Abstract

A model for the coherent transport of excitons along linear, one-dimensional arrays of quantum dots accounting for spontaneous emission is presented. The interdot coupling is made by means of the coherent emission and reabsorption of photons. The long-range nature of the coupling leads to nontrivial dynamics in the polarization and in the exciton population with qualitatively different behaviors for chains with periods just less than or just greater than integer multiples of half the wavelength of the optical transition. Biexponential radiative decay of an initially well-localized population is predicted.

© 1995 Optical Society of America

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References

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  1. T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
    [CrossRef]
  2. J. J. Hopfield, Phys. Rev. 112,1555 (1958).
    [CrossRef]
  3. D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
    [CrossRef]
  4. J. S. Avery, Proc. Phys. Soc. 88, 1 (1966).
    [CrossRef]
  5. T. Förster, Z. Naturf. 4a, 321 (1949).
  6. V. M. Agranovich, A. O. Dubovskii, Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (1966) [JETP Lett. 3, 223 (1966)];D. S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
    [PubMed]

1993 (2)

T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
[CrossRef]

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

1966 (2)

J. S. Avery, Proc. Phys. Soc. 88, 1 (1966).
[CrossRef]

V. M. Agranovich, A. O. Dubovskii, Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (1966) [JETP Lett. 3, 223 (1966)];D. S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
[PubMed]

1958 (1)

J. J. Hopfield, Phys. Rev. 112,1555 (1958).
[CrossRef]

1949 (1)

T. Förster, Z. Naturf. 4a, 321 (1949).

Agranovich, V. M.

V. M. Agranovich, A. O. Dubovskii, Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (1966) [JETP Lett. 3, 223 (1966)];D. S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
[PubMed]

Avery, J. S.

J. S. Avery, Proc. Phys. Soc. 88, 1 (1966).
[CrossRef]

Citrin, D. S.

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

Dubovskii, A. O.

V. M. Agranovich, A. O. Dubovskii, Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (1966) [JETP Lett. 3, 223 (1966)];D. S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
[PubMed]

Förster, T.

T. Förster, Z. Naturf. 4a, 321 (1949).

Hanamura, E.

T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
[CrossRef]

Hopfield, J. J.

J. J. Hopfield, Phys. Rev. 112,1555 (1958).
[CrossRef]

Manabe, Y.

T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
[CrossRef]

Tokihiro, T.

T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
[CrossRef]

Phys. Rev. (1)

J. J. Hopfield, Phys. Rev. 112,1555 (1958).
[CrossRef]

Phys. Rev. B (2)

D. S. Citrin, Phys. Rev. B 47, 3832 (1993).
[CrossRef]

T. Tokihiro, Y. Manabe, E. Hanamura, Phys. Rev. B 47, 2019 (1993).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. M. Agranovich, A. O. Dubovskii, Pis’ma Zh. Eksp. Teor. Fiz. 3, 345 (1966) [JETP Lett. 3, 223 (1966)];D. S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
[PubMed]

Proc. Phys. Soc. (1)

J. S. Avery, Proc. Phys. Soc. 88, 1 (1966).
[CrossRef]

Z. Naturf. (1)

T. Förster, Z. Naturf. 4a, 321 (1949).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a quantum-dot chain with period L. The index n labels the quantum dots relative to that marked 0.

Fig. 2
Fig. 2

Exciton population in QD n as a function of scaled time τ assuming that QD n = 0 is initially excited. yex = (a) 0.9π, (b) 1.1π, (c) 1.9π, and (d) 2.1π for n = 0 (solid curve), 1 (long-dashed curve), 2 (short-dashed curve), 5 (dotted–dashed curve). Note that N0(0) = 1.

Fig. 3
Fig. 3

Total exciton population as a function of scaled time τ assuming that QD n = 0 is initially excited. yex = 0.9π (solid curve), 1.1π (long-dashed curve), ∞ (short-dashed curve).

Equations (15)

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D ϕ , α β 1 ( ε ) = ε 2 E ex , α 2 2 E ex , α δ α β Σ ϕ , α β ( ε ) ,
k α , j β ( ε ) = κ 2 b 1 d 3 r 1 d 3 r 2 p k α * ( r 1 ) × [ T r 1 e i κ r ] p j β ( r 2 ) ,
κ 2 T 1 τ e i κ r = κ 2 ( 1 r ^ r ^ ) 1 r e i κ r + ( 1 i κ r ) × ( 1 3 r ^ r ^ ) 1 r 3 e i κ r + 4 π 3 1 δ 3 ( r ) .
[ κ 2 T 1 r e i κ r ] on - site ( 1 3 r ^ r ^ ) 1 r 3 static dipole dipole energy + 4 π 3 1 δ 3 ( r ) depolarization shift i κ 3 2 ( 1 + r ^ r ^ ) single QD radiative width , [ κ 2 T 1 r e i κ r ] intersite = ( 1 i κ r k j ) ( 1 3 r ^ k j r ^ k j ) 1 r k j 3 e i κ r k j short - ranged coupling κ 2 ( 1 r ^ k j r ^ k j ) 1 r k j e i κ r k j long - ranged coupling .
Σ k α , j β ( ε ) = ( Δ k , α β i γ k , α β ) δ k j ξ k α , j β y | k j | × e i y | k j | ( 1 δ k j ) ,
Δ k , α β = b 1 d 3 r 1 d 3 r 2 p k α * ( r 1 ) 1 3 r ^ r ^ r 3 p k β ( r 2 ) + 4 π 3 b 1 d 3 r 1 p k α * ( r 1 ) p k β ( r 1 ) ,
γ k , α β = ½ κ 3 b 1 d 3 r 1 d 3 r 2 p k α * ( r 1 ) × ( 1 + r ^ r ^ ) p j β ( r 2 ) ,
ξ k α , j β = κ 3 b 1 [ d 3 r 1 p k α * ( r 1 ) ] ( 1 r ^ k j r ^ k j ) × [ d 3 r 2 p j β ( r 2 ) ] .
γ = ξ = κ 3 b 1 | d 3 r 1 p k ( r 1 ) | 2 .
Δ = b 1 | F ex ( 0 ) | 2 | e R | 2 × [ 4 π 3 2 d 3 r 1 d 3 r 2 G * ( r 1 ) G ( r 2 ) r 3 ] ,
γ = ξ = b 1 κ 3 | F ex ( 0 ) | 2 | e R | 2 | d 3 r 1 G ( r 1 ) | 2 .
Σ ϕ ( ε ) = Σ k k ( ε ) + γ y log [ 2 e i y ( cos y cos ϕ ) ] .
Im ε ϕ Im Σ ϕ ( E ex + i 0 + ) = γ ( 1 y ¯ ex y ex ) + π γ y ex Θ ( cos ϕ cos y ex ) ,
D n ( t ) = ( 2 i sin y ex ) ν e i E ˜ ex t / e γ t / ( 1 y ¯ ex / y ex ) × Γ ( ν + 1 ) Γ ( ν + n + 1 ) p v n ( i cot y ex ) ,
N ( t ) = 1 π [ y ¯ ex e 2 γ t / [ 1 ( y ¯ ex π ) / y ex ] + ( π y ¯ ex ) e 2 γ t / ( 1 y ¯ ex / y ex ) ] .

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