Abstract

I theoretically demonstrate the population inversion of collective two-level atoms using photonic crystals in three-dimensional (3D) systems by self-consistent solution of the semiclassical Maxwell-Bloch equations. In the semiclassical theory, while electrons are quantized to ground and excited states, electromagnetic fields are treated classically. For control of spontaneous emission and steady-state population inversion of two-level atoms driven by an external laser which is generally considered impossible, large contrasts of electromagnetic local densities of states (EM LDOS’s) are necessary. When a large number of two-level atoms are coherently excited (Dicke model), the above properties can be recaptured by the Maxwell-Bloch equations based on the first-principle calculation. In this paper, I focus on the realistic 1D PC’s with finite structures perpendicular to periodic directions in 3D systems. In such structures, there appear pseudo photonic band gaps (PBG’s) in which light leaks into air regions, unlike complete PBG’s. Nevertheless, these pseudo PBG’s provide large contrasts of EM LDOS’s in the vicinity of the upper photonic band edges. I show that the realistic 1D PC’s in 3D systems enable the control of spontaneous emission and population inversion of collective two-level atoms driven by an external laser. This finding facilitates experimental fabrication and realization.

© 2012 OSA

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  1. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 582486–2489 (1987).
    [CrossRef] [PubMed]
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 582059–2062 (1987).
    [CrossRef] [PubMed]
  3. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69681 (1946).
  4. P. W. Milloni and J. H. Eberly, Laser Physics (Wiley, 2009).
  5. M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A 385182–5192 (1988).
    [CrossRef] [PubMed]
  6. S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett. 781888–1891 (1997).
    [CrossRef]
  7. T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
    [CrossRef] [PubMed]
  8. S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
    [CrossRef] [PubMed]
  9. B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 1881969–1975 (1969).
    [CrossRef]
  10. M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A 64033801 (2001).
    [CrossRef]
  11. M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A 69053810 (2004).
    [CrossRef]
  12. S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt. 3S103–S120 (2001).
    [CrossRef]
  13. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 9399–110 (1954).
    [CrossRef]
  14. F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A 21730–1737 (1970).
    [CrossRef]
  15. R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
    [CrossRef]
  16. R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A 111507–1521 (1975).
    [CrossRef]
  17. H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A 83053811 (2011).
    [CrossRef]
  18. H. Takeda, “Collective population evolution of two-level atoms based on mean-field theory,” Phys. Rev. A 85, 023837 (2012).
    [CrossRef]
  19. A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).
  20. I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. 35, 1094–1096 (2010).
    [CrossRef] [PubMed]
  21. M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
    [CrossRef] [PubMed]
  22. U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
    [CrossRef] [PubMed]
  23. S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
    [CrossRef]
  24. 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, 200–203 (2004).
    [CrossRef] [PubMed]
  25. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
    [CrossRef] [PubMed]
  26. J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
    [CrossRef] [PubMed]
  27. M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
    [CrossRef] [PubMed]
  28. L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover Publications, Inc., New York, 1987).
  29. I. Kang and F. W. Wise, “Electronic structure and optical properties of PbS and PbSe quantum dots,” J. Opt. Soc. Am. B 141632–1646 (1997).
    [CrossRef]
  30. P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
    [CrossRef]
  31. M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
    [CrossRef]
  32. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  33. K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 583896–3908 (1998).
    [CrossRef]
  34. P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
    [CrossRef]

2012 (3)

H. Takeda, “Collective population evolution of two-level atoms based on mean-field theory,” Phys. Rev. A 85, 023837 (2012).
[CrossRef]

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

2011 (3)

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A 83053811 (2011).
[CrossRef]

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
[CrossRef] [PubMed]

2010 (3)

I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. 35, 1094–1096 (2010).
[CrossRef] [PubMed]

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
[CrossRef]

2009 (1)

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

2007 (1)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

2006 (1)

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
[CrossRef]

2005 (1)

T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
[CrossRef] [PubMed]

2004 (3)

M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A 69053810 (2004).
[CrossRef]

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 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,” Nature 432, 200–203 (2004).
[CrossRef] [PubMed]

2003 (1)

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

2001 (2)

S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt. 3S103–S120 (2001).
[CrossRef]

M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A 64033801 (2001).
[CrossRef]

1998 (1)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 583896–3908 (1998).
[CrossRef]

1997 (2)

I. Kang and F. W. Wise, “Electronic structure and optical properties of PbS and PbSe quantum dots,” J. Opt. Soc. Am. B 141632–1646 (1997).
[CrossRef]

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett. 781888–1891 (1997).
[CrossRef]

1988 (1)

M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A 385182–5192 (1988).
[CrossRef] [PubMed]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 582486–2489 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 582059–2062 (1987).
[CrossRef] [PubMed]

1975 (1)

R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A 111507–1521 (1975).
[CrossRef]

1971 (1)

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
[CrossRef]

1970 (1)

F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A 21730–1737 (1970).
[CrossRef]

1969 (1)

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 1881969–1975 (1969).
[CrossRef]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 9399–110 (1954).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69681 (1946).

