Abstract

We calculate the integrated-pulse quantum efficiency of single-photon sources in the cavity quantum electrodynamics (QED) strong-coupling regime. An analytical expression for the quantum efficiency is obtained in the Weisskopf-Wigner approximation. Optimal conditions for a high quantum efficiency and a temporally localized photon emission rate are examined. We show the condition under which the earlier result of Law and Kimble [J. Mod. Opt. 44, 2067 (1997)] can be used as the first approximation to our result.

© 2005 Optical Society of America

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References

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  1. C. K. Law and H. J. Kimble, “Deterministic generation of a bit-stream of single-photon pulses,” J. Mod. Opt. 44, 2067 (1997).
  2. J. F. Clauser, “Experimental distinction between the quantum and classical field-theoretical prediction for the photoelectric effect,” Phys. Rev. D 9, 853 (1974).
    [CrossRef]
  3. F. Diedrich and H. Walther, “Nonclassical radiation of single stored ion,” Phys. Rev. Lett. 58, 203 (1987).
    [CrossRef] [PubMed]
  4. T. Basche, W. E. Moerner, M. Orrit and H. Talon, “Photon antibunching in the fluorescence of a single dye molecule trapped in a solid,” Phys. Rev. Lett. 69, 1516 (1992).
    [CrossRef] [PubMed]
  5. C. Kurtsiefer, S. Mayer, P. Zarda and H. Weinfurter, “Stable solid-state source of single photons,” Phys.Rev. Lett. 85, 290 (2000).
    [CrossRef] [PubMed]
  6. P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse and S. K. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature 406, 968 (2000).
    [CrossRef] [PubMed]
  7. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502 (2001).
    [CrossRef] [PubMed]
  8. Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single-photon source,” Science 295, 102 (2002).
    [CrossRef]
  9. C. H. Bennet, G. Brassard and A. Eckert, “Quantum cryptography,” Sci. Am. 267(4), 50 (1992).
  10. E. Knill, R. Laflamme and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46 (2001).
    [CrossRef] [PubMed]
  11. H. J. Kimble, “Structure and dynamics in cavity quantum electrodynamics,” in Cavity Quantum Electrodynamics, P. R. Berman ed. (Academic Press, Boston, 1994), pp. 203-266.
  12. J. P. Relthmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197 (2004).
    [CrossRef]
  13. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200 (2004).
    [CrossRef] [PubMed]
  14. E. Peter, P. Senellart, D. Marthou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
    [CrossRef] [PubMed]
  15. J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of dingle photons from one atom trapped in a cavity,” Science 303, 1992 (2004).
    [CrossRef] [PubMed]
  16. A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
    [CrossRef] [PubMed]
  17. S. Y. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation,” J. Exp. & Theo. Phys. 95, 805 (2002).
    [CrossRef]
  18. C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002).
    [CrossRef] [PubMed]
  19. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies (Abstract),” Phys. Rev. 69, 681 (1946).
  20. M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89, 233602 (2002).
    [CrossRef] [PubMed]
  21. V. Weisskopf and E. Wigner, “Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie,” Z. Phys. 63, 54 (1930).
    [CrossRef]
  22. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge, New York, 1997).
  23. L. A. Lugiato, “Theory of optical bistability,” in Progress in Optics, XXI, E. Wolf ed. (Elsevier Science Publishers B. V., New York, 1984), pp. 69-216.
    [CrossRef]
  24. J. Vuckovic, M. Pelton, A. Scherer, and Y. Yamamoto, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. A 66, 023808 (2002).
    [CrossRef]
  25. B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
    [CrossRef]
  26. G. Brassard, N. Lutkenhaus, T. Mor and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330 (2000).
    [CrossRef] [PubMed]

Cavity Quantum Electrodynamics

H. J. Kimble, “Structure and dynamics in cavity quantum electrodynamics,” in Cavity Quantum Electrodynamics, P. R. Berman ed. (Academic Press, Boston, 1994), pp. 203-266.

J. Exp. & Theo. Phys.

S. Y. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field correlation,” J. Exp. & Theo. Phys. 95, 805 (2002).
[CrossRef]

J. Mod. Opt.

C. K. Law and H. J. Kimble, “Deterministic generation of a bit-stream of single-photon pulses,” J. Mod. Opt. 44, 2067 (1997).

Nature

P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse and S. K. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature 406, 968 (2000).
[CrossRef] [PubMed]

E. Knill, R. Laflamme and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46 (2001).
[CrossRef] [PubMed]

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002).
[CrossRef] [PubMed]

J. P. Relthmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197 (2004).
[CrossRef]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200 (2004).
[CrossRef] [PubMed]

Phys. Rev.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies (Abstract),” Phys. Rev. 69, 681 (1946).

