Abstract

We report the observation of coherent two-photon free-induction decay (FID) in a three-level Λ system excited by a low-intensity square-modulated laser pulse. Using electromagnetically induced transparency in an Rb85 cold atomic cloud, for what we believe to be the first time, we observe FID signals with coherence time exceeding the relevant atomic excited-state natural lifetime. Because of the on-resonance enhancement, the two-photon FID signal can be observed at the falling edge without using heterodyne means.

© 2010 Optical Society of America

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  1. F. Bloch, Phys. Rev. 70, 460 (1946).
    [CrossRef]
  2. R. G. Brewer and R. L. Shoemaker, Phys. Rev. Lett. 27, 631 (1971).
    [CrossRef]
  3. R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972).
    [CrossRef]
  4. D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
    [CrossRef]
  5. M. M. T. Loy, Phys. Rev. Lett. 36, 1454 (1976).
    [CrossRef]
  6. P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
    [CrossRef]
  7. D. G. Gold and E. L. Hahn, Phys. Rev. A 16, 324 (1977).
    [CrossRef]
  8. H. W. H. Lee and J. E. Wessel, Phys. Rev. Lett. 59, 1416 (1987).
    [CrossRef]
  9. K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
    [CrossRef]
  10. U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
    [CrossRef]
  11. J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).
  12. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  13. D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
    [CrossRef]
  14. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]

2009 (1)

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

2005 (1)

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

2002 (1)

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

1997 (2)

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

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

1987 (1)

H. W. H. Lee and J. E. Wessel, Phys. Rev. Lett. 59, 1416 (1987).
[CrossRef]

1977 (2)

P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
[CrossRef]

D. G. Gold and E. L. Hahn, Phys. Rev. A 16, 324 (1977).
[CrossRef]

1976 (1)

M. M. T. Loy, Phys. Rev. Lett. 36, 1454 (1976).
[CrossRef]

1975 (1)

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

1972 (1)

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972).
[CrossRef]

1971 (1)

R. G. Brewer and R. L. Shoemaker, Phys. Rev. Lett. 27, 631 (1971).
[CrossRef]

1946 (1)

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

Bjorkholm, J. E.

P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
[CrossRef]

Bloch, F.

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

Brewer, R. G.

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972).
[CrossRef]

R. G. Brewer and R. L. Shoemaker, Phys. Rev. Lett. 27, 631 (1971).
[CrossRef]

Cahn, S.

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Chen, J. F.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Du, S.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Fleischhauer, M.

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

Gold, D. G.

D. G. Gold and E. L. Hahn, Phys. Rev. A 16, 324 (1977).
[CrossRef]

Gordon, J. P.

P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

Hahn, E. L.

D. G. Gold and E. L. Hahn, Phys. Rev. A 16, 324 (1977).
[CrossRef]

Harris, S. E.

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

Imamoglu, A.

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

Ishikawa, K.

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

Kim, J.-T.

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Kumarakrishnan, A.

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Lee, H. W. H.

H. W. H. Lee and J. E. Wessel, Phys. Rev. Lett. 59, 1416 (1987).
[CrossRef]

Liao, P. F.

P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

Loy, M. M. T.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

M. M. T. Loy, Phys. Rev. Lett. 36, 1454 (1976).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Marangos, J. P.

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

Shim, U.

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Shoemaker, R. L.

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972).
[CrossRef]

R. G. Brewer and R. L. Shoemaker, Phys. Rev. Lett. 27, 631 (1971).
[CrossRef]

Sleator, T.

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Takahashi, Y.

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

Toyoda, K.

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

Wang, S.

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Wei, D.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Wessel, J. E.

H. W. H. Lee and J. E. Wessel, Phys. Rev. Lett. 59, 1416 (1987).
[CrossRef]

Wong, G. K. L.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

Yabuzaki, T.

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

J. Appl. Phys. (1)

U. Shim, S. Cahn, A. Kumarakrishnan, T. Sleator, and J.-T. Kim, J. Appl. Phys. 41, 3688 (2002).
[CrossRef]

Phys. Rev. (1)

F. Bloch, Phys. Rev. 70, 460 (1946).
[CrossRef]

Phys. Rev. A (4)

D. G. Gold and E. L. Hahn, Phys. Rev. A 16, 324 (1977).
[CrossRef]

R. G. Brewer and R. L. Shoemaker, Phys. Rev. A 6, 2001 (1972).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

K. Toyoda, Y. Takahashi, K. Ishikawa, and T. Yabuzaki, Phys. Rev. A 56, 1564 (1997).
[CrossRef]

Phys. Rev. Lett. (5)

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

M. M. T. Loy, Phys. Rev. Lett. 36, 1454 (1976).
[CrossRef]

P. F. Liao, J. E. Bjorkholm, and J. P. Gordon, Phys. Rev. Lett. 39, 15 (1977).
[CrossRef]

H. W. H. Lee and J. E. Wessel, Phys. Rev. Lett. 59, 1416 (1987).
[CrossRef]

R. G. Brewer and R. L. Shoemaker, Phys. Rev. Lett. 27, 631 (1971).
[CrossRef]

Phys. Today (1)

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

Rev. Mod. Phys. (1)

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

Other (1)

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. A 81, 033844 (2010).

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Figures (3)

Fig. 1
Fig. 1

Schematics of Rb 85 energy levels for (a1) on-resonance and (b1) off-resonance EIT systems. (a2) and (b2) are, respectively, the measured on-resonance and off-resonance EIT transmission as functions of the two-photon detuning δ, taken at an optical depth α 0 L = 2 and coupling Rabi frequency Ω c = 1.4 γ 13 .

Fig. 2
Fig. 2

Two-photon FIDs with on-resonance ( Δ = 0 ) EIT excited by a weak square probe pulse driven by different coupling laser powers at an optical depth α 0 L = 2 .

Fig. 3
Fig. 3

Two-photon FIDs with off-resonance ( Δ = 2 π × 10 MHz ) EIT excited by a weak square probe pulse at α 0 L = 2 and Ω c = 1.4 γ 13 .

Equations (4)

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

a ˙ 2 = γ 12 a 2 + i Ω c * 2 a 3 , a ˙ 3 = i Ω p 2 + i Ω c 2 a 2 + i ( Δ + i γ 13 ) a 3 ,
E p ( z , t ) z + 1 c E p ( z , t ) t = i 2 ω p c ε 0 P ( z , t ) ,
a 3 ( t > 0 ) = i Ω p Ω e sin ( Ω e t 2 ) e ( γ 13 + γ 12 ) t / 2 ,
E fid ( t ) i ω p L 2 c ε 0 P ( t ) = α 0 L γ 13 Ω e E 0 Θ ( t ) sin ( Ω e t 2 ) e ( γ 13 + γ 12 ) t / 2 ,

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