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover Publications, Inc., New York, 1987).

Arecchi, F. T.

F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A 21730–1737 (1970).
[CrossRef]

Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Barrett, S. D.

T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
[CrossRef] [PubMed]

Belyanin, A. A.

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

Benner, H.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A 111507–1521 (1975).
[CrossRef]

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
[CrossRef]

Bose, R.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

Busch, K.

Busch, Kurt

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Carmichael, H. J.

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
[CrossRef] [PubMed]

Courtens, E.

F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A 21730–1737 (1970).
[CrossRef]

Dantas, N. O.

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (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, 200–203 (2004).
[CrossRef] [PubMed]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 9399–110 (1954).
[CrossRef]

Doherty, A. C.

T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
[CrossRef] [PubMed]

Drescher, M.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Dunzer, F.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover Publications, Inc., New York, 1987).

P. W. Milloni and J. H. Eberly, Laser Physics (Wiley, 2009).

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, 200–203 (2004).
[CrossRef] [PubMed]

Essig, S.

Falt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Florescu, M.

M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A 69053810 (2004).
[CrossRef]

M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A 64033801 (2001).
[CrossRef]

S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt. 3S103–S120 (2001).
[CrossRef]

Forchel, A.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (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, 200–203 (2004).
[CrossRef] [PubMed]

Gonzaga, T. N.

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
[CrossRef]

Gregersen, N.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Haake, F.

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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, 200–203 (2004).
[CrossRef] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Hoeppe, U.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Hofling, S.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Hofmann, C.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Hughes, S.

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
[CrossRef] [PubMed]

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
[CrossRef]

Huisman, S. R.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

John, S.

H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A 83053811 (2011).
[CrossRef]

M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A 69053810 (2004).
[CrossRef]

S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt. 3S103–S120 (2001).
[CrossRef]

M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A 64033801 (2001).
[CrossRef]

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 583896–3908 (1998).
[CrossRef]

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett. 781888–1891 (1997).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 582486–2489 (1987).
[CrossRef] [PubMed]

Kamp, M.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

Kang, I.

Keldysh, L. V.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (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, 200–203 (2004).
[CrossRef] [PubMed]

Kistner, C.

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Kocharovsky, V. V.

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

Kocharovsky, Vl. V.

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

Kuchenmeister, J.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Kuhn, S.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Lagendijk, A.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

Leistikow, M. D.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

Lermer, M.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

Lindberg, M.

M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A 385182–5192 (1988).
[CrossRef] [PubMed]

Löffler, A.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Lugiato, L. A.

R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A 111507–1521 (1975).
[CrossRef]

Manga Rao, V. S. C.

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
[CrossRef]

Milloni, P. W.

P. W. Milloni and J. H. Eberly, Laser Physics (Wiley, 2009).

Mollow, B. R.

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 1881969–1975 (1969).
[CrossRef]

Monte, A. F. G.

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
[CrossRef]

Mork, J.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Mosk, A. P.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

Naves, P. M.

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
[CrossRef]

Niegemann, J.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

Nielsen, T. R.

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Pan, L.

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Pestov, D. S.

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69681 (1946).

Quang, T.

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett. 781888–1891 (1997).
[CrossRef]

Rakher, M. T.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

Reinecke, T. L.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

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, 200–203 (2004).
[CrossRef] [PubMed]

Savage, C. M.

M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A 385182–5192 (1988).
[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, 200–203 (2004).
[CrossRef] [PubMed]

Schneider, C.

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Schwendimann, P.

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
[CrossRef]

Se.k, G.

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[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, 200–203 (2004).
[CrossRef] [PubMed]

Srinivasan, K.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

Stace, T. M.

T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
[CrossRef] [PubMed]

Staude, I.

Strauss, M.

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Takeda, H.