Phys. Rev. A

J. Vuckovic, M. Pelton, A. Scherer, and Y. Yamamoto, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. A 66, 023808 (2002).
[CrossRef]

Phys. Rev. D

J. F. Clauser, “Experimental distinction between the quantum and classical field-theoretical prediction for the photoelectric effect,” Phys. Rev. D 9, 853 (1974).
[CrossRef]

Phys. Rev. Lett.

F. Diedrich and H. Walther, “Nonclassical radiation of single stored ion,” Phys. Rev. Lett. 58, 203 (1987).
[CrossRef] [PubMed]

T. Basche, W. E. Moerner, M. Orrit and H. Talon, “Photon antibunching in the fluorescence of a single dye molecule trapped in a solid,” Phys. Rev. Lett. 69, 1516 (1992).
[CrossRef] [PubMed]

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502 (2001).
[CrossRef] [PubMed]

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

E. Peter, P. Senellart, D. Marthou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[CrossRef] [PubMed]

G. Brassard, N. Lutkenhaus, T. Mor and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330 (2000).
[CrossRef] [PubMed]

Phys.Rev. Lett.

C. Kurtsiefer, S. Mayer, P. Zarda and H. Weinfurter, “Stable solid-state source of single photons,” Phys.Rev. Lett. 85, 290 (2000).
[CrossRef] [PubMed]

Progress in Optics, XXI, E. Wolf ed.

L. A. Lugiato, “Theory of optical bistability,” in Progress in Optics, XXI, E. Wolf ed. (Elsevier Science Publishers B. V., New York, 1984), pp. 69-216.
[CrossRef]

Rep. Prog. Phys.

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
[CrossRef]

Sci. Am.

C. H. Bennet, G. Brassard and A. Eckert, “Quantum cryptography,” Sci. Am. 267(4), 50 (1992).

Science

Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K. Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, “Electrically driven single-photon source,” Science 295, 102 (2002).
[CrossRef]

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic generation of dingle photons from one atom trapped in a cavity,” Science 303, 1992 (2004).
[CrossRef] [PubMed]

Z. Phys.

V. Weisskopf and E. Wigner, “Berechnung der naturlichen Linienbreite auf Grund der Diracschen Lichttheorie,” Z. Phys. 63, 54 (1930).
[CrossRef]

Other

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge, New York, 1997).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic description of a lossy two-level emitter interacting with a single mode in a leaky optical cavity. g 0 is the coupling constant between the emitter and the cavity field. A p , A p * and B k B k * are the coupling constants between the emitter, a single photon and their respective reservoir (R 1, R 2) fields.

Fig. 2.
Fig. 2.

Plots for the time dependence of (a) the emission probabilities of single photons Po (t), and (b) the emission rates n(t), in three different cavity regimes: optimal cavity regime for κ = g02/ κγ, good cavity regime for g02/κ > κγ, and bad cavity regime for κ > g02/κγ, (red dot, blue square and green triangle, respectively) with κ/2π = (50,20,100)GHz , respectively.

Equations (13)

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

η q = [ g 0 2 ( g 0 2 + κγ ) ] · [ κ ( κ + γ ) ] .
H ̂ I ( t ) = ħ g 0 ( σ ̂ + a ̂ e i Δ t + h . c . ) + ħ p ( A p * σ ̂ d ̂ p + e i δ p t + h . c . ) + ħ k ( B k * a ̂ b ̂ k + e i δ k t + h . c . )
ψ ( t ) = E ( t ) e , 0 0 R 1 0 R 2 + C ( t ) g , 1 0 R 1 0 R 2 +
p S p ( t ) g , 0 1 p R 1 0 R 2 + k O k ( t ) g , 0 0 R 1 1 k R 2
E ̇ ( t ) = i g 0 exp ( i Δ t ) C ( t ) γE ( t ) , C ̇ ( t ) = i g 0 exp ( i Δ t ) E ( t ) κC ( t )
S p ( t ) = i A p * 0 t dt exp ( i δ p t ) E ( t ) , O k ( t ) = i B k * 0 t dt exp ( i δ k t ) C ( t )
E ( t ) = exp [ ( K 2 ) t ] · [ cos ( gt ) + Γ 2 g sin ( gt ) ]
C ( t ) = exp [ ( K 2 ) t ] · [ i g 0 g sin ( gt ) ]
P o ( t ) = 2 κ 0 t dt C ( t ) 2 = η q { 1 exp ( K t ) [ 1 + K 2 2 g 2 sin 2 ( gt ) + K 2 g sin ( 2 gt ) ] }
η c = g 0 2 g 0 2 + κγ 2 C 0 2 C 0 + 1 , η extr = κ κ + γ
n ( t ) dP o ( t ) dt = 2 κ g 0 2 g 2 exp ( K t ) sin 2 ( gt )
P ( t ) 2 C 1 2 C 1 + 1
η q = F p F p + f · κ κ + γ = β · κ κ + γ

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