Abstract

We present a rigorous medium-dependent theory for describing the quantum field emitted and detected from a single quantum dot exciton, strongly coupled to a planar photonic crystal nanocavity, from which the exact spectrum is derived. By using simple mode decomposition techniques, this exact spectrum is subsequently reduced to two separate user-friendly forms, in terms of the leaky cavity mode emission and the radiation mode emission. On application to study exciton-cavity coupling in the strong coupling regime, besides a pronounced modification of the usual vacuum Rabi spectral doublet, we predict several new effects associated with the leaky cavity mode emission, including the appearance of an off-resonance cavity mode and a loss-induced on-resonance spectral triplet. The cavity mode emission is shown to completely dominate the emitted spectrum, even for large cavity-exciton detunings, whereby the usual cavity-QED formulas developed for radiation-mode emission drastically fail. These predictions are in qualitative agreement with several “mystery observations” reported in recent experiments, and apply to a wide range of semiconductor cavities.

© 2009 Optical Society of America

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  1. A. Einstein, "On the quantum theory of radiation" (English Translation), Z. Phys. 18, 121 (1917). Translated into English in Van derWaerden Sources of Quantum Mechanics (North Holland 1967) pp. 63-77. English translation by D. ter Haar, "The Old Quantum Theory," Pergamon Press, New York, p. 167 (1967).
  2. E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin, and V. Thierry-Mieg, "Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities," Appl. Phys. Lett. 79, 2865 (2001).
    [CrossRef]
  3. D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
    [CrossRef]
  4. W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (2005).
    [CrossRef] [PubMed]
  5. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
    [CrossRef] [PubMed]
  6. 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]
  7. E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M Gerard, and J. Bloch, "Exciton-photon strongcoupling regime for a single quantum dot embedded in a microcavity," Phys. Rev. Lett. 95, 067401 (2005).
    [CrossRef] [PubMed]
  8. J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
    [CrossRef] [PubMed]
  9. K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
    [CrossRef] [PubMed]
  10. D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
    [CrossRef] [PubMed]
  11. See, e.g., J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, H. J. Kimble, "Deterministic generation of single photons from one atom trapped in a cavity," Science 303, 1992 (2004).
    [CrossRef] [PubMed]
  12. M. Kaniber, A. Laucht, A. Neumann, J. M. Villas-Bas, M. Bichler, M.-C. Amann, and J. J. Finley, "Investigation of the nonresonant dot-cavity coupling in two-dimensional photonic crystal nanocavities," Phys. Rev. B161303(R) (2008).
    [CrossRef]
  13. H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
    [CrossRef]
  14. S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
    [CrossRef] [PubMed]
  15. M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (2004).
    [CrossRef]
  16. For simplicity we are assuming that F(R) is the same for both cavity and radiation leakage, but in reality this will depend on a number of factors, including the specific collection geometry of the detector.
  17. H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
    [CrossRef] [PubMed]
  18. L. C. Andreani, G. Panzarini, and J-M. Gerard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
    [CrossRef]
  19. G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
    [CrossRef]
  20. A. Auffeves, B. Besga, J. M. Gerard, and J. P. Poizat, "Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity," Phys. Rev. A 77, 063833 (2008).
    [CrossRef]
  21. T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
    [CrossRef]
  22. Note an important correction to the emission spectrum in [21], namely G(R,rd;ω) and not Im[G(R,rd;ω)] appears, since a principal value term was neglected in that paper.
  23. See, e.g., "Statistical Methods in Quantum Optics 2," H. J. Carmichael, Springer, p. 235. (2008).
  24. T. Takagahara, "Theory of exciton dephasing in semiconductor quantum dots," Phys. Rev. B 60, 2638 (1999).
    [CrossRef]
  25. B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
    [CrossRef]
  26. In the limit of only radiative decay and simple cavity and exciton modes, we confirm complete agreement between our PC-projected Green function spectrum and the master equation solution, which is to be expected for the model cavity structure if Γh = 0 (no in-plane decay).
  27. See, e.g., V. S. C. Manga Rao and S. Hughes, "Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient "on chip" single photon gun," Phys. Rev. Lett. 99, 193901 (2007).
    [CrossRef]

