson, M. D.

M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, 1988).

MacAdam, K. B.

K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
[CrossRef]

Maguire, L. P.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

Matthias, E.

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

McLeod, I. C.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Meschede, D.

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

Mese, E.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

Meystre, P.

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[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]

R. Grimm and J. Mlynek, “Light-pressure-induced line-shape asymmetry of the saturation dip in an atomic gas,” Phys. Rev. Lett. 63, 232-235 (1989).
[CrossRef] [PubMed]

R. Grimm and J. Mlynek, “Light-pressure-induced nonlinear dispersion in a Doppler-broadened medium: theory and experimental proposal,” J. Opt. Soc. Am. B 5, 1655-1660 (1988).
[CrossRef]

Moon, G.

G. Moon and H. R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294-298 (2008).
[CrossRef]

G. Moon and H. R. Noh, “Theoretical calculation of the saturated absorption spectrum for a multilevel atom,” J. Korean Phys. Soc. 50, 1037-1043 (2007).
[CrossRef]

Murnick, D. E.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Nakayama, S.

S. Nakayama, “Optical pumping effects in high resolution laser spectroscopy,” Phys. Scr. T70, 64-74 (1997).
[CrossRef]

S. Nakayama, “Theoretical analysis of Rb and Cs D2 lines in Doppler-free spectrosopic techniques with optical pumping,” Jpn. J. Appl. Phys., Part 1 24, 1-7 (1985).
[CrossRef]

Namiotka, R. K.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
[CrossRef]

Natarajan, V.

Noh, H. R.

G. Moon and H. R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294-298 (2008).
[CrossRef]

G. Moon and H. R. Noh, “Theoretical calculation of the saturated absorption spectrum for a multilevel atom,” J. Korean Phys. Soc. 50, 1037-1043 (2007).
[CrossRef]

Oh, C. H.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Pappas, P. G.

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Rinneberg, H.

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

Sagle, J.

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
[CrossRef]

Sargent, M.

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[CrossRef]

Schmidt, O.

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

Scholten, R. E.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

Smith, D. A.

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631-637 (2004).
[CrossRef]

Song, S. H.

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

Steinbach, A.

K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
[CrossRef]

Tarleton, E.

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

Timmermann, A.

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

van Bijnen, R. M. W.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

Wieman, C. E.

K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
[CrossRef]

Wynands, R.

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

Am. J. Phys. (2)

K. B. MacAdam, A. Steinbach, and C. E. Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098-1111 (1992).
[CrossRef]

D. A. Smith and I. G. Hughes, “The role of hyperfine pumping in multilevel systems exhibiting saturated absorption,” Am. J. Phys. 72, 631-637 (2004).
[CrossRef]

Appl. Phys. B (2)

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

O. Schmidt, K. M. Knaak, R. Wynands, and D. Meschede, “Cesium saturation spectroscopy revisited: how to reverse peaks and observe narrow resonances,” Appl. Phys. B 59, 167-178 (1994).
[CrossRef]

J. Korean Phys. Soc. (2)

H. Y. Jung, K. B. Im, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Dependence of the saturated absorption signals of the Cs D2 line on the external magnetic field,” J. Korean Phys. Soc. 33, 277-280 (1998).

G. Moon and H. R. Noh, “Theoretical calculation of the saturated absorption spectrum for a multilevel atom,” J. Korean Phys. Soc. 50, 1037-1043 (2007).
[CrossRef]

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

J. Phys. B (2)

J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B 29, 2629-2643 (1996).
[CrossRef]

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. E. Scholten, “Theoretical calculation of saturated absorption spectra for multi-level atoms,” J. Phys. B 39, 2709-2720 (2006).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

S. Nakayama, “Theoretical analysis of Rb and Cs D2 lines in Doppler-free spectrosopic techniques with optical pumping,” Jpn. J. Appl. Phys., Part 1 24, 1-7 (1985).
[CrossRef]

