Abstract

A theory of resonant optical breathers in the presence of single and biexciton transitions in an ensemble of inhomogeneously broadened semiconductor quantum dots is constructed. Explicit analytical expressions for the breather shape and parameters for experimental investigations are proposed.

© 2006 Optical Society of America

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References

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  1. S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
    [CrossRef]
  2. G. T. Adamashvili and S. V. Manakov, Solid State Commun. 48, 381 (1983).
    [CrossRef]
  3. G. T. Adamashvili, Opt. Spektrosk. 176, 1400 (1992).
  4. G. T. Adamashvili, Opt. Spektrosk. 76, 3 (1994).
  5. G. T. Adamashvili, Opt. Spektrosk. 80, 251 (1996).
  6. D. Bimberg, M. Grundmann, and L. Lednetsov, Quantum Dot Heterostructures (Wiley, 1999).
  7. G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
    [CrossRef]
  8. H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
    [CrossRef]
  9. S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
    [CrossRef]
  10. J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
    [CrossRef] [PubMed]
  11. N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
    [CrossRef] [PubMed]
  12. P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
    [CrossRef] [PubMed]
  13. L. Allen and J. N. Eberly, Optical Resonance and Two Level Atoms (Wiley-Interscience, 1975).
  14. T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
    [CrossRef]
  15. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).
  16. V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

2003 (2)

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

2002 (1)

G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
[CrossRef]

2001 (1)

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

1998 (2)

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

1996 (1)

G. T. Adamashvili, Opt. Spektrosk. 80, 251 (1996).

1994 (1)

G. T. Adamashvili, Opt. Spektrosk. 76, 3 (1994).

1992 (1)

G. T. Adamashvili, Opt. Spektrosk. 176, 1400 (1992).

1983 (1)

G. T. Adamashvili and S. V. Manakov, Solid State Commun. 48, 381 (1983).
[CrossRef]

1973 (1)

T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
[CrossRef]

1969 (1)

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Adamashvili, G. T.

G. T. Adamashvili, Opt. Spektrosk. 80, 251 (1996).

G. T. Adamashvili, Opt. Spektrosk. 76, 3 (1994).

G. T. Adamashvili, Opt. Spektrosk. 176, 1400 (1992).

G. T. Adamashvili and S. V. Manakov, Solid State Commun. 48, 381 (1983).
[CrossRef]

Allen, L.

L. Allen and J. N. Eberly, Optical Resonance and Two Level Atoms (Wiley-Interscience, 1975).

Bimberg, D.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

D. Bimberg, M. Grundmann, and L. Lednetsov, Quantum Dot Heterostructures (Wiley, 1999).

Bonadeo, N. H.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Borri, P.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Danckwerts, J.

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

Dodd, R. K.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).

Eberly, J. N.

L. Allen and J. N. Eberly, Optical Resonance and Two Level Atoms (Wiley-Interscience, 1975).

Eilbeck, J. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).

Erland, J.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Forstner, J.

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

Gammon, D.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Gibbon, J. D.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).

Giessen, H.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Grun, M.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Grundmann, M.

D. Bimberg, M. Grundmann, and L. Lednetsov, Quantum Dot Heterostructures (Wiley, 1999).

Haas, S.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Hetterich, M.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Hohenester, U.

G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
[CrossRef]

Iajima, N.

T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
[CrossRef]

Katzer, D. S.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Klingshirn, C.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Knorr, A.

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Koch, S.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Kuhl, J.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Langbein, W.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Lednetsov, L.

D. Bimberg, M. Grundmann, and L. Lednetsov, Quantum Dot Heterostructures (Wiley, 1999).

Linden, S.

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

Manakov, S. V.

G. T. Adamashvili and S. V. Manakov, Solid State Commun. 48, 381 (1983).
[CrossRef]

V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

McCall, S. L.

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Molinari, E.

G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
[CrossRef]

Morris, H. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).

Novikov, S. P.

V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

Ouyang, D.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Panzarini, G.

G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
[CrossRef]

Park, D.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Pitaevski, L. P.

V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

Schneider, S.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Sellin, R.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

Sellin, R. L.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Steel, D. G.