2008

A. Auffeves, B. Besga, J. M. Gerard, and J. P. Poizat, "Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity," Phys. Rev. A 77, 063833 (2008).
[CrossRef]

2007

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

See, e.g., V. S. C. Manga Rao and S. Hughes, "Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient "on chip" single photon gun," Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

2006

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
[CrossRef]

2005

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

W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (2005).
[CrossRef] [PubMed]

2004

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

See, e.g., J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, H. J. Kimble, "Deterministic generation of single photons from one atom trapped in a cavity," Science 303, 1992 (2004).
[CrossRef] [PubMed]

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (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]

2003

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

2002

B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
[CrossRef]

2001

E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin, and V. Thierry-Mieg, "Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities," Appl. Phys. Lett. 79, 2865 (2001).
[CrossRef]

2000

H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
[CrossRef]

1999

L. C. Andreani, G. Panzarini, and J-M. Gerard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

T. Takagahara, "Theory of exciton dephasing in semiconductor quantum dots," Phys. Rev. B 60, 2638 (1999).
[CrossRef]

1989

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J-M. Gerard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Andreas L¨offler, C.

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Atature, A.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Auffeves, A.

A. Auffeves, B. Besga, J. M. Gerard, and J. P. Poizat, "Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity," Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Axt, V. M.

B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Besga, B.

A. Auffeves, B. Besga, J. M. Gerard, and J. P. Poizat, "Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity," Phys. Rev. A 77, 063833 (2008).
[CrossRef]

Brecha, R. J.

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Carmichael, H.

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Cui, G.

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

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]

Diamante, E.

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

Dung, H. T.

H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
[CrossRef]

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]

Falt, S.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Fattal, D.

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

Forchel, A.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

G¨otzinger, S.

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[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]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Hofmann, C.

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Hours, J.

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

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Hughes, S.

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

Imamo?glu, A.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Inoue, J-I.

T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
[CrossRef]

Inoue, K.

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

Keldysh, L. V.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

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]

Kimble, H. J.

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Knoll, L.

H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
[CrossRef]

Krummheuer, B.

B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
[CrossRef]

Kuhn, S.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Kuhn, T.

B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
[CrossRef]

Kulakovskii, V. D.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Lagendijk, A.

M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (2004).
[CrossRef]

Lemaitre, A.

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

Liu, R.-B.

W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (2005).
[CrossRef] [PubMed]

Loffler, A.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Martrou, D.

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

Moreau, E.

E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin, and V. Thierry-Mieg, "Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities," Appl. Phys. Lett. 79, 2865 (2001).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Ochiai, T.

T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
[CrossRef]

Panzarini, G.

L. C. Andreani, G. Panzarini, and J-M. Gerard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Peter, E.

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

Press, D.

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

Raizen, M. G.

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Raymer, M. G.

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

Reinecke, T. L.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Rice, P. R.

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Robert, I.

E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin, and V. Thierry-Mieg, "Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities," Appl. Phys. Lett. 79, 2865 (2001).
[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]

Sakoda, K.

T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
[CrossRef]

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]

Sek, G.

J. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

Senellart, P.

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

Sham, L. J.

W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (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]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

Suttorp, L.G.

M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (2004).
[CrossRef]

Takagahara, T.

T. Takagahara, "Theory of exciton dephasing in semiconductor quantum dots," Phys. Rev. B 60, 2638 (1999).
[CrossRef]

Welsch, D-G.

H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
[CrossRef]

Winger, M.

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Wubs, M.

M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (2004).
[CrossRef]

Yamamoto, Y.

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

Yao, W.

W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (2005).
[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]

Appl. Phys. Lett.

