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]

2005 (2)

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]

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

2004 (3)

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]

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]

2002 (6)

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

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]

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]

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]

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]

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]

2001 (2)

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]

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

2000 (3)

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

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]

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

1997 (2)

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

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

1992 (2)

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

1987 (1)

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

1974 (1)

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

1946 (1)

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

1930 (1)

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

Basche, T.

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]

Beattie, N. S.

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]

Bennet, C. H.

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

Bloch, J.

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]

Boca, A.

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]

Boozer, A. D.

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]

Brassard, G.

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

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

Buck, J. R.

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]

Buratto, S. K.

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]

Carson, P. J.

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]

Clauser, J. F.

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

Cooper, K.

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]

Dale, Y.

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]

Deppe, D. G.

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]

Diedrich, F.

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

Eckert, A.

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

Ell, C.

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]

Fattal, D.

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]

Forchel, A.

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]

Gerard, J. M.

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]

Gibbs, H. M.

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]

Hendrickson, J.

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]

Hennrich, M.

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

Hofmann, C.

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]

Hours, J.

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]

Imamoglu, A.

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]

Kardynal, B. E.

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]

Karlovich, T. B.

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]

Keldysh, L. V.

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]

Khitrova, G.

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]

Kilin, S. Y.

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]

Kimble, H. J.

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]

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

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 .

Knill, E.

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

Kuhn, A.

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

Kuhn, S.

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]

Kulakovskii, V. D.

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]

Kurtsiefer, C.

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

Kuzmich, A.

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]

Laflamme, R.

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

Law, C. K.

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

Lemaitre, A.

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]

Lobo, C. J.

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]

Loffler, A.

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]

Lounis, B.

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

Lugiato, L. A.

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]

Lutkenhaus, N.

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

Marthou, D.

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]

Mason, M. D.

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]

Mayer, S.

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

McKeever, J.

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]

Michler, P.

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]

Milburn, G. J.

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

Miller, R.

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]

Moerner, W. E.

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]

Mor, T.

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

Orrit, M.

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

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]

Pelton, M.

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]

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]

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]

Pepper, M.

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]

Peter, E.

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]

Plant, J.

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]

Purcell, E. M.

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

Reinecke, T. L.

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]

Reitzenstein, S.

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]

Relthmaier, J. P.

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]

Rempe, G.

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

Ritchie, D. A.

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]

Rupper, G.

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]

Sanders, B.

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

Santori, C.

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]

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]

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]

Scherer, A.

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]

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]

Scully, M. O.

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

Sek, G.

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]

Senellart, P.

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]

Shchekin, O. B.

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]

Shields, A. J.

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]

Solomon, G.

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]

Solomon, G. S.

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]

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]

Stevenson, R. M.

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]

Strouse, G. F.

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]

Talon, H.

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]

Vuckovic, J.

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]

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]

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]

Walther, H.

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

Weinfurter, H.

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

Weisskopf, V.

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

Wigner, E.

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

Yamamoto, Y.

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]

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]

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]

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]

Yoshie, T.

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]

Yuan, Z.

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]

Zarda, P.

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

Zhang, B.

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]

Zubairy, M. S.

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

J. Exp. & Theo. Phys. (1)

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. (1)

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

Nature (5)

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. (1)

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

Phys. Rev. A (1)

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 (1)

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. (8)

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

Rep. Prog. Phys. (1)

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

Sci. Am. (1)

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

Science (2)

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. 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]

Z. Phys. (1)

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

Other (3)

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

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]

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 .

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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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