Opt. Commun. (1)

G. Moon and H. R. Noh, “Observation of nonstationary effects in saturation spectroscopy,” Opt. Commun. 281, 294-298 (2008).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

M. L. Harris, C. S. Adams, S. L. Cornish, I. C. McLeod, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006).
[CrossRef]

W. Gawlik, “Nonstationary effects in velocity-selective optical pumping,” Phys. Rev. A 34, 3760-3769 (1986).
[CrossRef] [PubMed]

K. B. Im, H. Y. Jung, C. H. Oh, S. H. Song, P. S. Kim, and H. S. Lee, “Saturated absorption signals for the Cs D2 line,” Phys. Rev. A 63, 034501 (2001).
[CrossRef]

P. G. Pappas, M. M. Burns, D. D. Hinshelwood, M. S. Feld, and D. E. Murnick, “Saturation spectroscopy with laser optical pumping in atomic barium,” Phys. Rev. A 21, 1955-1968 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

R. Grimm and J. Mlynek, “Light-pressure-induced line-shape asymmetry of the saturation dip in an atomic gas,” Phys. Rev. Lett. 63, 232-235 (1989).
[CrossRef] [PubMed]

Phys. Scr. (1)

S. Nakayama, “Optical pumping effects in high resolution laser spectroscopy,” Phys. Scr. T70, 64-74 (1997).
[CrossRef]

Z. Phys. A (1)

H. Rinneberg, T. Huhle, E. Matthias, and A. Timmermann, “Influence of atomic alignment on crossover signals in saturation spectroscopy,” Z. Phys. A 295, 17-25 (1980).
[CrossRef]

Other (5)

W. Demtröder, Laser Spectroscopy (Springer, 1998).

M. D. Levenson and S. S. Kano, Introduction to Nonlinear Laser Spectroscopy (Academic, 1988).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Basic Processes and Applications (Wiley, 1992).

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, 2007).
[CrossRef]

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, 1960).

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Figures (7)

Fig. 1
Fig. 1

(a) Hyperfine-energy-level diagram for the D 2 line of a Rb 87 atom. (b) Energy-level diagram for the transition F g = 1 F e = 2 .

Fig. 2
Fig. 2

Numerical and analytic populations (a) P 1 m ( m = 1 , 0 , 1 ) for F g = 1 F e = 0 , 1 , 2 and (b) P 2 m ( m = 2 , , 2 ) for F g = 2 F e = 1 , 2 , 3 , where v = 0 , Ω R = 0.32 Γ ( s 0 = 0.2 ) , and t = 12.6 μ s .

Fig. 3
Fig. 3

(a) Comparison of L 0 ( a , b ) with the numerical results [ L ( a , b ) ] . (b) Comparison of the peak value and the FWHM.

Fig. 4
Fig. 4

Experimental schematic. ECDL, external cavity diode laser; λ 2 , half-wave-plate; λ 4 , quarter-wave-plate; (P)BS, (polarizing) beam splitter; M, mirror; PD, photodiode; and GT, Glan Thompson polarizer.

Fig. 5
Fig. 5

Experimental, numerical, analytic, and Nakayama’s results for the SAS spectra at the transition F g = 1 F e = 0 , 1 , 2 when the pump-probe polarization configurations are (a) σ + σ + , (b) σ + σ , (c) π π , and (d) π π .

Fig. 6
Fig. 6

Experimental, numerical, analytic, and Nakayama’s results for the SAS spectra at the transition F g = 2 F e = 1 , 2 , 3 . The pump-probe polarization configurations are (a) σ + σ + , (b) σ + σ , (c) π π , and (d) π π .

Fig. 7
Fig. 7

Decomposition of the calculated SAS spectrum for the transition F g = 2 F e = 3 . The solid, dashed, dotted, and dashed-dotted curves denote the term for the sum, saturation, optical pumping, and light pressure, respectively.

