Abstract

In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.

© 2013 Optical Society of America

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  1. R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
    [CrossRef]
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    [CrossRef]
  3. V. Vaičaitis and Š. Paulikas, Opt. Commun. 247, 187 (2005).
    [CrossRef]
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    [CrossRef]
  5. K. Hartinger and R. Bartels, Appl. Phys. Lett. 93, 151102 (2008).
    [CrossRef]
  6. R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
    [CrossRef]
  7. K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
    [CrossRef]
  8. V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
    [CrossRef]
  9. D. J. Jackson and J. J. Wynne, Phys. Rev. Lett. 49, 543 (1982).
    [CrossRef]
  10. M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
    [CrossRef]
  11. L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. A. Gogyan and Yu. Malakyan, Phys. Rev. A 78, 053401 (2008).
    [CrossRef]
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    [CrossRef]
  16. O. Kinrot and Y. Prior, Phys. Rev. A 50, R1999 (1994).
    [CrossRef]
  17. H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
    [CrossRef]
  18. M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
    [CrossRef]
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    [CrossRef]
  20. G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
    [CrossRef]

2013 (1)

L. Deng, C. Zhu, and E. W. Hagley, Phys. Rev. Lett. 110, 210401 (2013).
[CrossRef]

2012 (1)

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

2010 (1)

2009 (2)

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
[CrossRef]

2008 (3)

K. Hartinger and R. Bartels, Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

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

2006 (1)

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

2005 (1)

V. Vaičaitis and Š. Paulikas, Opt. Commun. 247, 187 (2005).
[CrossRef]

2002 (1)

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

1999 (1)

E. J. Brown, Q. G. Zhang, and M. Dantus, J. Chem. Phys. 110, 5772 (1999).
[CrossRef]

1998 (2)

M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
[CrossRef]

H. C. Tran, P. C. John, J. Gao, and J. G. Eden, Opt. Lett. 23, 70 (1998).
[CrossRef]

1996 (1)

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

1994 (1)

O. Kinrot and Y. Prior, Phys. Rev. A 50, R1999 (1994).
[CrossRef]

1991 (1)

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

1984 (1)

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

1982 (1)

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

1973 (1)

R. B. Miles and S. E. Harris, IEEE J. Quantum Electron. 9, 470 (1973).
[CrossRef]

Acioli, L. H.

Ariunbold, G. O.

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Aumiler, D.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Ban, T.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Bartels, R.

K. Hartinger and R. Bartels, Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

Baumert, T.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

Bayer, T.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Boyd, R. W.

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

Brown, E. J.

E. J. Brown, Q. G. Zhang, and M. Dantus, J. Chem. Phys. 110, 5772 (1999).
[CrossRef]

Dantus, M.

E. J. Brown, Q. G. Zhang, and M. Dantus, J. Chem. Phys. 110, 5772 (1999).
[CrossRef]

de Vivie-Riedle, R.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Deng, L.

L. Deng, C. Zhu, and E. W. Hagley, Phys. Rev. Lett. 110, 210401 (2013).
[CrossRef]

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
[CrossRef]

Eden, J. G.

Ferraz, J.

Gaeta, L.

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Gao, J.

Garrett, W. R.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
[CrossRef]

Gauthier, D. J.

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

Gerber, G.

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

Gogyan, A.

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

Grosser, M.

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

Hagley, E. W.

L. Deng, C. Zhu, and E. W. Hagley, Phys. Rev. Lett. 110, 210401 (2013).
[CrossRef]

Harris, S. E.

R. B. Miles and S. E. Harris, IEEE J. Quantum Electron. 9, 470 (1973).
[CrossRef]

Hartinger, K.

K. Hartinger and R. Bartels, Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

Homoelle, D.

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Ivanov, S. S.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Jackson, D. J.

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

Jarutis, V.

V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
[CrossRef]

John, P. C.

Kinrot, O.

O. Kinrot and Y. Prior, Phys. Rev. A 50, R1999 (1994).
[CrossRef]

Kobe, K.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Krasinski, J.

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

Krug, M.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Malakyan, Yu.

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

Malcuit, M. S.

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

Manz, J.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Meyer, W.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Miles, R. B.

R. B. Miles and S. E. Harris, IEEE J. Quantum Electron. 9, 470 (1973).
[CrossRef]

Moll, K. D.

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Paulikas, Š.

V. Vaičaitis and Š. Paulikas, Opt. Commun. 247, 187 (2005).
[CrossRef]

Payne, M. G.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
[CrossRef]

Pentaris, D.

V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
[CrossRef]

Pichler, G.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Prior, Y.