H. Takeda, “Collective population evolution of two-level atoms based on mean-field theory,” Phys. Rev. A 85, 023837 (2012).
[CrossRef]

H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A 83053811 (2011).
[CrossRef]

Thiel, M.

von Freymann, G.

Vos, W. L.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

Wegener, M.

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

Wise, F. W.

Wolff, C.

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. 35, 1094–1096 (2010).
[CrossRef] [PubMed]

Wong, C. W.

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

Worschech, L.

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 582059–2062 (1987).
[CrossRef] [PubMed]

Yao, P.

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
[CrossRef]

Yeganegi, E.

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[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, 200–203 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

S. Reitzenstein, N. Gregersen, C. Kistner, M. Strauss, C. Schneider, L. Pan, T. R. Nielsen, S. Hofling, J. Mork, and A. Forchel, “Oscillatory variations in the Q factors of high quality micropillar cavities,” Appl. Phys. Lett. 94061108 (2009).
[CrossRef]

M. T. Rakher, R. Bose, C. W. Wong, and K. Srinivasan, “Spectroscopy of 1.55 μm PbS quantum dots on Si photonic crystal cavities with a fiber taper waveguide,” Appl. Phys. Lett. 96161108 (2010).
[CrossRef]

J. Non-Crystalline Solids (1)

P. M. Naves, T. N. Gonzaga, A. F. G. Monte, and N. O. Dantas, “Band gap energy of PbS quantum dots in oxide glasses as a function of concentration,” J. Non-Crystalline Solids 3523633–3635 (2006).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A: Pure Appl. Opt. 3S103–S120 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photonics Rev. 4499–516 (2010).
[CrossRef]

Laser Phys. (1)

A. A. Belyanin, V. V. Kocharovsky, Vl. V. Kocharovsky, and D. S. Pestov, “Novel schemes and prospects of superradiant lasing in heterostructures,” Laser Phys. 13161–167 (2003).

Nature (3)

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, 200–203 (2004).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Se.k, 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,” Nature 432, 197–200 (2004).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (3)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 9399–110 (1954).
[CrossRef]

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69681 (1946).

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 1881969–1975 (1969).
[CrossRef]

Phys. Rev. A (8)

M. Florescu and S. John, “Single-atom switching in photonic crystals,” Phys. Rev. A 64033801 (2001).
[CrossRef]

M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: Engineering the vacuum for all-optical switching,” Phys. Rev. A 69053810 (2004).
[CrossRef]

M. Lindberg and C. M. Savage, “Steady-state two-level atomic population inversion via a quantized cavity field,” Phys. Rev. A 385182–5192 (1988).
[CrossRef] [PubMed]

F. T. Arecchi and E. Courtens, “Cooperative phenomena in resonant electromagnetic propagation,” Phys. Rev. A 21730–1737 (1970).
[CrossRef]

R. Bonifacio, P. Schwendimann, and F. Haake, “Quantum statistical theory of superradiance. I,” Phys. Rev. A 4302–313 (1971).
[CrossRef]

R. Bonifacio and L. A. Lugiato, “Cooperative radiation processes in two-level systems: Superfluorescence,” Phys. Rev. A 111507–1521 (1975).
[CrossRef]

H. Takeda and S. John, “Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals,” Phys. Rev. A 83053811 (2011).
[CrossRef]

H. Takeda, “Collective population evolution of two-level atoms based on mean-field theory,” Phys. Rev. A 85, 023837 (2012).
[CrossRef]

Phys. Rev. E (1)

K. Busch and S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 583896–3908 (1998).
[CrossRef]

Phys. Rev. Lett. (8)

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Hofling, J. Mork, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[CrossRef] [PubMed]

M. D. Leistikow, A. P. Mosk, E. Yeganegi, S. R. Huisman, A. Lagendijk, and W. L. Vos, “Inhibited spontaneous emission of quantum dots observed in a 3D photonic band gap,” Phys. Rev. Lett. 107, 193903 (2011).
[CrossRef] [PubMed]

U. Hoeppe, C. Wolff, J. Kuchenmeister, J. Niegemann, M. Drescher, H. Benner, and Kurt Busch, “Direct observation of non-markovian radiation dynamics in 3D bulk photonic crystals”, Phys. Rev. Lett. 108, 043603 (2012).
[CrossRef] [PubMed]

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic systems,” Phys. Rev. Lett. 781888–1891 (1997).
[CrossRef]

