Abstract

We propose a simple and effective way of creating pure dark superposition states. The generation of pure states is carried out by using bichromatic radiation with controllable polarization ellipticity. We experimentally confirm analytic formulas for polarization ellipticity to obtain mm pure dark states in the system of Zeeman sublevels of alkali atoms. For Rb87 we experimentally accumulated 60% of the atoms in the 0–0 dark state and 50% into the (±1)(±1) dark states.

© 2006 Optical Society of America

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  1. M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  2. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
    [CrossRef]
  3. J. Vanier, Appl. Phys. B 81, 421 (2005).
    [CrossRef]
  4. A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
    [CrossRef]
  5. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
    [CrossRef]
  6. Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
    [CrossRef] [PubMed]
  7. T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
    [CrossRef] [PubMed]
  8. A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
    [CrossRef]

2006 (1)

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

2005 (4)

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

2004 (2)

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

2002 (1)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

André, A.

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Clairon, A.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

de Clercq, E.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Dimarcq, N.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Eisaman, M. D.

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Gawlik, W.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Guerandel, S.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Happer, W.

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Hollberg, L.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Holleville, D.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Jau, Y.-Y.

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Kargapoltsev, S. V.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Kimball, D. F.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Kitching, J.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Kuzma, N. N.

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Lukin, M. D.

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

Marangos, J.

M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Miron, E.

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Post, A. B.

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

Rochester, S. M.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Taichenachev, A. V.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Vanier, J.

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

Velichansky, V. L.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Walsworth, R. L.

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

Weis, A.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Wynands, R.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Yashchuk, V. V.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

Yudin, V. I.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Zanon, T.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Zibrov, A. S.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

Zibrov, S. A.

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

Appl. Phys. B (1)

J. Vanier, Appl. Phys. B 81, 421 (2005).
[CrossRef]

J. Phys. B (1)

A. André, M. D. Eisaman, R. L. Walsworth, A. S. Zibrov, and M. D. Lukin, J. Phys. B 38, S589 (2005).
[CrossRef]

JETP Lett. (1)

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, S. V. Kargapoltsev, R. Wynands, J. Kitching, and L. Hollberg, JETP Lett. 80, 236 (2004).
[CrossRef]

Phys. Rev. (1)

A. V. Taichenachev, V. I. Yudin, V. L. Velichansky, A. S. Zibrov, and S. A. Zibrov, Phys. Rev. 73, 013812 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

Y.-Y. Jau, E. Miron, A. B. Post, N. N. Kuzma, and W. Happer, Phys. Rev. Lett. 93, 160802 (2004).
[CrossRef] [PubMed]

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, Phys. Rev. Lett. 94, 193002 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, Rev. Mod. Phys. 74, 1153 (2002).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Three-level Λ scheme, polarization ellipses a 1 , a 2 , orientation of the magnetic field B and wave vector k. (b) Light-induced transitions driven by the σ + and σ circularly polarized components for the m m resonance. (c) Experimental setup. ECLD, extended cavity laser diodes; PL, phase locking electronics; D1, D2 photodiodes PBS, polarized beam splitter.

Fig. 2
Fig. 2

Contrast of the Rb 87 CPT resonances on the ellipticity ϵ of the ϵ ( ϵ ) configuration at different two-photon m m transitions: a, m = + 1 ; b, m = 0 ; c, m = 1 . Accumulated populations in the states of Eq. (4) reach 51%, 58%, 51%, correspondingly.

Fig. 3
Fig. 3

(Left) Contrast of the Rb 85 CPT resonances on the ellipticity ϵ of the ϵ ( ϵ ) configuration at different two-photon m m transitions: a, m = + 2 ; b, m = + 1 ; c, m = 0 ; d, m = 1 ; e, m = 2 . Accumulated populations in the states of Eq. (4) reach 25%, 30%, 31%, 30%, 25%, correspondingly. (Right) Transmission of the Rb 85 CPT resonances on the two-photon detuning at different polarization ellipticity ( ω 1 is swept and ω 2 is tuned to the maximum of Doppler absorption). Full frequency scanning range equals 40 MHz . a, ϵ = 21 ° ; b, ϵ = 9.5 ° ; c, ϵ = 0 ° ellipticity of the applied polarization components.

Equations (4)

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E ( z , t ) = E 1 ( z ) a 1 e i ω 1 t + E 2 ( z ) a 2 e i ω 2 t + c.c.
1 + F m 1 + F + m = tan ( ϵ 1 + π 4 ) tan ( ϵ 2 + π 4 ) ,
sin ( 2 ϵ ) = m ( 1 + F ) .
dark ( m ) = N { F , m i ( E 1 E 2 ) F + 1 , m } .

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