Equations (67)

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d d t P F m = F e = F 1 F + 1 R F , m F e , m + q Γ s 0 2 P F m Q F e m + q 1 + 4 ( δ pu + Δ F e F + 1 ) 2 Γ 2 + F e = F 1 F + 1 m e = m 1 m + 1 Γ R F , m F e , m e Q F e m e ,
d d t P F m = F e = F 1 F + 1 m e = m 1 m + 1 Γ R F , m F e , m e Q F e m e ,
d d t Q F e m = R F , m q F e , m Γ s 0 2 P F m q Q F e m 1 + 4 ( δ pu + Δ F e F + 1 ) 2 Γ 2 F g = F , F m g = m 1 m + 1 Γ R F g , m g F e , m Q F e m ,
R F g , m g F e , m e = ( 2 L e + 1 ) ( 2 J e + 1 ) ( 2 J g + 1 ) ( 2 F e + 1 ) ( 2 F g + 1 ) × [ { L e J e S J g L g 1 } { J e F e I F g J g 1 } ( F g 1 F e m g m e m g m e ) ] 2 ,
T ( δ ) = exp [ α ( δ ) l ] ,
α ( δ ) = d v 3 λ 2 2 π n π u e ( v u ) 2 × F e = F 1 F + 1 m = F F R F , m F e , m + q ( P F m Q F e m + q ) 1 + 4 ( δ pr + Δ F e F + 1 ) 2 Γ 2 ,
T D ( δ ) = exp [ α D ( δ ) l ] ,
α D ( δ ) = d v 3 λ 2 2 π n π u e ( v u ) 2 × F e = F 1 F + 1 m = F F R F , m F e , m + q ( 1 8 ) 1 + 4 ( δ pr + Δ F e F + 1 ) 2 Γ 2 ,
Δ T ( δ ) = d v 3 λ 2 2 π n l π u e ( v u ) 2 × F e = F 1 F + 1 m = F F R F , m F e , m + q ( P F m Q F e m + q ( 1 8 ) ) 1 + 4 ( δ pr + Δ F e F + 1 ) 2 Γ 2 .
g ̇ 1 = Γ s 24 ( f 1 g 1 ) Γ g 1 ,
g ̇ 2 = Γ s 8 ( f 2 g 2 ) Γ g 2 ,
g ̇ 3 = Γ s 4 ( f 3 g 3 ) Γ g 3 ,
f ̇ 1 = Γ s 24 ( f 1 g 1 ) + Γ 12 g 1 ,
f ̇ 2 = Γ s 8 ( f 2 g 2 ) + Γ 3 g 1 + Γ 4 g 2 ,
f ̇ 3 = Γ s 4 ( f 3 g 3 ) + Γ 12 g 1 + Γ 4 g 2 + Γ 2 g 3 ,
24 g ̈ 1 + 2 ( 12 + s ) Γ g ̇ 1 + 11 12 Γ 2 s g 1 = 0 ,
8 g ̈ 2 + 2 ( 4 + s ) Γ g ̇ 2 + 3 4 Γ 2 s g 2 = s 3 Γ 2 g 1 ,
4 g ̈ 3 + 2 ( 2 + s ) Γ g ̇ 3 + s 2 Γ 2 g 3 = Γ 2 s 12 ( g 1 + 3 g 2 ) .
f 1 = 1 8 exp [ 11 288 s Γ t ] ,
f 2 = 1 32 exp [ 11 288 s Γ t ] + 3 32 exp [ 3 32 s Γ t ] ,
f 3 = 13 800 exp [ 11 288 s Γ t ] + 3 32 exp [ 3 32 s Γ t ] + 3 200 exp [ 1 8 s Γ t ] .
