Abstract

We investigate the light emission characteristics for single two level quantum dot (QD) in a realistic photonic crystal (PC) L3 cavity based upon the local coupling strength between the QD and cavity together with the Green’s function in which the propagation function related to the position of the detector is taken into account. We find for a PC cavity that the line shape of the propagation function in frequency domain is identical to that of the cavity and independent on the detector's position. We confirm that this identity is not influenced by the horizontal decay of the cavity. Furthermore, it is revealed that the vacuum fluorescence spectrum of the coupled system never give the triplet in strong coupling regime. Our work demonstrates that the experimental spectral-triplet in coupled system of single QD and PC cavity cannot be individually understood by vacuum Rabi splitting without including other physics mechanism.

© 2013 Optical Society of America

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  5. J. P. Reithmaier, G. Sek, A. Löffler, 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,” Nature432(7014), 197–200 (2004).
    [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,” Nature432(7014), 200–203 (2004).
    [CrossRef] [PubMed]
  7. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
    [CrossRef] [PubMed]
  8. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
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  9. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
    [CrossRef] [PubMed]
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  11. R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
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  12. R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
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  13. E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
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  14. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
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  15. W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
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    [CrossRef] [PubMed]
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  24. X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
    [CrossRef] [PubMed]
  25. M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
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    [CrossRef] [PubMed]
  28. L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
    [CrossRef]
  29. G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
    [CrossRef]
  30. O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999).
    [CrossRef]

2013

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

2012

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

2010

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

2009

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[CrossRef]

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express17(5), 3322–3330 (2009).
[CrossRef] [PubMed]

2008

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

2007

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, 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(11), 117402 (2007).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

2006

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

T. Ochiai, J.-i. Inoue, and K. Sakoda, “Spontaneous emission from a two-level atom in a bisphere microcavity,” Phys. Rev. A74(6), 063818 (2006).
[CrossRef]

2005

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

2004

J. P. Reithmaier, G. Sek, A. Löffler, 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,” Nature432(7014), 197–200 (2004).
[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,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

M. Wubs, L. G. Suttorp, and A. Lagendijk, “Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,” Phys. Rev. A70(5), 053823 (2004).
[CrossRef]

2003

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

2002

C. Monroe, “Quantum information processing with atoms and photons,” Nature416(6877), 238–246 (2002).
[CrossRef] [PubMed]

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

2001

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

1999

O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B16(2), 275–285 (1999).
[CrossRef]

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

1989

H. J. 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. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

Arakawa, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys.6(4), 279–283 (2010).
[CrossRef]

Asano, T.

M. Yamaguchi, T. Asano, and S. Noda, “Third emission mechanism in solid-state nanocavity quantum electrodynamics,” Rep. Prog. Phys.75(9), 096401 (2012).
[CrossRef] [PubMed]

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B80(15), 155326 (2009).
[CrossRef]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Badolato, A.

M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoğlu, “Quantum dot spectroscopy using cavity quantum electrodynamics,” Phys. Rev. Lett.101(22), 226808 (2008).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Brecha, R. J.

H. J. 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. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

Carmichael, H. J.

H. J. 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. A40(10), 5516–5519 (1989).
[CrossRef] [PubMed]

Chang, H.-S.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chang, W.-H.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chen, G.

G. Chen, Y.-C. Yu, X.-L. Zhuo, Y.-G. Huang, H. Jiang, J.-F. Liu, C.-J. Jin, and X.-H. Wang, “Ab initio determination of local coupling interaction in arbitrary nanostructures: Application to photonic crystal slabs and cavities,” Phys. Rev. B87(19), 195138 (2013).
[CrossRef]

Chen, W.-Y.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

Chyi, J.-I.

W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, and T.-M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett.96(11), 117401 (2006).
[CrossRef] [PubMed]

del Valle, E.

E. del Valle, F. P. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B79(23), 235326 (2009).
[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,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Doherty, A. C.

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

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,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Englund, D.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Faraon, A.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Forchel, A.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, 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(11), 117402 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, 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,” Nature432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007).
[CrossRef]

Furusawa, A.

J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Fushman, I.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys.4(11), 859–863 (2008).
[CrossRef]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vucković, “Controlling cavity reflectivity with a single quantum dot,” Nature450(7171), 857–861 (2007).
[CrossRef] [PubMed]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Gérard, J. M.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Gérard, J.-M.

L. C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B60(19), 13276–13279 (1999).
[CrossRef]

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,” Nature432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Gippius, N. A.

R. Johne, N. A. Gippius, and G. Malpuech, “Entangled photons from a strongly coupled quantum dot-cavity system,” Phys. Rev. B79(15), 155317 (2009).
[CrossRef]

R. Johne, N. A. Gippius, G. Pavlovic, D. D. Solnyshkov, I. A. Shelykh, and G. Malpuech, “Entangled photon pairs produced by a quantum dot strongly coupled to a microcavity,” Phys. Rev. Lett.100(24), 240404 (2008).
[CrossRef] [PubMed]

Götzinger, S.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, 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(11), 117402 (2007).
[CrossRef] [PubMed]

Gu, B.-Y.

