Abstract

Pairs of pulses from an incoherent source are used to investigate the time-resolved four-wave mixing response of atomic rubidium when a two-photon resonance is involved in the nonlinear process. By varying the relative polarization of the pulse pairs, we are able to select the quantum pathways and clearly distinguish optical and quantum interferences.

© 2005 Optical Society of America

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References

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  1. R. N. Zare, Science 279, 1875 (1998).
    [CrossRef] [PubMed]
  2. D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
    [CrossRef]
  3. V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
    [CrossRef]
  4. D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
    [CrossRef]
  5. D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
    [CrossRef]
  6. J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
    [CrossRef]
  7. N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
    [CrossRef]
  8. V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
    [CrossRef]
  9. J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
    [CrossRef] [PubMed]
  10. D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
    [CrossRef]
  11. T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
    [CrossRef]
  12. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
    [CrossRef]
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    [CrossRef]
  14. W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
    [CrossRef]
  15. D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
    [CrossRef] [PubMed]

2004 (3)

N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
[CrossRef]

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

2002 (3)

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

2001 (2)

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

1998 (4)

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
[CrossRef]

R. N. Zare, Science 279, 1875 (1998).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

1997 (1)

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

1988 (1)

D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

1982 (1)

D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
[CrossRef]

Acioli, L. H.

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

Baumert, T.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Blanchet, V.

V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
[CrossRef]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Bosco, C. A.C.

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

Bouchene, M. A.

V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
[CrossRef]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Brixner, T.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Chatel, B.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

Cogdell, R. J.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

Dayan, B.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

DeBeer, D.

D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

Degert, J.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
[CrossRef]

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

Felinto, D.

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

Friesem, A. A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

Gerber, G.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Girard, B.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
[CrossRef]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Graefe, O.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Hartmann, S. R.

D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

Herek, J. L.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

Horn, C.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Jackson, D. J.

D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
[CrossRef]

Krampert, G.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Liese, D.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Magno, W. C.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Motzkus, M.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

Nicole, C.

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

Nussenzveig, P.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
[CrossRef]

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

Pe’er, A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

Pfeifer, T.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Prandini, R. B.

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

Selle, R.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
[CrossRef]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Tabosa, J. W.R.

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

Usadi, E.

D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

Vianna, S. S.

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

Wohlleben, W.

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

Wollenhaupt, M.

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

Wynne, J. J.

D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
[CrossRef]

Yelin, D.

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

Zare, R. N.

R. N. Zare, Science 279, 1875 (1998).
[CrossRef] [PubMed]

Zeidler, D.

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
[CrossRef]

Nature (2)

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, and M. Motzkus, Nature 417, 533 (2002).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Phys. Rev. A (4)

D. Felinto, C. A.C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
[CrossRef]

D. Oron, N. Dudovich, D. Yelin, and Y. Silberberg, Phys. Rev. A 65, 043408 (2002).
[CrossRef]

S. S. Vianna, P. Nussenzveig, W. C. Magno, and J. W.R. Tabosa, Phys. Rev. A 58, 3000 (1998).
[CrossRef]

W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
[CrossRef]

Phys. Rev. Lett. (7)

D. DeBeer, E. Usadi, and S. R. Hartmann, Phys. Rev. Lett. 60, 1262 (1988).
[CrossRef] [PubMed]

D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
[CrossRef]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
[CrossRef]

T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, Phys. Rev. Lett. 92, 208301 (2004).
[CrossRef]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef]

J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
[CrossRef]

N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
[CrossRef]

Science (1)

R. N. Zare, Science 279, 1875 (1998).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Relevant rubidium energy levels diagram of the FWM process. (b) Outline of the experimental setup.

Fig. 2
Fig. 2

FWM spectrum for λ dye = 602.5 nm and spectrometer resolution of 2 cm 1 . The solid curve is the theoretical fit based on Eqs. (3, 4, 5) for τ = 0 .

Fig. 3
Fig. 3

FWM signal as a function of τ for three polarization configurations. (a) E ( t ) E ( t + τ ) and E 4 E IR , (b) all beams have parallel polarizations, (c) and (d) E ( t ) E ( t + τ ) and E 4 E IR .

Fig. 4
Fig. 4

Possible paths for the two-photon absorption when (a) all polarizations are parallel and when delayed pulses have perpendicular polarizations and the signal is detected (b) parallel and (c) perpendicular to the polarization of the IR .

Equations (5)

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

P ( 3 ) ( ω 4 ) = ϵ 0 d ω 1 d ω 2 d ω 3 χ ( 3 ) ( ω 4 ; ω 1 , ω 2 , ω 3 ) E ( ω 1 ) E ( ω 2 ) E * ( ω 3 ) δ ( ω 1 + ω 2 ω 3 ω 4 ) ,
E ( ω i , τ ) = E ( ω i ) [ e ̂ a + e ̂ b exp ( i ω i τ ) ] , i = 1 , 2 ,
I ( τ ) I 3 I dye 2 exp [ ( 2 ω L ω 3 ω 4 ) 2 4 α 2 ] [ A ( τ ) B ] ( ω 4 ω a b ) 2 + ( γ a b ) 2 d ω 4 ,
A ( τ ) = { 2 + 4 exp ( α 2 τ 2 4 ) cos [ ( ω 3 + ω 4 ) τ 2 ] + cos [ ( ω 3 + ω 4 ) τ ] + exp [ α 2 τ 2 ] } ,
B = { 1 ( ω 3 + ω 4 ω a c ) 2 + γ a c 2 + R 2 ( ω 3 + ω 4 ω a d ) 2 + γ a d 2 + 2 R [ ( ω 3 + ω 4 ω a c ) ( ω 3 + ω 4 ω a d ) γ a c γ a d ] [ ( ω 3 + ω 4 ω a d ) 2 + γ a d 2 ] [ ( ω 3 + ω 4 ω a c ) 2 + γ a c 2 ] } ,

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