P F m = P F F + 1 m ( δ + k v ) + P F F m ( δ + Δ F F + 1 + k v ) + P F F 1 m ( δ + Δ F 1 F + 1 + k v ) ( 2 8 ) ,
P 1 1 = 1 8 exp [ 11 288 s 0 Γ t 1 + 4 δ 2 Γ 2 ] + 1 8 exp [ 35 288 s 0 Γ t 1 + 4 ( δ + Δ 1 2 ) 2 Γ 2 ] + 1 8 exp [ 1 9 s 0 Γ t 1 + 4 ( δ + Δ 0 2 ) 2 Γ 2 ] 2 8 .
Δ T ( δ ) = m = F F d v 3 λ 2 2 π n l π u e ( v u ) 2 ( R F , m F + 1 , m + q 1 + 4 ( δ k v ) 2 Γ 2 + R F , m F , m + q 1 + 4 ( δ + Δ F F + 1 k v ) 2 Γ 2 + R F , m F 1 , m + q 1 + 4 ( δ + Δ F 1 F + 1 k v ) 2 Γ 2 ) [ P F F + 1 m ( δ + k v ) + P F F m ( δ + Δ F F + 1 + k v ) + P F F 1 m ( δ + Δ F 1 F + 1 + k v ) ( 3 8 ) ] .
d v 3 λ 2 2 π n l π u e ( v u ) 2 P F μ m ( C 2 + k v ) 1 + 4 ( C 1 k v ) 2 Γ 2 .
k 1 C 0 exp [ ( C 1 k u ) 2 ] ,
C 0 = 3 λ 2 2 π n l Γ π 2 k u .
3 λ 2 2 π n l π u exp [ ( C 1 k u ) 2 ] d v k 1 1 + 4 Γ 2 ( C 1 k v ) 2 exp [ k 2 s 0 Γ t 1 + 4 Γ 2 ( C 2 + k v ) 2 ] = C 0 exp [ ( C 1 k u ) 2 ] k 1 [ 1 L ( C 1 + C 2 Γ , k 2 s 0 Γ t ) ] ,
L ( a , b ) = 1 2 π 1 1 + 4 y 2 exp [ b 1 + 4 ( a y ) 2 ] d y .
η = b 1 + b + 4 ( a y ) 2 = η 0 1 + η 0 ,
exp [ b 1 + 4 ( a y ) 2 ] 1 b 1 + b + 4 ( a y ) 2 .
L ( a , b ) L 0 ( a , b ) = b b + 1 ( 1 + b + 1 ) 4 a 2 + ( 1 + b + 1 ) 2 .
C 0 exp [ ( C 1 k u ) 2 ] k 1 k 2 L 0 ( C 1 + C 2 Γ , k 2 s 0 Γ t ) .
3 λ 2 2 π n l π u exp [ ( C 1 k u ) 2 ] d v k 1 1 + 4 Γ 2 ( C 1 k v ) 2 p 3 + p 4 s 0 [ 1 + 4 ( C 2 + k v ) 2 Γ 2 ] 1 p 1 + p 2 s 0 [ 1 + 4 ( C 2 + k v ) 2 Γ 2 ] 1 = C 0 exp [ ( C 1 k u ) 2 ] { p 3 p 1 + ( p 4 p 2 p 3 p 1 ) L 0 ( C 1 + C 2 Γ , p 2 p 1 s 0 ) } .
Δ T ( δ ) = μ ν m = F F C 0 exp [ ( δ + Δ ν F + 1 k u ) 2 ] R F , , m ν , m + q M F μ m ( 2 δ + Δ μ F + 1 + Δ ν F + 1 ) ,
Δ T ( δ ) = C 0 { S F + 1 ( δ ) + S F ( δ + Δ F F + 1 ) + S F 1 ( δ + Δ F 1 F + 1 ) + e ( Δ F F + 1 2 k u ) 2 X F F + 1 ( δ + Δ F F + 1 2 ) + e ( Δ F 1 F + 1 2 k u ) 2 X F 1 F + 1 ( δ + Δ F 1 F + 1 2 ) + e ( Δ F 1 F 2 k u ) 2 X F 1 F ( δ + Δ F 1 F + 1 + Δ F F + 1 2 ) } .