O. Kinrot and Y. Prior, Phys. Rev. A 50, R1999 (1994).
[CrossRef]

Reischl, B.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Rutz, S.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Sarpe-Tudoran, C.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Sautenkov, V. A.

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Schreiber, E.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Scully, M. O.

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Skenderovic, H.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Sokolov, A. V.

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Thalweiser, R.

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

Tran, H. C.

Vaicaitis, V.

V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
[CrossRef]

V. Vaičaitis and Š. Paulikas, Opt. Commun. 247, 187 (2005).
[CrossRef]

Vdovic, S.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Vianna, S. S.

Vitanov, N. V.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Vujicic, N.

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

Wollenhaupt, M.

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Wöste, L.

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

Wynne, J. J.

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

Yang, W.

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Zhang, Q. G.

E. J. Brown, Q. G. Zhang, and M. Dantus, J. Chem. Phys. 110, 5772 (1999).
[CrossRef]

Zhu, C.

L. Deng, C. Zhu, and E. W. Hagley, Phys. Rev. Lett. 110, 210401 (2013).
[CrossRef]

Appl. Phys. Lett. (1)

K. Hartinger and R. Bartels, Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. W. Boyd, D. J. Gauthier, J. Krasinski, and M. S. Malcuit, IEEE J. Quantum Electron. 20, 1074 (1984).
[CrossRef]

R. B. Miles and S. E. Harris, IEEE J. Quantum Electron. 9, 470 (1973).
[CrossRef]

J. Chem. Phys. (1)

E. J. Brown, Q. G. Zhang, and M. Dantus, J. Chem. Phys. 110, 5772 (1999).
[CrossRef]

J. Phys. Chem. (1)

R. de Vivie-Riedle, K. Kobe, J. Manz, W. Meyer, B. Reischl, S. Rutz, E. Schreiber, and L. Wöste, J. Phys. Chem. 100, 7789 (1996).
[CrossRef]

New J. Phys. (1)

M. Krug, T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, S. S. Ivanov, and N. V. Vitanov, New J. Phys. 11, 105051 (2009).
[CrossRef]

Opt. Commun. (2)

M. G. Payne, L. Deng, and W. R. Garrett, Opt. Commun. 146, 257 (1998).
[CrossRef]

V. Vaičaitis and Š. Paulikas, Opt. Commun. 247, 187 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (1)

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

Phys. Rev. A (4)

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

O. Kinrot and Y. Prior, Phys. Rev. A 50, R1999 (1994).
[CrossRef]

H. Skenderović, T. Ban, N. Vujičić, D. Aumiler, S. Vdović, and G. Pichler, Phys. Rev. A 77, 063816 (2008).
[CrossRef]

G. O. Ariunbold, W. Yang, A. V. Sokolov, V. A. Sautenkov, and M. O. Scully, Phys. Rev. A 85, 023424 (2012).
[CrossRef]

Phys. Rev. Lett. (5)

L. Deng, C. Zhu, and E. W. Hagley, Phys. Rev. Lett. 110, 210401 (2013).
[CrossRef]

T. Baumert, M. Grosser, R. Thalweiser, and G. Gerber, Phys. Rev. Lett. 67, 3753 (1991).
[CrossRef]

K. D. Moll, D. Homoelle, L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

V. Vaičaitis, V. Jarutis, and D. Pentaris, Phys. Rev. Lett. 103, 103901 (2009).
[CrossRef]

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

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Figures (5)

Fig. 1.
Fig. 1.

Upper left: picture of beam spots after the interaction with sodium when all input beams arrive simultaneously and beam intensities are at maximum. Positions 1, 2, and 3 depict the original beam, and all others are generated by various mixing processes. Upper right: scheme of the beams. Lower: scheme for generation of UV beams at intermediate positions as a result of mixing of photons from two beams. UV spots are oriented in 2k1+k2, 2k2+k1,, etc. directions.

Fig. 2.
Fig. 2.

Upper row: Feynman diagrams for negative delays. Lower row: diagrams for positive delays, the first one representing time development of the excited state while the second and third representing development of the ground state.

Fig. 3.
Fig. 3.

Energy-level diagram of sodium with indicated three-photon resonances, which generate the wave-mixing signal in the UV.

Fig. 4.
Fig. 4.

Excitation power dependence of time-resolved transient grating signal at 268 nm observed for 804 nm excitation. Average pulse energy per input beam is indicated. N(Na)=6.2×1015cm3.

Fig. 5.
Fig. 5.

Time and frequency-resolved transient grating signal around 285 nm for 856 nm excitation (a) and single wavelength trace (b). The inset in (b) shows sudden disappearance of the signal for positive delay times. N(Na)=9.9×1015cm3.

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