E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin, and V. Thierry-Mieg, "Single-mode solid-state single photon source based on isolated quantum dots in pillar microcavities," Appl. Phys. Lett. 79, 2865 (2001).
[CrossRef]

Nature

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003).
[CrossRef] [PubMed]

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. P. Reithmaier, 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-semiconductor microcavity system," Nature 432, 197 (2004).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, A. Atature, S. Falt, E. L. Hu, A. Imamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Phys. Rev. A

H. T. Dung, L. Knoll and D-G. Welsch, "Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity," Phys. Rev. A 62, 053804 (2000).
[CrossRef]

M. Wubs, L.G. Suttorp and A. Lagendijk. "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 53823 (2004).
[CrossRef]

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

A. Auffeves, B. Besga, J. M. Gerard, and J. P. Poizat, "Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity," Phys. Rev. A 77, 063833 (2008).
[CrossRef]

T. Ochiai, J-I. Inoue, and K. Sakoda, "Spontaneous emission from a two-level atom in a bisphere microcavity," Phys. Rev. A 74, 063818 (2006).
[CrossRef]

H. Carmichael, R. J. Brecha, M. G. Raizen, H. J. Kimble, and P. R. Rice, "Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators," Phys. Rev. A 40, 5516 (1989).
[CrossRef] [PubMed]

Phys. Rev. B

L. C. Andreani, G. Panzarini, and J-M. Gerard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B 60, 13276 (1999).
[CrossRef]

T. Takagahara, "Theory of exciton dephasing in semiconductor quantum dots," Phys. Rev. B 60, 2638 (1999).
[CrossRef]

B. Krummheuer, V. M. Axt, and T. Kuhn, "Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots," Phys. Rev. B 65, 195313 (2002).
[CrossRef]

Phys. Rev. Lett.

See, e.g., V. S. C. Manga Rao and S. Hughes, "Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient "on chip" single photon gun," Phys. Rev. Lett. 99, 193901 (2007).
[CrossRef]

S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007).
[CrossRef] [PubMed]

D. Press, S. Gotzinger, S. Reitzenstein, C. Hofmann, A. Loffler, M. Kamp, A. Forchel, and Y. Yamamoto, "Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime," Phys. Rev. Lett. 98, 117402 (2007).
[CrossRef] [PubMed]

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

D. Fattal, E. Diamante, K. Inoue, and Y. Yamamoto, "Quantum teleportation with a quantum dot single photon source," Phys. Rev. Lett. 92, 7904 (2004).
[CrossRef]

W. Yao, R-B Liu, and L. J. Sham, "Theory of control of the spin-photon interface for quantum networks," Phys. Rev. Lett. 95, 030504 (2005).
[CrossRef] [PubMed]

Science

See, e.g., J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, H. J. Kimble, "Deterministic generation of single photons from one atom trapped in a cavity," Science 303, 1992 (2004).
[CrossRef] [PubMed]

Other

M. Kaniber, A. Laucht, A. Neumann, J. M. Villas-Bas, M. Bichler, M.-C. Amann, and J. J. Finley, "Investigation of the nonresonant dot-cavity coupling in two-dimensional photonic crystal nanocavities," Phys. Rev. B161303(R) (2008).
[CrossRef]

For simplicity we are assuming that F(R) is the same for both cavity and radiation leakage, but in reality this will depend on a number of factors, including the specific collection geometry of the detector.

Note an important correction to the emission spectrum in [21], namely G(R,rd;ω) and not Im[G(R,rd;ω)] appears, since a principal value term was neglected in that paper.

See, e.g., "Statistical Methods in Quantum Optics 2," H. J. Carmichael, Springer, p. 235. (2008).

A. Einstein, "On the quantum theory of radiation" (English Translation), Z. Phys. 18, 121 (1917). Translated into English in Van derWaerden Sources of Quantum Mechanics (North Holland 1967) pp. 63-77. English translation by D. ter Haar, "The Old Quantum Theory," Pergamon Press, New York, p. 167 (1967).

