Abstract

We report the observation of the interferometric response in parametric four-wave mixing in rubidium atoms excited by a pair of ultrashort pulses. For pulses with orthogonal polarizations and in the presence of the two-photon transition 5S–5D reveals a one-photon quantum interference, in contrast to the optical interference observed when the pulses have parallel polarization. For opposite circular polarizations no interference is observed in the fluorescence of the two-photon transition, in contrast to the one- and two-photon interferences exhibited in the nonlinear process.

© 2010 Optical Society of America

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  1. N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).
    [CrossRef] [PubMed]
  2. N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
    [CrossRef] [PubMed]
  3. T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).
  4. V. Blanchet, M. A. Bouchene, and B. Girard, J. Chem. Phys. 108, 4862 (1998).
    [CrossRef]
  5. H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
    [CrossRef]
  6. J. Ferraz, D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 30, 1876 (2005).
    [CrossRef] [PubMed]
  7. J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
    [CrossRef] [PubMed]
  8. Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
    [CrossRef]
  9. A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
    [CrossRef]
  10. D. Felinto, C. A. C. Bosco, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 64, 063413 (2001).
    [CrossRef]
  11. D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).
    [CrossRef]
  12. W. C. Magno, R. B. Prandini, P. Nussenzveig, and S. S. Vianna, Phys. Rev. A 63, 063406 (2001).
    [CrossRef]

2008 (1)

A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
[CrossRef]

2006 (1)

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

2005 (1)

2004 (3)

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).
[CrossRef]

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

2001 (3)

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

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]

2000 (1)

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

1998 (1)

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

1995 (1)

J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
[CrossRef] [PubMed]

Acioli, L. H.

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

J. Ferraz, D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 30, 1876 (2005).
[CrossRef] [PubMed]

D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).
[CrossRef]

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

Allen, J. R.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Barros, H. G.

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

Blanchet, V.

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

Brownell, J. H.

J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
[CrossRef] [PubMed]

Dayan, B.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

Dudovich, N.

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

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

Eden, J. G.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Faeder, S. M. G.

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

Felinto, D.

J. Ferraz, D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 30, 1876 (2005).
[CrossRef] [PubMed]

D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).
[CrossRef]

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

Ferraz, J.

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

J. Ferraz, D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 30, 1876 (2005).
[CrossRef] [PubMed]

Gao, J.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Girard, B.

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

Gogyan, A.

A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
[CrossRef]

Hartmann, S. R.

J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
[CrossRef] [PubMed]

Hornung, T.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Kompa, K. L.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Lozano, W.

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

Lu, X.

J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
[CrossRef] [PubMed]

Lu, Z. H.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Magno, W. C.

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

Malakyan, Yu.

A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
[CrossRef]

Meier, R.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Motzkus, M.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Nussenzveig, P.

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

Oron, D.

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

Prandini, R. B.

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

Proch, D.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Senin, A. A.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Silberberg, Y.

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

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

Vianna, S. S.

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

J. Ferraz, D. Felinto, L. H. Acioli, and S. S. Vianna, Opt. Lett. 30, 1876 (2005).
[CrossRef] [PubMed]

D. Felinto, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 70, 043403 (2004).
[CrossRef]

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

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

Zeidler, D.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

Zhu, C. J.

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

Appl. Phys. B (1)

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Proch, and M. Motzkus, Appl. Phys. B 71, 277 (2000).

IEEE J. Sel. Top. Quantum Electron. (1)

Z. H. Lu, C. J. Zhu, A. A. Senin, J. R. Allen, J. Gao, and J. G. Eden, IEEE J. Sel. Top. Quantum Electron. 10, 159 (2004).
[CrossRef]

J. Chem. Phys. (1)

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

Opt. Lett. (1)

Phys. Rev. A (5)

H. G. Barros, J. Ferraz, W. Lozano, L. H. Acioli, and S. S. Vianna, Phys. Rev. A 74, 055402 (2006).
[CrossRef]

A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
[CrossRef]

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, Phys. Rev. A 70, 043403 (2004).
[CrossRef]

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

Phys. Rev. Lett. (3)

J. H. Brownell, X. Lu, and S. R. Hartmann, Phys. Rev. Lett. 75, 3265 (1995).
[CrossRef] [PubMed]

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

N. Dudovich, B. Dayan, S. M. G. Faeder, and Y. Silberberg, Phys. Rev. Lett. 86, 47 (2001).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Rb energy levels. (b) Experimental setup. The fluorescence is collected at 90°, while the PFWM signal is collected in the forward direction; both at λ s = 420 nm .

Fig. 2
Fig. 2

Fluorescence for pulse pairs delayed by τ = 0 ps and τ = 45 ps with (a) parallel polarizations, (b) linear orthogonal polarizations, and (c) opposite circular polarizations.

Fig. 3
Fig. 3

PFWM for pulse pairs delayed by τ = 0 ps and τ = 45 ps with (a) parallel polarizations, (b) linear orthogonal polarizations and (c) opposite circular polarizations.

Fig. 4
Fig. 4

Examples of two-photon paths for orthogonal (a) and opposite circular (b) polarizations.

Equations (5)

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

| ρ 13 ( τ ) | 2 | F α α ( 0 ) + e i ω 21 τ F α β ( τ ) + e i ω 32 τ F β α ( τ ) + e i ω 31 τ F ( 0 ) β β | 2 .
F α β ( τ ) = μ 12 , α μ 23 , β 2 d t t + τ d t × e i ω 32 t e i ω 21 t E α ( t ) E β ( t ) ,
ρ 33 ( t ) e t T 33 m | ρ 13 m ( 2 ) | 2 .
P ( 3 ) ( ω s = 2 ω L ω i ) Tr [ μ ρ ( 3 ) ] = μ 41 ρ 14 ( 3 ) + c.c .
I PFWM | m ρ 13 m ( 2 ) | 2 .

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