Abstract

Subkilohertz spectroscopy by coherent population trapping (CPT) has been performed in Na atomic vapor. The system employs a frequency-swept acousto-optic modulator for bichromatic excitation as well as a heterodyne–lock-in detection technique that permits the direct measurement of the CPT dispersion curves at a good signal-to-noise ratio. A CPT linewidth of 400 Hz was measured as well as a steep refractive-index dispersion of as much as 3.3×10-10 Hz-1, corresponding to a group velocity of 1800 m/s.

© 2004 Optical Society of America

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    [CrossRef]

2003

2002

2001

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, J. Opt. Soc. Am. B 18, 1545 (2001).
[CrossRef]

2000

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

M. Erhard, S. Nussman, and H. Helm, Phys. Rev. A 62, 061802 (2000).
[CrossRef]

M. Mitsunaga, M. Yamashita, and H. Inoue, Phys. Rev. A 62, 013817 (2000).
[CrossRef]

1999

R. Wynands and A. Nagel, Appl. Phys. B 68, 1 (1999).
[CrossRef]

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

1998

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

1997

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

1996

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

1976

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Asahi, H.

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Brandt, S.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

Danzmann, K.

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Erhard, M.

M. Erhard, S. Nussman, and H. Helm, Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Harada, K.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Helm, H.

M. Erhard, S. Nussman, and H. Helm, Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Hollberg, L.

Homann, F.

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

Ikonen, E.

Inoue, H.

M. Mitsunaga, M. Yamashita, and H. Inoue, Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kitching, J.

Knappe, S.

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

Lindvall, T.

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Merimaa, M.

Meschede, D.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

Mitsunaga, M.

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Motomura, K.

Müller, G.

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

Müller, M.

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

Nagel, A.

R. Wynands and A. Nagel, Appl. Phys. B 68, 1 (1999).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

Nussman, S.

M. Erhard, S. Nussman, and H. Helm, Phys. Rev. A 62, 061802 (2000).
[CrossRef]

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Rinkleff, R.

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

Rinkleff, R.-H.

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

Robinson, H. G.

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Stähler, M.

Taichenachev, A.

Tittonen, I.

Weis, A.

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Wicht, A.

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

Wynands, R.

M. Stähler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, Opt. Lett. 27, 1472 (2002).
[CrossRef]

S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, J. Opt. Soc. Am. B 18, 1545 (2001).
[CrossRef]

R. Wynands and A. Nagel, Appl. Phys. B 68, 1 (1999).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

Yamashita, M.

M. Mitsunaga, M. Yamashita, and H. Inoue, Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Yudin, V.

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Appl. Phys. B

R. Wynands and A. Nagel, Appl. Phys. B 68, 1 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Nature

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Nuovo Cimento B

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, Nuovo Cimento B 36, 5 (1976).
[CrossRef]

Opt. Commun.

G. Müller, A. Wicht, R. Rinkleff, and K. Danzmann, Opt. Commun. 127, 37 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Mitsunaga, M. Yamashita, and H. Inoue, Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Phys. Rev. A

M. Erhard, S. Nussman, and H. Helm, Phys. Rev. A 62, 061802 (2000).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 62, 060501 (2000).
[CrossRef]

M. Müller, F. Homann, R.-H. Rinkleff, A. Wicht, and K. Danzmann, Phys. Rev. A 64, 013803 (2001).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, Phys. Rev. A 56, R1063 (1997).
[CrossRef]

R. Wynands, A. Nagel, S. Brandt, D. Meschede, and A. Weis, Phys. Rev. A 58, 196 (1998).
[CrossRef]

Phys. Rev. Lett.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. 83, 4277 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the heterodyne-detected CPT experiment: PBSs, polarizing beam splitters; NPBS, nonpolarizing beam splitter; PDs, photodiodes; LPF, low-pass filter; PC, personal computer; RDL, ring dye laser; LO, local oscillator; IF, intermediate frequency; other abbreviations defined in text. Inset, energy-level diagram.

Fig. 2
Fig. 2

(a) Absorption and (b) dispersion curves of a typical heterodyne-detected CPT signal. Filled circles, experiment; solid curve, theory representing the least-squares fit dispersion curve. Vg, group velocity.

Fig. 3
Fig. 3

Dispersion curves for five values of Ic.

Fig. 4
Fig. 4

(a) Measured dispersion dn/dν0 and (b) linewidth (Δν) as functions of Ic.

Equations (3)

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

Epl=Ep exp-α0l21-Ωc24γγs-iΔp,
VcΔp=ErEpexp-α0l2α0lγsΩc2γΔp2+γs2,
VsΔp=ErEpexp-α0l2α0lΔpΩc2γΔp2+γs2,

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