Abstract

High-resolution spectroscopy of hyperfine Zeeman components in a sodium atomic vapor has been performed by a coherent population trapping (CPT) technique. The measurement features the simple configuration of a single laser source with a frequency-swept double-pass acousto-optic modulator. Well-resolved CPT dip signals in the presence of longitudinal or transverse static magnetic fields can be nicely explained by a theory based on two-photon resonance.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
    [CrossRef]
  14. M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
    [CrossRef]
  15. A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  22. C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef] [PubMed]
  23. R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1–25 (1999).
    [CrossRef]
  24. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
    [CrossRef]
  25. R. Höller, F. Renzoni, L. Windholz, and J. H. Xu, “Coherent population trapping on the sodium D1 line in high magnetic fields,” J. Opt. Soc. Am. B 14, 2221–2226 (1997).
    [CrossRef]
  26. J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
    [CrossRef]
  27. M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne interference of inequivalent nuclear sites,” Phys. Rev. Lett. 52, 1484–1487 (1984).
    [CrossRef]
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    [CrossRef]

2001 (1)

C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

2000 (5)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

M. Erhard, S. Nussman, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802 (2000).
[CrossRef]

M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
[CrossRef]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

1999 (3)

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1–25 (1999).
[CrossRef]

1998 (3)

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett. 23, 804–806 (1998).
[CrossRef]

1997 (5)

1996 (2)

1995 (2)

1991 (2)

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

K.-J. Boller, A. Imamoḡlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

1984 (1)

M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne interference of inequivalent nuclear sites,” Phys. Rev. Lett. 52, 1484–1487 (1984).
[CrossRef]

1983 (1)

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

1976 (2)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r. f. 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]

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Sub-natural 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 r. f. transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
[CrossRef]

Arimondo, E.

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]

Baluschev, S.

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Behroozl, C. H.

C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Boller, K.-J.

K.-J. Boller, A. Imamoḡlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Brewer, R. G.

M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne interference of inequivalent nuclear sites,” Phys. Rev. Lett. 52, 1484–1487 (1984).
[CrossRef]

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

Burkett, W. H.

Celikov, A. A.

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

Cronin-Golomb, M.

DeVoe, R. G.

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

Donoghue, J.

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Erhard, M.

M. Erhard, S. Nussman, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

Gozzini, A.

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

Grove, T. T.

Ham, B. S.

Harris, S. E.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

K.-J. Boller, A. Imamoḡlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Helm, H.

M. Erhard, S. Nussman, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Hemmer, P. R.

Höller, R.

Huss, A. F.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

Imamog¯lu, A.

K.-J. Boller, A. Imamoḡlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Imamog¯u, A.

Imoto, N.

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[CrossRef]

Inoue, H.

M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Katz, D. P.

Kim, M. K.

Kintzer, E. S.

M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne interference of inequivalent nuclear sites,” Phys. Rev. Lett. 52, 1484–1487 (1984).
[CrossRef]

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

Korsunsky, E. A.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

E. A. Korsunsky, W. Maichen, and L. Windholz, “Dynamics of coherent optical pumping in a sodium atomic beam,” Phys. Rev. A 56, 3908–3915 (1997).
[CrossRef]

Kumar, P.

Lammegger, R.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

Leinfellner, N.

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

Li, Y.

Y. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
[CrossRef] [PubMed]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozl, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Lü, B.

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef] [PubMed]

Maichen, W.

E. A. Korsunsky, W. Maichen, and L. Windholz, “Dynamics of coherent optical pumping in a sodium atomic beam,” Phys. Rev. A 56, 3908–3915 (1997).
[CrossRef]

Manuszak, D.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

Mitsunaga, M.

M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
[CrossRef]

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[CrossRef]

M. Mitsunaga, T. Mukai, K. Watanabe, and T. Mukai, “Dressed-atom spectroscopy of cold Cs atoms,” J. Opt. Soc. Am. B 13, 2696–2700 (1996).
[CrossRef]

M. Mitsunaga, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne interference of inequivalent nuclear sites,” Phys. Rev. Lett. 52, 1484–1487 (1984).
[CrossRef]

Mlynek, J.

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

Moi, L.

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

Mukai, T.

Nagel, A.

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1–25 (1999).
[CrossRef]

Nussman, S.

M. Erhard, S. Nussman, and H. Helm, “Power broadening and Doppler effects of coherent dark resonances in Rb,” Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r. f. 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]

Peer, N.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

Renzoni, F.

Schmidt, H.

Shahriar, M. S.

Shariar, M. S.

Sharpe, S. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

Shverdin, M.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

Sudarshanam, V. S.

Velichansky, V. L.

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

Watanabe, K.

Windholz, L.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, “Efficient Raman sideband generation in a coherent atomic medium,” Phys. Rev. A 63, 013802 (2000).
[CrossRef]

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

E. A. Korsunsky, W. Maichen, and L. Windholz, “Dynamics of coherent optical pumping in a sodium atomic beam,” Phys. Rev. A 56, 3908–3915 (1997).
[CrossRef]

R. Höller, F. Renzoni, L. Windholz, and J. H. Xu, “Coherent population trapping on the sodium D1 line in high magnetic fields,” J. Opt. Soc. Am. B 14, 2221–2226 (1997).
[CrossRef]

Wong, W. C.