S 2 ( δ ) = 253 9600 L 0 ( 2 δ Γ , 11 288 τ ) + 9 128 L 0 ( 2 δ Γ , 3 32 τ ) + 3 400 L 0 ( 2 δ Γ , 1 8 τ ) ,
S 1 ( δ ) = 5 48 L 0 ( 2 δ Γ , 35 288 τ ) ,
S 0 ( δ ) = 1 24 L 0 ( 2 δ Γ , 1 9 τ ) ,
X 1 2 ( δ ) = 1 21 L 0 ( 2 δ Γ , 35 288 τ ) + 25 384 L 0 ( 2 δ Γ , 11 288 τ ) + 5 128 L 0 ( 2 δ Γ , 3 32 τ ) ,
X 0 2 ( δ ) = 7 192 L 0 ( 2 δ Γ , 1 9 τ ) + 1 24 L 0 ( 2 δ Γ , 11 288 τ ) ,
X 0 1 ( δ ) = 5 192 L 0 ( 2 δ Γ , 1 9 τ ) + 1 24 L 0 ( 2 δ Γ , 35 288 τ ) ,
T D ( δ ) = exp [ l C 0 8 { k 1 exp [ ( δ k u ) 2 ] + k 2 exp [ ( δ + Δ F F + 1 k u ) 2 ] + k 3 exp [ ( δ + Δ F 1 F + 1 k u ) 2 ] } ] ,
Δ T LP ( δ ) = d v 3 λ 2 2 π n l π u e ( v u ) 2 F e = F 1 F + 1 1 1 + 4 ( δ k v + Δ F e F + 1 ) 2 Γ 2 m = F F R F , m F e , m + q ( t m F s v 1 8 ) ,
F s = 5 16 k Γ s 0 1 + s 0 + 4 ( δ + k v ) 2 Γ 2 .
C 0 5 s 0 ϵ r t 64 4 + s 0 1 + s 0 μ m = F F exp [ ( δ k u ) 2 ] R 2 , m μ , m + q Γ 3 ( 2 δ + Δ μ 3 ) [ 2 ( 2 δ + Δ μ 3 ) 2 + ( 2 + s 0 ) Γ 2 ] 2 ,
35 96 C 0 s 0 ϵ r t 4 + s 0 1 + s 0 δ Γ [ 2 + s 0 + 8 ( δ Γ ) 2 ] 2 .
5 8 L 0 ( 2 δ Γ , s 0 ) + 5 16 L 0 ( 2 δ Γ , τ 9 ) 127 440 L 0 ( 2 δ Γ , 2 25 τ ) 119 800 L 0 ( 2 δ Γ , 3 25 τ ) 5503 26400 L 0 ( 2 δ Γ , 7 225 τ ) + 35 96 s 0 ϵ r t 4 + s 0 1 + s 0 δ Γ [ 2 + s 0 + 8 ( δ Γ ) 2 ] 2 ,
S 2 ( δ ) = 43 600 L 0 ( 11 288 τ ) + 1 32 L 0 ( 3 32 τ ) + 1 800 L 0 ( τ 8 ) ,
S 1 ( δ ) = 5 224 L 0 ( 35 288 τ ) ,
S 0 ( δ ) = 1 48 L 0 ( τ 9 ) ,
X 1 2 ( δ ) = 53 672 L 0 ( 35 288 τ ) + 19 960 L 0 ( 11 288 τ ) + 1 160 L 0 ( τ 8 ) + 5 64 L 0 ( 3 32 τ ) ,
X 0 2 ( δ ) = 1 24 L 0 ( τ 9 ) + 13 2400 L 0 ( 11 288 τ ) + 1 200 L 0 ( τ 8 ) + 1 32 L 0 ( 3 32 τ ) ,
X 0 1 ( δ ) = 5 96 L 0 ( τ 9 ) 5 84 L 0 ( 35 288 τ ) .