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Taniuti, T.

T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
[CrossRef]

Weber, C.

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

Woggon, U.

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Zaharov, V. E.

V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

Appl. Phys. Lett. (1)

S. Schneider, P. Borri, W. Langbein, U. Woggon, J. Forstner, A. Knorr, R. Sellin, D. Ouyang, and D. Bimberg, Appl. Phys. Lett. 83, 3668 (2003).
[CrossRef]

J. Math. Phys. (1)

T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
[CrossRef]

Opt. Spektrosk. (3)

G. T. Adamashvili, Opt. Spektrosk. 176, 1400 (1992).

G. T. Adamashvili, Opt. Spektrosk. 76, 3 (1994).

G. T. Adamashvili, Opt. Spektrosk. 80, 251 (1996).

Phys. Rev. (1)

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[CrossRef]

Phys. Rev. B (1)

G. Panzarini, U. Hohenester, and E. Molinari, Phys. Rev. B 65, 165322 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

H. Giessen, A. Knorr, S. Haas, S. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grun, and C. Klingshirn, Phys. Rev. Lett. 81, 4260 (1998).
[CrossRef]

J. Forstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003).
[CrossRef] [PubMed]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. 87, 157401 (2001).
[CrossRef] [PubMed]

Science (1)

N. H. Bonadeo, J. Erland, D. Gammon, D. Park, D. S. Katzer, and D. G. Steel, Science 282, 1473 (1998).
[CrossRef] [PubMed]

Solid State Commun. (1)

G. T. Adamashvili and S. V. Manakov, Solid State Commun. 48, 381 (1983).
[CrossRef]

Other (4)

D. Bimberg, M. Grundmann, and L. Lednetsov, Quantum Dot Heterostructures (Wiley, 1999).

L. Allen and J. N. Eberly, Optical Resonance and Two Level Atoms (Wiley-Interscience, 1975).

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, 1982).

V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevski, Teoria Solitonov Metod Obratnoi Zadachi (Nauka, 1980) (in Russian).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the SQD energetic levels.

Fig. 2
Fig. 2

Results of simulations show the time–space dynamics of the strength of the electrical field for the small amplitude breather.

Equations (16)

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

ω T 1 , T T 1 , 2 ,
ω Ω 1 T 1 T 2
i ρ n m t = l ( n H l ρ l m ρ n l l H n ) , n , m , l , = 1 , 2 , 3 .
c 2 2 E + η 2 2 E t 2 + 4 π 2 P t 2 = 0 ,
E = l = ± 1 E ̂ l Z l , ρ 21 = ρ ̂ 21 Z 1 , ρ 32 = ρ ̂ 32 Z 1 ,
Z l = exp [ i l ( k z ω t ) ] ,
k = ± 1 Z l ( 2 i l k c 2 E ̂ z + 2 i l η 2 ω E ̂ t + c 2 2 E ̂ z 2 η 2 2 E ̂ t 2 ) = 4 π ω 2 P .
P = i N μ 12 2 b 3 l = ± 1 l Z l F [ ( 1 ν 2 ) sin 2 b Θ + 4 ν 2 sin b Θ ] ,
Θ ( z , t ) = α = 1 n = + ϵ α Y n F n ( α ) ( ζ , τ ) ,
i l Λ l t + 2 Λ l y 2 + Λ l 2 Λ l = 0 ,
2 κ ω Ω 2 k c 2 Q + κ Ω 2 c 2 Q 2 R Ω = 0 ,
p = c 2 κ v 2 + v 2 R Ω 3 2 κ ( ω + Ω + R 2 κ Ω 2 ) ,
q = R 2 κ Ω ( ω + Ω + R 2 κ Ω 2 ) , R = 4 π ω 2 μ 12 2 N F .
Θ = 4 η 0 q sin ( Ω t Q z + φ 1 ) cosh 2 η 0 φ 2 ,
φ 1 = 2 ξ 0 z p + 2 [ 2 ( ξ 0 2 η 0 2 ) ξ 0 v p ] t φ 0 ,
φ 2 = z p + ( 4 ξ 0 v p ) t y 0 .

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