Abstract

The spontaneous emission (SE) of quantum dot (QD) excitons into surface plasmons in a cylindrical nanowire is investigated theoretically. Maxwell’s equations with appropriate boundary conditions are solved numerically to obtain the dispersion relations of surface plasmons. The SE rate of QD excitons is found to be greatly enhanced at certain values of the exciton bandgap. Application in generation of remote entangled states via superradiance is also pointed out and may be observable with current technology.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. H. Ritchie, Phys. Rev. 106, 874 (1957).
    [CrossRef]
  2. H. A. Atwater, Sci. Am. 296, 56 (2007).
    [CrossRef] [PubMed]
  3. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
    [CrossRef]
  4. R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
    [CrossRef]
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  6. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, Opt. Lett. 22, 475 (1997).
    [CrossRef] [PubMed]
  7. H. F. Arnoldus and T. F. George, Phys. Rev. A 37, 761 (1988).
    [CrossRef] [PubMed]
  8. A. Neogi, H. Morkoç, T. Kuroda, and A. Tackeuchi, Opt. Lett. 30, 93 (2005).
    [CrossRef] [PubMed]
  9. R. Paiella, Appl. Phys. Lett. 87, 111104 (2005).
    [CrossRef]
  10. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
    [CrossRef] [PubMed]
  11. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
    [CrossRef]
  12. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  13. From the numerical results, the imaginary parts of ω for the bound modes are actually very small (10−4~10−5 of the real parts).
  14. In fact, the exciton eventually decays into free space. Since the coupling to the surface plasmons is so strong, one can roughly neglect the effect from vacuum fluctuations in the regime of t<1/γ0.
  15. Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
    [CrossRef] [PubMed]
  16. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
    [CrossRef] [PubMed]

2007 (4)

R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
[CrossRef]

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

2006 (1)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

2005 (2)

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
[CrossRef] [PubMed]

1997 (1)

1988 (1)

H. F. Arnoldus and T. F. George, Phys. Rev. A 37, 761 (1988).
[CrossRef] [PubMed]

1974 (1)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
[CrossRef]

1957 (1)

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

Arnoldus, H. F.

H. F. Arnoldus and T. F. George, Phys. Rev. A 37, 761 (1988).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Brandes, T.

Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
[CrossRef] [PubMed]

Brongersma, M. L.

R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
[CrossRef]

Chang, D. E.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Chen, Y. N.

Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
[CrossRef] [PubMed]

Chuu, D. S.

Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
[CrossRef] [PubMed]

Demler, E. A.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
[CrossRef]

George, T. F.

H. F. Arnoldus and T. F. George, Phys. Rev. A 37, 761 (1988).
[CrossRef] [PubMed]

Hemmer, P. R.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Kobayashi, T.

Kuroda, T.

Lukin, M. D.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Morimoto, A.

Morkoç, H.

Mukherjee, A.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

Neogi, A.

Ngai, K. L.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
[CrossRef]

Paiella, R.

R. Paiella, Appl. Phys. Lett. 87, 111104 (2005).
[CrossRef]

Park, H.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

Pfeiffer, C. A.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Tackeuchi, A.

Takahara, J.

Taki, H.

Yamagishi, S.

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

Zia, R.

R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
[CrossRef]

Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

R. Paiella, Appl. Phys. Lett. 87, 111104 (2005).
[CrossRef]

Nat. Nanotechnol. (1)

R. Zia and M. L. Brongersma, Nat. Nanotechnol. 2, 426 (2007).
[CrossRef]

Nat. Phys. (1)

D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, Nat. Phys. 3, 807 (2007).
[CrossRef]

Nature (2)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. (1)

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Phys. Rev. A (1)

H. F. Arnoldus and T. F. George, Phys. Rev. A 37, 761 (1988).
[CrossRef] [PubMed]

Phys. Rev. B (1)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, Phys. Rev. B 10, 3038 (1974).
[CrossRef]

Phys. Rev. Lett. (2)

Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
[CrossRef] [PubMed]

Sci. Am. (1)

H. A. Atwater, Sci. Am. 296, 56 (2007).
[CrossRef] [PubMed]

Other (3)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

From the numerical results, the imaginary parts of ω for the bound modes are actually very small (10−4~10−5 of the real parts).

In fact, the exciton eventually decays into free space. Since the coupling to the surface plasmons is so strong, one can roughly neglect the effect from vacuum fluctuations in the regime of t<1/γ0.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Schematic view of the model; a silver nanowire is embedded inside GaN material and a colloidal QD is put on top of it. (b)–(d) Dispersion relations of surface plasmons for the modes n = 0 , 1, and 2, respectively. The solid (dashed) curves represent the bound (nonbound) modes. The units for vertical and horizontal lines are Ω = ω ω p and K = k z c ω p .

Fig. 2
Fig. 2

SE rates ( Γ sp ) into n = 0 3 modes for (a) R = 0.1 and (b) R = 0.5 . The unit of Γ sp is normalized to free-space decay rate ( γ 0 ) .

Fig. 3
Fig. 3

Variations of Re [ b 2 ( t ) ] , Im [ b 2 ( t ) ] , and b 2 ( t ) 2 [inset of (a)] as functions of time for ω 0 = 0.602 ω p (solid curves) and 0.748 ω p (dashed–dotted curves). In plotting the figures, the interdot distance z 0 is set equal to 0.35 ( ω p a c ) with radius R = 0.1 . The dashed curves in (a) and (b) are the results for ω 0 = 0.602 ω p with the inclusion of the contributions from other channels: the free-space decay rate Γ f ( = γ 0 ) and nonradiative decay rate Γ non ( γ 0 ) .

Equations (4)

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

S ( k z , ω ) = [ μ I K I a J n ( K I a ) J n ( K I a ) μ O K O a H n ( 1 ) ( K O a ) H n ( 1 ) ( K O a ) ] [ ( ω c ) 2 ε I ( ω ) μ I K I a J n ( K I a ) J n ( K I a ) ( ω c ) 2 ε O ( ω ) μ O K O a H n ( 1 ) ( K O a ) H n ( 1 ) ( K O a ) ] n 2 k z 2 [ 1 ( K O a ) 2 1 ( K I a ) 2 ] 2 = 0 ,
Γ sp = 2 π n = 0 k z i d E ρ ( k z i ) 2 d ( ω 0 ω k z ) d k z k z i ,
Ψ ( t ) = b 1 ( t ) ; 0 + b 2 ( t ) ; 0 + n , k z b n , k z ( t ) ; 1 n , k z ,
{ b 1 ( t ) = e 2 Γ sp t ( 1 + e 2 Γ sp t ) 2 , b 2 ( t ) = e i k 0 z 0 2 Γ sp t ( 1 + e 2 Γ sp t ) 2 . }

Metrics