Abstract

Nondegenerate four-wave mixing is analyzed with respect to biexcitonic contributions in the third-order nonlinear susceptibility χ3. The presence of biexcitons causes a distinct asymmetry in the frequency dependence of self-diffraction. By measurement of the dependence of the intensity of the self-diffracted signal on detuning between the two incident laser beams, the biexciton binding energy is determined to be EXX=7.8 meV for cadmium sulfur quantum dots of R=7.5 nm embedded in glass. Thus, even for weakly confined II–VI quantum dots with R2.7aB, a confinement-induced enhancement of EXX was found.

© 1998 Optical Society of America

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References

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  1. U. Woggon, Optical Properties of Semiconductor Quantum Dots, Vol.??136 of Springer Tracts in Modern Physics (Springer, New York, 1997).
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    [CrossRef]
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    [CrossRef]
  5. E. L. Pollock and S. W. Koch, J. Chem. Phys. 94, 6776 (1991).
    [CrossRef]
  6. R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
    [CrossRef]
  7. U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
    [CrossRef]
  8. Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
    [CrossRef]
  9. S. V. Nair and T. Takagahara, Phys. Rev. B 53, R10516 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. E. Hanamura, Phys. Rev. B 46, 4718 (1992).
    [CrossRef]
  12. U. Woggon and M. Portuné, Phys. Rev. B 51, 4719 (1995).
    [CrossRef]
  13. J. R. Taylor, Error Analysis (VCH, Deerfield Beach, Fla., 1988).
  14. T. Bäck and H.-P. Schwefel, IEEE Trans. Evolutionary Computation 1, 3 (1993).
    [CrossRef]

1996 (2)

S. V. Nair and T. Takagahara, Phys. Rev. B 53, R10516 (1996).
[CrossRef]

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

1995 (1)

U. Woggon and M. Portuné, Phys. Rev. B 51, 4719 (1995).
[CrossRef]

1994 (2)

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
[CrossRef]

1993 (1)

T. Bäck and H.-P. Schwefel, IEEE Trans. Evolutionary Computation 1, 3 (1993).
[CrossRef]

1992 (1)

E. Hanamura, Phys. Rev. B 46, 4718 (1992).
[CrossRef]

1991 (2)

E. L. Pollock and S. W. Koch, J. Chem. Phys. 94, 6776 (1991).
[CrossRef]

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

1990 (1)

Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

1989 (1)

T. Takagahara, Phys. Rev. B 39, 10206 (1989).
[CrossRef]

1988 (1)

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

Bäck, T.

T. Bäck and H.-P. Schwefel, IEEE Trans. Evolutionary Computation 1, 3 (1993).
[CrossRef]

Banyai, L.

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

Birkedal, D.

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Erland, J.

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Gilliot, P.

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

Gogolin, O.

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Hanamura, E.

E. Hanamura, Phys. Rev. B 46, 4718 (1992).
[CrossRef]

Hönerlage, B.

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

Hu, Y. Z.

Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

Hvam, J. M.

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Katayanagi, S.

Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
[CrossRef]

Klingshirn, C.

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Koch, S. W.

E. L. Pollock and S. W. Koch, J. Chem. Phys. 94, 6776 (1991).
[CrossRef]

Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

Langbein, W.

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Levy, R.

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

Lindberg, M.

Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

Lyssenko, V. G.

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Mager, L.

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

Masumoto, Y.

Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
[CrossRef]

Mishina, T.

Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
[CrossRef]

Nair, S. V.

S. V. Nair and T. Takagahara, Phys. Rev. B 53, R10516 (1996).
[CrossRef]

Pollock, E. L.

E. L. Pollock and S. W. Koch, J. Chem. Phys. 94, 6776 (1991).
[CrossRef]

Portuné, M.

U. Woggon and M. Portuné, Phys. Rev. B 51, 4719 (1995).
[CrossRef]

Schwefel, H.-P.

T. Bäck and H.-P. Schwefel, IEEE Trans. Evolutionary Computation 1, 3 (1993).
[CrossRef]

Singh, J.

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Takagahara, T.

S. V. Nair and T. Takagahara, Phys. Rev. B 53, R10516 (1996).
[CrossRef]

T. Takagahara, Phys. Rev. B 39, 10206 (1989).
[CrossRef]

Taylor, J. R.

J. R. Taylor, Error Analysis (VCH, Deerfield Beach, Fla., 1988).

Wind, O.

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Woggon, U.

U. Woggon and M. Portuné, Phys. Rev. B 51, 4719 (1995).
[CrossRef]

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

U. Woggon, Optical Properties of Semiconductor Quantum Dots, Vol.??136 of Springer Tracts in Modern Physics (Springer, New York, 1997).

IEEE Trans. Evolutionary Computation (1)

T. Bäck and H.-P. Schwefel, IEEE Trans. Evolutionary Computation 1, 3 (1993).
[CrossRef]

J. Chem. Phys. (1)

E. L. Pollock and S. W. Koch, J. Chem. Phys. 94, 6776 (1991).
[CrossRef]

J. Lumin. (1)

U. Woggon, O. Wind, W. Langbein, O. Gogolin, and C. Klingshirn, J. Lumin. 59, 135 (1994).
[CrossRef]

Phys. Rev. B (8)

Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev. B 50, 18658 (1994).
[CrossRef]

S. V. Nair and T. Takagahara, Phys. Rev. B 53, R10516 (1996).
[CrossRef]

R. Levy, L. Mager, P. Gilliot, and B. Hönerlage, Phys. Rev. B 44, 11286 (1991).
[CrossRef]

L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142 (1988).
[CrossRef]

T. Takagahara, Phys. Rev. B 39, 10206 (1989).
[CrossRef]

Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 42, 1713 (1990).
[CrossRef]

E. Hanamura, Phys. Rev. B 46, 4718 (1992).
[CrossRef]

U. Woggon and M. Portuné, Phys. Rev. B 51, 4719 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

D. Birkedal, J. Singh, V. G. Lyssenko, J. Erland, and J. M. Hvam, Phys. Rev. Lett. 76, 672 (1996).
[CrossRef] [PubMed]

Other (2)

J. R. Taylor, Error Analysis (VCH, Deerfield Beach, Fla., 1988).

U. Woggon, Optical Properties of Semiconductor Quantum Dots, Vol.??136 of Springer Tracts in Modern Physics (Springer, New York, 1997).

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Figures (3)

Fig. 1
Fig. 1

Excitation and decay scheme of the multilevel system: Although the excitonic level is completely resonant with the stationary frequency, here denoted by Ω1, the biexcitonic level is off by 2ωXX.

Fig. 2
Fig. 2

Comparison of the response of a two-level system (TLS) and a multilevel system involving the biexciton state EXX. The main parameter is the biexciton binding energy: The smaller the binding energy, the more pronounced is the asymmetry. Note the characteristic minimum on the high-energy side of the detuning. The other parameters are T1=100 ps and T2=67 fs.

Fig. 3
Fig. 3

Experimental data for CdS quantum dots (QDs), where R2.7aB was measured at T=50 T. The inset shows the linear absorption spectrum with the exciting laser beam for zero detuning indicated by an arrow. The numerical fit of the experimental data yields a biexciton binding energy of EXX=7.8 meV (see text).

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