S 3 ( δ ) = 5 8 L 0 ( s 0 ) + 5 16 L 0 ( τ 9 ) 127 440 L 0 ( 2 25 τ ) 119 800 L 0 ( 3 25 τ ) 5503 26 400 L 0 ( 7 225 τ ) + 35 96 s 0 ϵ r t 4 + s 0 1 + s 0 δ Γ [ 2 + s 0 + 8 ( δ Γ ) 2 ] 2 ,
S 2 ( δ ) = 5 784 L 0 ( 3 32 τ ) + 1087 11 760 L 0 ( 5 72 τ ) ,
S 1 ( δ ) = 513 76 160 L 0 ( 19 800 τ ) + 8437 3 561 600 L 0 ( 59 7200 τ ) + 4227 360 400 L 0 ( 9 200 τ ) ,
X 2 3 ( δ ) = 143 5880 L 0 ( 3 32 τ ) + 52 735 L 0 ( 5 72 τ ) 5 32 L 0 ( τ 9 ) + 89 704 L 0 ( 2 25 τ ) + 49 640 L 0 ( 3 25 τ ) + 1213 21 120 L 0 ( 7 225 τ ) ,
X 1 3 ( δ ) = 169 9520 L 0 ( 19 800 τ ) + 5577 148 400 L 0 ( 59 7200 τ ) + 2951 608 175 L 0 ( 9 200 τ ) + 21 3520 L 0 ( 2 25 τ ) 7 9600 L 0 ( 3 25 τ ) + 549 35 200 L 0 ( 7 225 τ ) ,
X 1 2 ( δ ) = 457 15 232 L 0 ( 19 800 τ ) + 8151 237 440 L 0 ( 59 7200 τ ) + 8119 486 540 L 0 ( 9 200 τ ) + 1 210 L 0 ( 3 32 τ ) + 9 560 L 0 ( 5 72 τ ) .
S 3 ( δ ) = 1 48 L 0 ( s 0 ) 1 8 L 0 ( τ 9 ) + 131 880 L 0 ( 2 25 τ ) + 133 2400 L 0 ( 3 25 τ ) + 4507 26 400 L 0 ( 7 225 τ ) + 35 96 s 0 ϵ r t 4 + s 0 1 + s 0 δ Γ [ 2 + s 0 + 8 ( δ Γ ) 2 ] 2 ,
S 2 ( δ ) = 83 14 112 L 0 ( 3 32 τ ) + 761 11 760 L 0 ( 5 72 τ ) ,
S 1 ( δ ) = 3 5440 L 0 ( 19 800 τ ) + 143 254 400 L 0 ( 59 7200 τ ) 23 2 162 400 L 0 ( 9 200 τ ) ,
X 2 3 ( δ ) = 5 96 L 0 ( s 0 ) + 391 8820 L 0 ( 3 32 τ ) + 5 64 L 0 ( τ 9 ) + 1661 7350 L 0 ( 5 72 τ ) + 17 352 L 0 ( 2 25 τ ) + 77 1920 L 0 ( 3 25 τ ) 217 21 120 L 0 ( 7 225 τ ) ,
X 1 3 ( δ ) = 1633 19 040 L 0 ( 19 800 τ ) + 16 159 296 800 L 0 ( 59 7200 τ ) + 556 693 4 865 400 L 0 ( 9 200 τ ) 9 220 L 0 ( 2 25 τ ) 217 9600 L 0 ( 3 25 τ ) 881 35 200 L 0 ( 7 225 τ ) + 3 64 L 0 ( τ 9 ) + 1 32 L 0 ( s 0 ) ,
X 1 2 ( δ ) = 1 56 L 0 ( 19 800 τ ) + 1859 59 360 L 0 ( 59 7200 τ ) 659 228 960 L 0 ( 9 200 τ ) 61 23 520 L 0 ( 3 32 τ )
11 19 600 L 0 ( 5 72 τ ) .

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