J. Mlynek, W. C. Wong, R. G. DeVoe, E. S. Kintzer, and R. G. Brewer, “Raman heterodyne detection of nuclear magnetic resonance,” Phys. Rev. Lett. 50, 993–996 (1983).
[CrossRef]

Wynands, R.

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1–25 (1999).
[CrossRef]

Xiao, M.

B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Λ system under the influence of coherent population trapping,” Opt. Lett. 23, 804–806 (1998).
[CrossRef]

Y. Li and M. Xiao, “Observation of quantum interference between dressed states in an electromagnetically induced transparency,” Phys. Rev. A 51, 4959–4962 (1995).
[CrossRef] [PubMed]

Xu, J. H.

Yamashita, M.

M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Yin, G. Y.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, “Efficient nonlinear frequency conversion in an all-resonant double-Λ system,” Phys. Rev. Lett. 84, 5308–5311 (2000).
[CrossRef] [PubMed]

Appl. Phys. B (1)

R. Wynands and A. Nagel, “Precision spectroscopy with coherent dark states,” Appl. Phys. B 68, 1–25 (1999).
[CrossRef]

Eur. Phys. J. D (1)

S. Baluschev, N. Leinfellner, E. A. Korsunsky, and L. Windholz, “Electromagnetically induced transparency in a sodium vapour cell,” Eur. Phys. J. D 2, 5–10 (1998).
[CrossRef]

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

Lett. Nuovo Cimento (1)

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L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
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Nuovo Cimento B (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, “An experimental method for the observation of r. f. transitions and laser beat resonances in oriented Na vapor,” Nuovo Cimento B 36, 5–20 (1976).
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Opt. Commun. (1)

A. M. Akulshin, A. A. Celikov, and V. L. Velichansky, “Sub-natural absorption resonances on the D1 line of rubidium induced by coherent population trapping,” Opt. Commun. 84, 139–143 (1991).
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Opt. Lett. (6)

Phys. Rev. A (7)

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M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
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M. Mitsunaga, M. Yamashita, and H. Inoue, “Absorption imaging of electromagnetically induced transparency in cold sodium atoms,” Phys. Rev. A 62, 013817 (2000).
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Other (1)

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Figures (7)

Fig. 1
Fig. 1

Laser-coupling scheme and hyperfine Zeeman energy diagram of the Na atom. Zeeman splitting of the excited state is neglected for simplicity.

Fig. 2
Fig. 2

Schematic of the experimental setup for CPT hyperfine Zeeman spectroscopy: PBSs, polarizing beam splitters; PMT, photomultiplier tube. The orientation of static magnetic field B is the longitudinal case (Bk) that corresponds to Fig. 5. For the transverse case (Bk, Fig. 6), Helmholtz coils are rotated such that B is along the direction of the probe polarization.

Fig. 3
Fig. 3

Typical CPT spectrum as a function of frequency difference δν in the absence of a static magnetic field. The depth of the CPT dip is ∼40% of the total fluorescence intensity.

Fig. 4
Fig. 4

Circles, experimentally obtained CPT linewidth (FWHM) as a function of total laser power density when probe and pump beams have equal intensity. Solid curve, theoretical fit ΓCPT(I)=Γ0+βI.

Fig. 5
Fig. 5

CPT spectra as a function of the frequency difference δν for various B fields when Bk.

Fig. 6
Fig. 6

CPT spectra as a function of frequency difference δν for various B fields when Bk and Bp.

Fig. 7
Fig. 7

B field versus hyperfine Zeeman transition frequencies. Open circles, experimental results for Bk. Filled circles, experimental results for Bk. Solid curves, theory based on the Breit–Rabi formula [Eq. (9)]. Curve a corresponds to the transition |2, 2|1, 1 (ΔmF=1), b to |2, 1|1, 1 (ΔmF=0), c to |2, 2|1, 0 (ΔmF=2), d to |2, 1|1, 0 (ΔmF=1) and |2, 0|1, 1 (ΔmF=-1), e to |2, 0|1, 0 (ΔmF=0), f to |2, -1|1, 1 (ΔmF=-2) and |2, 1|1, -1 (ΔmF=2), g to |2, -1|1, 0 (ΔmF=-1) and |2, 0|1, -1 (ΔmF=1), h to |2, -1|1, -1 (ΔmF=0), i to |2, -2|1, 0 (ΔmF=-2), and j to |2, -2|1, -1 (ΔmF=-1).

Equations (15)

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|1, 2=|2, 2,
|2, 1=cos α1|2, 1+sin α1|1, 1,
|2, 0=cos α0|2, 0+sin α0|1, 0,
|2, -1=cos α-1|2, -1+sin α-1|1, -1,
|2, -2=|2, -2,
|1, -1=cos α-1|1, -1-sin α-1|2, -1,
|1, 0=cos α0|1, 0-sin α0|2, 0,
|1, 1=cos α1|1, 1-sin α1|2, 1,
E(F=2, mF)=hνhfs[-1/8+1/2(1+mFx+x2)1/2]
(mF-2),
E(F=2, -2)=hνhfs(3/8-x/2),
E(F=1, mF)=hνhfs[-1/8-1/2(1+mFx+x2)1/2],
x=2μBBhνhfs.
νp-νc=[E(F=2, mF)-E(F=1, mF)]/h.
ΓCPT(I)=Γ0+βI,

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