Abstract

The frequency of the dark resonance in coherent population trapping experiments has been measured as a function of the degree of ellipticity and the intensity of the probe light. The results have been used to find the quantum limit of sensitivity of an optical magnetometer based on the nonlinear Faraday effect.

© 2000 Optical Society of America

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References

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  1. M. Arditi and T. R. Carver, Phys. Rev. 124, 800 (1961); B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11 (1968); W. Happer, Rev. Mod. Phys. 44, 169 (1972).
    [CrossRef]
  2. C. Cohen-Tannoudji and J. Dupont-Roc, Phys. Rev. A 5, 968 (1972).
    [CrossRef]
  3. S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
    [CrossRef] [PubMed]
  4. A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
    [CrossRef] [PubMed]
  5. For a review on optical pumping magnetometers, see E. B. Alexandrov and V. A. Bonch-Bruevich, Opt. Eng. 31, 711 (1992); E. B. Alexandrov, M. V. Balabas, A. S. Pasgalev, A. K. Vershovskii, and N. N. Yakobson, Laser Phys. 6, 244 (1996).
  6. M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
    [CrossRef]
  7. M. O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360 (1992); M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).
  8. W. Gawlik, in Modern Nonlinear Optics, M. Evans and S. Kielich, eds., Vol. LXXXV of Advances in Chemical Physics Series (Wiley, New York, 1994), part 3, p. 733; D. Budker, D. J. Orlando, and V. Vashchuk, Am. J. Phys. 67, 589 (1999); F. Schuller and D. N. Stacey, Phys. Rev. A 60, 973 (2000).
    [CrossRef]
  9. V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
    [CrossRef]

2000

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

1999

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

1993

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

1992

M. O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360 (1992); M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).

For a review on optical pumping magnetometers, see E. B. Alexandrov and V. A. Bonch-Bruevich, Opt. Eng. 31, 711 (1992); E. B. Alexandrov, M. V. Balabas, A. S. Pasgalev, A. K. Vershovskii, and N. N. Yakobson, Laser Phys. 6, 244 (1996).

1972

C. Cohen-Tannoudji and J. Dupont-Roc, Phys. Rev. A 5, 968 (1972).
[CrossRef]

1961

M. Arditi and T. R. Carver, Phys. Rev. 124, 800 (1961); B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11 (1968); W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Alexandrov, E. B.

For a review on optical pumping magnetometers, see E. B. Alexandrov and V. A. Bonch-Bruevich, Opt. Eng. 31, 711 (1992); E. B. Alexandrov, M. V. Balabas, A. S. Pasgalev, A. K. Vershovskii, and N. N. Yakobson, Laser Phys. 6, 244 (1996).

Arditi, M.

M. Arditi and T. R. Carver, Phys. Rev. 124, 800 (1961); B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11 (1968); W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Bednar, C. J.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Bonch-Bruevich, V. A.

For a review on optical pumping magnetometers, see E. B. Alexandrov and V. A. Bonch-Bruevich, Opt. Eng. 31, 711 (1992); E. B. Alexandrov, M. V. Balabas, A. S. Pasgalev, A. K. Vershovskii, and N. N. Yakobson, Laser Phys. 6, 244 (1996).

Brandt, S.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

Carver, T. R.

M. Arditi and T. R. Carver, Phys. Rev. 124, 800 (1961); B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11 (1968); W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji and J. Dupont-Roc, Phys. Rev. A 5, 968 (1972).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji and J. Dupont-Roc, Phys. Rev. A 5, 968 (1972).
[CrossRef]

Fleischhauer, M.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

M. O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360 (1992); M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).

Gawlik, W.

W. Gawlik, in Modern Nonlinear Optics, M. Evans and S. Kielich, eds., Vol. LXXXV of Advances in Chemical Physics Series (Wiley, New York, 1994), part 3, p. 733; D. Budker, D. J. Orlando, and V. Vashchuk, Am. J. Phys. 67, 589 (1999); F. Schuller and D. N. Stacey, Phys. Rev. A 60, 973 (2000).
[CrossRef]

Hanch, T. W.

