Abstract

We report on the simultaneous observation, by delayed Bragg diffraction, of four- and six-wave mixing processes in a coherently prepared atomic ensemble consisting of cold cesium atoms. For each diffracted order, we observe different temporal pulse shapes and dependencies with the intensities of the exciting fields, evidencing the different mechanisms involved in each process. The various observations are well described by a simplified analytical theory, which considers the atomic system as an ensemble of three-level atoms in Λ configuration.

© 2010 Optical Society of America

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    [CrossRef]
  2. E. Arimondo, in Progress in Optics XXXV (Elsevier, 1996), Vol. 35, pp. 257–354.
    [CrossRef]
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  4. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
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  7. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
    [CrossRef] [PubMed]
  8. V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
    [CrossRef] [PubMed]
  9. G. C. Cardoso and J. W. R. Tabosa, Opt. Commun. 210, 271 (2002).
    [CrossRef]
  10. H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
    [CrossRef] [PubMed]
  11. Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
    [CrossRef] [PubMed]
  12. B. Ham, Phys. Rev. A 78, 011808(R) (2008).
    [CrossRef]
  13. C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
    [CrossRef] [PubMed]
  14. D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
    [CrossRef]
  15. D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
    [CrossRef]
  16. D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
    [CrossRef]
  17. G. J. Butterworth, J. Phys. E 1, 1165 (1968).
    [CrossRef]

2010 (2)

D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
[CrossRef]

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

2009 (1)

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

2008 (2)

B. Ham, Phys. Rev. A 78, 011808(R) (2008).
[CrossRef]

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

2007 (2)

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

2006 (1)

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2004 (1)

H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

2003 (1)

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

2002 (2)

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

G. C. Cardoso and J. W. R. Tabosa, Opt. Commun. 210, 271 (2002).
[CrossRef]

2000 (1)

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. At. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

1995 (1)

1968 (1)

G. J. Butterworth, J. Phys. E 1, 1165 (1968).
[CrossRef]

Anderson, B.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

Arimondo, E.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

E. Arimondo, in Progress in Optics XXXV (Elsevier, 1996), Vol. 35, pp. 257–354.
[CrossRef]

Belthangady, C.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Boyer, V.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Butterworth, G. J.

G. J. Butterworth, J. Phys. E 1, 1165 (1968).
[CrossRef]

Cardoso, G. C.

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

G. C. Cardoso and J. W. R. Tabosa, Opt. Commun. 210, 271 (2002).
[CrossRef]

Choi, K. S.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Chou, C.-W.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Crinin-Galomb, M.

de Riedmatten, H.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Deng, H.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Donoghue, J.

Du, S.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Felinto, D.

D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
[CrossRef]

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Fleischhauer, M.

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

Gonzalez, N.

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

Ham, B.

B. Ham, Phys. Rev. A 78, 011808(R) (2008).
[CrossRef]

Harris, S. E.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Hemmer, P. R.

Hernandez, G.

H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Imamoglu, A.

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

Kang, H.

H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Katz, D. P.

Khadka, U.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

Kimble, H. J.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Kolchin, P.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Kumar, P.

Laurat, J.

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Lett, P. D.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Lezama, A.

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

Lukin, M. D.

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. At. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

Marangos, J. P.

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

McCormick, C. F.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Moretti, D.

D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
[CrossRef]

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

Scully, M. O.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. At. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

Shahiar, M. S.

Tabosa, J. W. R.

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
[CrossRef]

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

G. C. Cardoso and J. W. R. Tabosa, Opt. Commun. 210, 271 (2002).
[CrossRef]

Xiao, M.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

Yin, G. Y.

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

Zhu, Y.

H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Adv. At. Mol. Opt. Phys. (1)

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. At. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

Eur. Phys. J. D (1)

D. Moretti, D. Felinto, and J. W. R. Tabosa, Eur. Phys. J. D 60, 373 (2010).
[CrossRef]

J. Phys. B (1)

D. Moretti, D. Felinto, J. W. R. Tabosa, and A. Lezama, J. Phys. B 43, 115502 (2010).
[CrossRef]

J. Phys. E (1)

G. J. Butterworth, J. Phys. E 1, 1165 (1968).
[CrossRef]

Opt. Commun. (1)

G. C. Cardoso and J. W. R. Tabosa, Opt. Commun. 210, 271 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

G. C. Cardoso and J. W. R. Tabosa, Phys. Rev. A 65, 033803 (2002).
[CrossRef]

D. Moretti, N. Gonzalez, D. Felinto, and J. W. R. Tabosa, Phys. Rev. A 78, 023811 (2008).
[CrossRef]

B. Ham, Phys. Rev. A 78, 011808(R) (2008).
[CrossRef]

Phys. Rev. Lett. (4)

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, Phys. Rev. Lett. 102, 013601(2009).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

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

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

Science (1)

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, Science 316, 1316 (2007).
[CrossRef] [PubMed]

Other (1)

E. Arimondo, in Progress in Optics XXXV (Elsevier, 1996), Vol. 35, pp. 257–354.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Zeeman three-level system considered in the theoretical model, indicating the coupling of each state with the respective writing and reading fields. (b) Propagation directions of writing (W, W ), reading (R, R ), and diffracted (FWM, SWM) beams.

Fig. 2
Fig. 2

(a) Measured temporal pulse shapes associated with the delayed FWM and SWM processes. (b) Calculated pulse shapes for I t = 2.8 I s and τ = 0.2 μs , with I s the saturation intensity of the transitions.

Fig. 3
Fig. 3

Retrieved energy associated with the FWM (open squares) and the SWM (filled circles) processes. The solid curves are the theoretical curves from Eqs. (2a, 2b) with I t = 2.2 I s . Both theoretical and experimental curves were normalized by the maximum retrieved energy U max , corresponding to the FWM pulse at I R = I t . For the experiment, we had U max = 1.3 pJ .

Equations (4)

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

σ M F 1 , M F ( t ) | Ω R | e γ t s I t Γ [ f r ( t ) I R + g r ( t ) I R ] × e i ( k R + k W k W ) · r ,
σ M F + 1 , M F ( t ) I R | Ω R | e γ t s I t Γ [ f r ( t ) g r ( t ) ] × e i ( 2 k R k R + k W k W ) · r ,
U FWM I R ( I t ) 2 0 | f r ( t ) I R + g r ( t ) I R | 2 d t ,
U SWM I R ( I R ) 2 ( I t ) 2 0 | f r ( t ) g r ( t ) | 2 d t .

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