Abstract

We report characterization of electromagnetically induced transparency (EIT) resonances in the D1 line of Rb87 under various experimental conditions. The dependence of the EIT linewidth on the power of the pump field was investigated at various temperatures for the ground states of the lambda system associated with different hyperfine levels of the atomic 5S12 state as well as magnetic sublevels of the same hyperfine level. Strictly linear behavior was observed in all cases. A theoretical analysis of our results shows that dephasing in the ground state is the main source of decoherence, with population exchange playing a minor role.

© 2006 Optical Society of America

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  1. S. E. Harris, Phys. Today 50(7), 36 (1997).
    [CrossRef]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  3. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
    [CrossRef] [PubMed]
  4. T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
    [CrossRef]
  5. M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
    [CrossRef]
  6. J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
    [CrossRef]
  7. S. Knappe, R. Wynands, J. Kitching, H. G. Robinson, and L. Hollberg, J. Opt. Soc. Am. B 18, 1545 (2001).
    [CrossRef]
  8. J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
    [CrossRef]
  9. M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
    [CrossRef]
  10. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
    [CrossRef] [PubMed]
  11. C. Y. Ye and A. S. Zibrov, Phys. Rev. A 65, 023806 (2002).
    [CrossRef]
  12. A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
    [CrossRef]
  13. H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
    [CrossRef]
  14. M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
    [CrossRef]
  15. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  16. W. Franzen, Proc. R. Soc. Med. 115, 850 (1959).

2006 (4)

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
[CrossRef]

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2003 (1)

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

2002 (2)

C. Y. Ye and A. S. Zibrov, Phys. Rev. A 65, 023806 (2002).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

2001 (3)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

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

1998 (1)

J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
[CrossRef]

1997 (2)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

1959 (1)

W. Franzen, Proc. R. Soc. Med. 115, 850 (1959).

André, A.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

Appel, J.

J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
[CrossRef]

Bednar, C. J.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

Chanelière, T.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Eisaman, M. D.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

Erhard, M.

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Fleischhauer, M.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

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

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Franzen, W.

W. Franzen, Proc. R. Soc. Med. 115, 850 (1959).

Godone, A.

J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
[CrossRef]

Harris, S. E.

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Helm, H.

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

Hollberg, L.

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

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Imamoglu, A.

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

Javan, A.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Jenkins, S. D.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Kennedy, T. A. B.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Kitching, J.

Knappe, S.

Kocharovskaya, O.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Kuzmich, A.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Lan, S.-Y.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Lee, H.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Levi, F.

J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
[CrossRef]

Lukin, M. D.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Lvovsky, A. I.

J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Marangos, J. P.

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

Marzlin, K.-P.

J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
[CrossRef]

Massou, F.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

Matsukevich, D.

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

Novikova, I.

Phillips, D. F.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Robinson, H. G.

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

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Rostovtsev, Y.

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

Scully, M. O.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Taichenachev, A. V.

Vanier, J.

J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
[CrossRef]

Velichansky, V. L.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Walsworth, R. L.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Wynands, R.

Ye, C. Y.

C. Y. Ye and A. S. Zibrov, Phys. Rev. A 65, 023806 (2002).
[CrossRef]

Yudin, V. I.

Zibrov, A. S.

I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, Opt. Lett. 31, 2353 (2006).
[CrossRef] [PubMed]

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

C. Y. Ye and A. S. Zibrov, Phys. Rev. A 65, 023806 (2002).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Appl. Phys. B (1)

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, Appl. Phys. B 76, 33 (2003).
[CrossRef]

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

Nature (2)

T. Chanelière, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature 438, 833 (2006).
[CrossRef]

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature 438, 837 (2006).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (5)

J. Vanier, A. Godone, and F. Levi, Phys. Rev. A 58, 2345 (1998).
[CrossRef]

M. Erhard and H. Helm, Phys. Rev. A 63, 043813 (2001).
[CrossRef]

J. Appel, K.-P. Marzlin, and A. I. Lvovsky, Phys. Rev. A 73, 013804 (2006).
[CrossRef]

C. Y. Ye and A. S. Zibrov, Phys. Rev. A 65, 023806 (2002).
[CrossRef]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, Phys. Rev. A 66, 013805 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, Phys. Rev. Lett. 79, 2959 (1997).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Proc. R. Soc. Med. (1)

W. Franzen, Proc. R. Soc. Med. 115, 850 (1959).

Rev. Mod. Phys. (1)

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

Other (1)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

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Figures (2)

Fig. 1
Fig. 1

(a) Relevant atomic level structure. The excited state a is coupled to two ground states b , c by a weak signal field with Rabi frequency Ω b and detuning δ and a stronger pump field with Rabi frequency Ω c and detuning Δ. Γ b and Γ c are rates of spontaneous emission into the respective states b and c , whereas γ b c describes the decay rate of coherences between these states. (b) Measured width of the Zeeman configuration EIT resonances as a function of the pump laser power for different temperatures together with linear fits and a fit to the theory of Javan and co-workers,[12, 13] assuming a decoherence rate of γ b c = 110 Hz . The inset shows an example of the measured EIT resonance.

Fig. 2
Fig. 2

Dependence of the EIT linewidth on the pump power for the hyperfine configuration. The lines are linear fits to the measured data. The left inset shows a fit of the population exchange theory[12] to the data acquired at T = 80 ° C , with γ b c = 117 Hz . The right inset shows the temperature dependence of the experimentally determined slopes together with a theoretical estimate.

Equations (10)

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ρ a b ( 1 ) = Ω b 1 Δ δ 2 + Ω c 2 i γ b c + δ 2 i Γ 2 ,
χ b = Ω b p ( Δ ) ρ a b d Δ , = N D a b 2 ϵ 0 ,
p ( Δ ) = ln 2 W d π e ln 2 ( Δ W d ) 2 ,
p Lorentz ( Δ ) = ln 2 W d π 1 1 + ( Δ W d ) 2 .
χ b = 2 π ln 2 i γ b c + δ 2 ( γ b c i δ 2 ) ( Γ + 2 W d 2 i δ 2 ) + 2 Ω c 2 .
α ( δ 2 ) = ω c Im ( χ b ) = α max α max α min 1 + ( 2 δ 2 FWHM ) 2 ,
α max = 2 ω c π ln 2 1 2 W d + Γ ,
α min = 2 ω c π ln 2 1 2 W d + Γ + 2 Ω c 2 γ b c ,
FWHM = 2 γ b c + 4 Ω c 2 2 W d + Γ .
FWHM 4 γ pe W d Γ + 2 Ω c 2 W d ,

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