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

Kanorsky, S. I.

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

Lukin, M. D.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Matsko, A. B.

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

Meschede, D.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

Mikhailov, E.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Nagel, A.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

Novikova, I.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Sautenkov, V. A.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Scully, M. O.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

M. O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360 (1992); M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).

Velichansky, V. L.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Weis, A.

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

Welch, G. R.

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

Wurster, J.

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

Wynands, R.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

Europhys. Lett.

A. Nagel, S. Brandt, D. Meschede, and R. Wynands, Europhys. Lett. 48, 385 (1999); D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Phys. Rev. Lett. 85, 2088 (2000).
[CrossRef] [PubMed]

Opt. Eng.

For a review on optical pumping magnetometers, see E. B. Alexandrov and V. A. Bonch-Bruevich, Opt. Eng. 31, 711 (1992); E. B. Alexandrov, M. V. Balabas, A. S. Pasgalev, A. K. Vershovskii, and N. N. Yakobson, Laser Phys. 6, 244 (1996).

Phys. Rev.

M. Arditi and T. R. Carver, Phys. Rev. 124, 800 (1961); B. S. Mathur, H. Tang, and W. Happer, Phys. Rev. 171, 11 (1968); W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[CrossRef]

Phys. Rev. A

C. Cohen-Tannoudji and J. Dupont-Roc, Phys. Rev. A 5, 968 (1972).
[CrossRef]

S. I. Kanorsky, A. Weis, J. Wurster, and T. W. Hanch, Phys. Rev. A 47, 1220 (1993).
[CrossRef] [PubMed]

V. A. Sautenkov, M. D. Lukin, C. J. Bednar, I. Novikova, E. Mikhailov, M. Fleischhauer, V. L. Velichansky, G. R. Welch, and M. O. Scully, Phys. Rev. A 62, 023810 (2000).
[CrossRef]

M. Fleischhauer, A. B. Matsko, and M. O. Scully, Phys. Rev. A 62, 013808 (2000).
[CrossRef]

Phys. Rev. Lett.

M. O. Scully and M. Fleischhauer, Phys. Rev. Lett. 69, 1360 (1992); M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).

Other

W. Gawlik, in Modern Nonlinear Optics, M. Evans and S. Kielich, eds., Vol. LXXXV of Advances in Chemical Physics Series (Wiley, New York, 1994), part 3, p. 733; D. Budker, D. J. Orlando, and V. Vashchuk, Am. J. Phys. 67, 589 (1999); F. Schuller and D. N. Stacey, Phys. Rev. A 60, 973 (2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Scheme of the atomic transitions studied in the experiment and used for the numerical simulations. (b) Idealized three-level scheme.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

(a) Position of the EIT resonance (in terms of longitudinal magnetic field) as a function of the degree of the incoming light’s ellipticity. Experimental data are shown as shapes, and theoretical results are shown as curves. Curves (1) and (4) correspond to the transitions F=2F=1 and F=2F=2, with an intensity of 1.1 mW/cm2; curves (2) and (3) correspond to the same transitions and an intensity of 0.54 mW/cm2. The measured values of the intensities are 1.2 mW/cm2 for (1) and (4) and 0.6 mW/cm2 for (2) and (3). (b) Ac-Stark shift for the transition F=2F=1 for various densities N of Rb vapor (in units of 1012 cm-3). The shift is quite constant for comparable low densities and starts to decrease for higher densities. A threshold density, at which the deviation from the theory becomes clear, corresponds to the low transmission for which the validity of our approximations is doubtful. For the particular cell this threshold is 1.7×1012 cm-3.

Equations (5)

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ddzΩ±2=-κγ0γrΩ2Ω+2Ω-22γ0γ+Ω2,
ddzϕ±=κγr2δ0/2-δ±2γ0γ+Ω2,
δϕ=-κγr2Δ00LdzΩ+z2-Ω-z2Ωz2,
δEIT=Ω+02-Ω-02Δ0.
δ0SQL=γ0fγrΔ038πλ2A1γ0tm1/2,

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