Abstract

We study the influence of shaping the phase of the optical field when time-delayed femtosecond pulse pairs excite a sequential two-photon transition in rubidium atoms. Propagation through this optically dense medium modifies the pulse profile. When an external phase is introduced into one of the pulses, partial cancellation of the two-photon absorption signal is observed for temporal delays much greater than the pulse duration. This behavior is qualitatively explained in terms of a negative group delay.

© 2005 Optical Society of America

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  1. D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
    [CrossRef]
  2. D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
    [CrossRef]
  3. N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).
  4. B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
    [CrossRef]
  5. V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, Phys. Rev. Lett. 78, 2716 (1997).
    [CrossRef]
  6. V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
    [CrossRef]
  7. J. Degert, W. Wohlleben, B. Chatel, M. Motzkus, and B. Girard, Phys. Rev. Lett. 89, 203003 (2002).
    [CrossRef]
  8. D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 25, 917 (2000).
    [CrossRef]
  9. M. Jacquey, S. Bonhommeau, and M. A. Bouchene, Opt. Lett. 28, 1272 (2003).
    [CrossRef] [PubMed]
  10. M. A. Bouchene, Phys. Rev. A 66, 065801 (2002).
    [CrossRef]
  11. J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
    [CrossRef]
  12. D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
    [CrossRef]

2003 (2)

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

M. Jacquey, S. Bonhommeau, and M. A. Bouchene, Opt. Lett. 28, 1272 (2003).
[CrossRef] [PubMed]

2002 (2)

M. A. Bouchene, Phys. Rev. A 66, 065801 (2002).
[CrossRef]

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

2001 (2)

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

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

2000 (1)

1999 (1)

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

1998 (2)

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

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

1997 (1)

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

1984 (1)

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Acioli, L. H.

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

D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 25, 917 (2000).
[CrossRef]

Balant, A. C.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[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]

Bonhommeau, S.

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.

M. Jacquey, S. Bonhommeau, and M. A. Bouchene, Opt. Lett. 28, 1272 (2003).
[CrossRef] [PubMed]

M. A. Bouchene, Phys. Rev. A 66, 065801 (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]

Chatel, B.

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

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

Dayan, B.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

Degert, J.

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

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

Dudovich, N.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

Faeder, S. M. G.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

Felinto, D.

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

D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 25, 917 (2000).
[CrossRef]

Girard, B.

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

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]

Grischkowsky, D.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Jacquey, M.

Meshulach, D.

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

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]

Nicole, C.

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

Rothenberg, J. E.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Silberberg, Y.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

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

Stock, S.

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

Vianna, S. S.

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

D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 25, 917 (2000).
[CrossRef]

Wohlleben, W.

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

J. Chem. Phys. (1)

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

Nature (1)

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

Opt. Lett. (2)

Phys. Rev. A (5)

M. A. Bouchene, Phys. Rev. A 66, 065801 (2002).
[CrossRef]

D. Meshulach and Y. Silberberg, Phys. Rev. A 60, 1287 (1999).
[CrossRef]

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. A 86, 47 (2001).

B. Chatel, J. Degert, S. Stock, and B. Girard, Phys. Rev. A 68, 041402 (2003).
[CrossRef]

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

Phys. Rev. Lett. (3)

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

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

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Two-photon transition 5 S 5 P 5 D , with intermediate one-photon resonance. (b) Spectrum of the femtosecond laser and the assumed phase function ϕ ( ω ) .

Fig. 2
Fig. 2

Diagram of the experimental setup. Fluorescence at 420 nm is collected at 90° from the center of the cell.

Fig. 3
Fig. 3

Experimental results for the 5 S 5 P 5 D transition of Rb atoms at 130 ° C for different positions of the phase plate.

Fig. 4
Fig. 4

Calculated square modulus of the functions f 12 ( τ ) and f 21 ( τ ) for (a) ϕ ( ω ) = 0 and (b) ϕ ( ω ) given by a smooth step function with ω d = ω 21 (the traces have been vertically displaced for better visualization).

Equations (5)

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

E 2 ( ω , z ) = E 1 ( ω , z , τ = 0 ) exp [ i ϕ ( ω ) ] E 0 ( ω , z ) exp [ i ϕ ( ω ) ] .
a 1 3 E T ( ω 21 ) E T ( ω 32 ) i π P E T ( ω ) E T ( ω 31 ω ) ω 21 ω d ω i π P E T ( ω ) E T ( ω 31 ω ) ω 21 ω d ω ,
ρ 33 opt f 12 ( τ ) 2 + f 21 ( τ ) 2 + 2 Re { f 12 ( τ ) f 21 * ( τ ) exp [ i ( ω 21 ω 32 ) τ ] } ,
f 12 ( τ ) = P d ω exp [ i ( ω 21 ω ) τ + i ϕ ( ω 31 ω ) ] × E 0 ( ω , z ) E 0 ( ω 31 ω , z ) ω 21 ω ,
f 21 ( τ ) = P d ω exp [ i ( ω 21 ω ) τ + i ϕ ( ω ) ] × E 0 ( ω , z ) E 0 ( ω 31 ω , z ) ω 21 ω .

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