X.-H. Wang, B.-Y. Gu, R. Wang, and H.-Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73(3), 565–582 (2001).
[CrossRef]

Hendrickson, J.

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J. Opt. Soc. Am. B

Nat. Photonics

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Nat. Phys.

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Nature

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Figures (5)

Fig. 1
Fig. 1

The schematic diagrams of the PC L3 cavity system. (a) Cross-section on central plane (z = 0 plane) of the PC L3 cavity. The location of the QD is r0 = (0, 0, 0) at the center of the cavity and the orientation d ^ is along y direction. (b) The 3D schematic diagram with the locations of 15 probe points.

Fig. 2
Fig. 2

(a) The multiplication factor of the PLDOS for the Sample#1. The propagation functions on probe points (b) A1 = (0, 0, 1.5) a, (c) B1 = (0, 0, 5.5) a and (d) C1 = (0, 0, 9.5) a.

Fig. 3
Fig. 3

(a) The local dipole spectra P( r 0 ,ω ) of the Sample#1. (b) The vacuum fluorescence spectra S( ω ) for the probe point C1 = (0, 0, 9.5)a. The wavelength detuning between transition wavelength of the QD and the resonant wavelength of the cavity (1232.92 nm) increases from −0.06 nm to 0.06 nm (from top to bottom).

Fig. 4
Fig. 4

The decay rate κ from the multiplication factor M( r 0 ,ω, d ^ ) with the corresponding Q factor, and the line width κ f of the propagation functions f( r p , r 0 ,ω ) , for different numbers of air hole layers in the L3 cavity.

Fig. 5
Fig. 5

(a) The local dipole spectra P( r 0 ,ω ) and (b) vacuum fluorescence spectra S( ω ) for the L3 cavities with less than 7 layers of air holes surrounding the defect. The transition wavelength of the QD is resonant with the resonant wavelength λ c of each cavity.

Tables (1)

Tables Icon

Table 1 κ f factors obtained by fitting f( r p , r 0 ,ω ) in Eq. (13) on every probe point.

Equations (19)

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S( ω )= 0 d t 1 0 d t 2 e iω( t 1 t 2 ) E ( ) ( r, t 1 ) E ( + ) ( r, t 2 ) .
S( ω )=f( r p , r 0 ,ω )P( r 0 ,ω )
f( r p , r 0 ,ω )= | K( r p , r 0 ,ω )d ε 0 | 2
K( r, r ,ω )= λ ω λ 2 E λ ( r ) E λ ( r ) ω 2 ω λ 2 = ω 2 c 2 G( r, r ,ω ) Iδ( r r ) ε r ( r,ω ) ,
[ ×× ε r ( r,ω ) ω 2 c 2 ]G( r, r ,ω )=Iδ( r r ),
P( r 0 ,ω )= { | ω ω 0 ω 0 2 d 2 ω 2 ε 0 d ^ K( r 0 , r 0 ,ω ) d ^ | 2 } 1 .
P( r 0 ,ω )= { [ ω ω 0 Δ( r 0 ,ω ) ] 2 +Γ ( r 0 ,ω ) 2 /4 } 1 ,
Γ( r 0 ,ω )=2π λ | g λ ( r 0 ) | 2 δ( ω ω λ ) = 2 ω 0 2 d 2 ω 2 ε 0 d ^ Im[ K( r 0 , r 0 ,ω ) ] d ^
Δ( r 0 ,ω )= 2π 0 Γ( r 0 , ω ) ω ω d ω = ω 0 2 d 2 ω 2 ε 0 d ^ Re[ K( r 0 , r 0 ,ω ) ] d ^
Γ( r 0 ,ω )= 2 ω 0 2 d 2 ε 0 c 2 d ^ Im[ G( r 0 , r 0 ,ω ) ]d= Γ 0 ω ω 0 M( r 0 ,ω, d ^ ),
S( ω )=f( r p , r 0 ,ω ) { [ ω ω 0 Δ( r 0 ,ω ) ] 2 +Γ ( r 0 ,ω ) 2 /4 } 1 ,
M( r 0 ,ω, d ^ )= 2 | g c ( r 0 ) | 2 Γ 0 κ/2 ( ω ω c ) 2 + ( κ/2 ) 2
E d ( r,t )= d 2π ε 0 c 2 0 ω 2 G( r, r 0 ,ω ) d ^ e iωt dω +c.c. = d 2π ε 0 0 K( r, r 0 ,ω ) d ^ e iωt dω +c.c. P ex ( r,t ) ε 0 ε r ( r 0 )
E local ( r,t>0 )= E 0 ( r )exp( i ω c t κ 2 t )+c.c.,
E 0 ( r )= i ω c d 2 ε 0 E c ( r ) E c * ( r 0 )· d ^ ,
E prop ( r,t>0 )= E 0 ( r )exp( i ω c t κ v 2 t )+c.c.
U( t )=U( 0 )exp( κt )=U( 0 )exp( ω c Q t ),
P( t )= dU( t ) dt =κU( t ).
P v ( t )= κ v U( t )= κ v U( 0 )exp( κt ).

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