In the limit of only radiative decay and simple cavity and exciton modes, we confirm complete agreement between our PC-projected Green function spectrum and the master equation solution, which is to be expected for the model cavity structure if Γh = 0 (no in-plane decay).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a planar semiconductor PC with an embedded QD; for a self-assembled QD, then the spatial position would be near the center of the slab to maximize coupling to the cavity mode. Also shown is a typical spatial profile of a confined cavity mode f c (r,ωc ), within the slab, dominated by fy c in this example (ωc is the cavity resonance frequency); the effective mode volume is less than 0.1μm3. The right side of the figure shows a side view of the cavity, indicating the vertical background radiation-leakage (γb ), as well as a vertical (κ v ) and horizontal (κ h ) cavity leakage. We define the cavity decay rates as Γ v/h = 2κ v/h , and the radiation decay rate as Γ b = 2γb .

Fig. 2.
Fig. 2.

Normalized light spectra from single QD photon emission in a planar PC cavity (c.f. Fig. (1)), with cavity decay rates Γ v = 0.1meV and Γ h = 0, and exciton decay rate Γ (see text and labels in the graph). In (a) is shown the spectrum for an initially excited-exciton, with two different exciton decay rates, with a cavity mode off-resonance (from the exciton) by 0.8 meV; the blue dashed curve is the usual radiation-mode decay (S rad), and the red solid curve shows the emitted spectrum from the leaky cavity mode (S cav). In (b), is shown the influence of detuning as a contour plot. (c) Similar to (a) (top frame) but computed from a master equation solution with pure dephasing (Γ′); the insets display the exciton and cavity mode dynamics. In (d) is shown the on-resonance case.

Fig. 3.
Fig. 3.

Detected spectra for various cavity-exciton detunings, using the same parameters as in Fig. (2), with Γ = 40μeV. All spectra are scaled by the same constant, and the background radiation decay is Γ b = 0.05μeV. (a) Cavity and radiation mode emission for a detuning of 8 meV. (b) Detuning of 4 meV. (c) Detuning of 1 meV showing only the cavity mode, where already S rad plays a negligible role. (d) On-resonance case, which shows both a pronounced enhancement of the emission (Purcell effect) and the strong coupling regime.

Fig. 4.
Fig. 4.

(a) An example cavity-mode spectrum that results from an off-resonant excitation, from a spectrally wandered exciton or an exciton-biexciton pair. (b) The sum of the off-resonant and on-resonance spectra, showing that the total on-resonance doublet survives. (c) The simple one exciton and one cavity-mode spectrum, but in the presence of in-plane loss or decay, showing the onset of a spectral triplet.

Equations (6)

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H = h ¯ ω x σ ̂ + σ ̂ + λ h ¯ ω λ a ̂ λ a ̂ λ i h ¯ λ ( σ ̂ + σ ̂ + ) ( g λ a ̂ λ g λ * a ̂ λ ) ,
E ̂ ( R , ω ) = 1 ε 0 K ( R , r d ; ω ) · μ [ σ ̂ ( ω ) + σ ̂ + ( ω ) ] ,
S ( R , ω ) = 0 d t 2 0 d t 1 e i ω ( t 2 t 1 ) E ̂ ( ) ( R , t 2 ) E ̂ ( + ) ( R , t 1 ) ,
S ( R , ω ) = K ( R , r d , ω ) · μ ε 0 2 ( σ ̂ ( ω ) ) σ ̂ ( ω ) .
S rad ( R , ω ) F ( R ) Γ b ( ω + ω x ) ( ω 2 ω c 2 + i ω Γ c ) ( ω 2 ω x 2 + i ω Γ ) ( ω 2 ω c 2 + i ω Γ c ) 4 g 2 ω c ω 2 ,
S cav ( R , ω ) F ( R ) Γ v 2 g ω c ( ω + ω x ) ( ω 2 ω c 2 + i ω Γ c ) ( ω 2 ω c 2 + i ω Γ v ) ( ω 2 ω x 2 + i ω Γ ) ( ω 2 ω c 2 + i ω Γ c ) 4 g 2 ω c ω 2 ,

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