T. M. Stace, A. C. Doherty, and S. D. Barrett, “Population inversion of a driven two-level system in a structureless bath,” Phys. Rev. Lett. 95106801 (2005).
[CrossRef] [PubMed]

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 582486–2489 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 582059–2062 (1987).
[CrossRef] [PubMed]

Other (3)

P. W. Milloni and J. H. Eberly, Laser Physics (Wiley, 2009).

L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover Publications, Inc., New York, 1987).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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Figures (6)

Fig. 1
Fig. 1

Structure of a realistic 1D PC composed of stacked layers of Si and SiO2. Dielectric constants of Si and SiO2 are εSi = 11.9 and εSiO2 = 2.25, respectively. Thicknesses of Si and SiO2 layers are tSi/a = 0.4 and tSiO2 /a = 0.6, respectively, where a = 516.3 nm is the lattice constant of 1D PC’s. Widths in the x and y directions are a. There is the origin (0, 0, 0) in the SiO2 region, and this structure is symmetric at the origin.

Fig. 2
Fig. 2

(a) Photonic band structure of the realistic 1D PC. A shaded region indicates the light cone in which light leaks into air regions. Below the light cone, solid and dashed lines indicate the doubly-degenerate and single modes, respectively. (b) x-polarized EM LDOS’s of the realistic 1D PC composed of 21 SiO2 layers at (x/a, y/a, z/a) = (0, 0, ±0.5) (Si region) and (0, 0, 0) (SiO2 region). A gray line indicates the EM LDOS in free space and is proportional to ω2.

Fig. 3
Fig. 3

(a) Collective spontaneous emission rate at (x/a, y/a, z/a) = (0, 0, 0) for 0.32 ≤ ωa/2πcl ≤ 0.38. ωAa/2πcl = 0.3300, 0.3442, 0.3479 and 0.3525 are focused. (b) Temporal behavior of 〈σ3(t)〉 for various atomic frequencies, using the first-principle Maxwell-Bloch theory (Sec. 2). Multiplying clt/a by a/cl = 1.721 × 10−3 ps gives real time.

Fig. 4
Fig. 4

(a) Ground and excited states for bare and dressed states in the left and right sketches, respectively. ΔAL < 0 is assumed. |i, m〉 indicates the |i〉 state with the photon number m of the frequency ωL. (b) Schematic model of EM LDOS’s near the upper photonic band edge. Lower and higher gray regions indicate the PBG and the propagation region, respectively.

Fig. 5
Fig. 5

(a) Spontaneous emission rate at (x/a, y/a, z/a) = (0, 0, 0) for 0.335 ≤ ωa/2πcl ≤ 0.350. I set up ωAa/2πcl = 0.3405 and ωLa/2πcl = 0.3415. (b) Temporal behavior of 〈σ3(t)〉 as a function of time at E0 = 2.0 × 106 V/m and 8.0 × 106 V/m, using the first-principle Maxwell-Bloch theory (Sec. 2). Multiplying clt/a by a/cl = 1.721 × 10−3 ps gives real time.

Fig. 6
Fig. 6

(a) Behavior of 〈σ3st as a function of E0 for various frequencies, using the first-principle Maxwell-Bloch theory (Sec. 2). ωAa/2πcl = 0.3405, 0.3415 and 0.3425 are considered. The laser frequency is ωLa/2πcl = 0.3415. Gray dashed and solid lines correspond to the behaviors of 〈σ3st at Np = 1 (single atom) and 125 (collective atoms), respectively, derived from Eq. (10). (b) Behavior of (c4γ+)/(s4γ) as a function of E0 at ωAa/2πcl = 0.3405 (ΔAL < 0). While circles indicate the numerical data, a gray line is the spline interpolation of them.

Equations (10)

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d d t [ σ 1 ( t ) σ 2 ( t ) σ 3 ( t ) ] = [ 0 ω A 0 ω A 0 2 d 0 E ( t ) / h ¯ 0 2 d 0 E ( t ) / h ¯ 0 ] [ σ 1 ( t ) σ 2 ( t ) σ 3 ( t ) ] ,
× E ( r , t ) = μ 0 H ( r , t ) t
× H ( r , t ) = P ( r , t ) t + ε 0 ε ( r ) E ( r , t ) t ,
ρ u , u ( ω ; r ) = 1 V λ | u E λ ( r ) | 2 δ ( ω ω λ ) ,
H = h ¯ ω A σ 22 d 0 E ( t ) ( σ 12 + σ 21 ) = h ¯ ω A σ 22 d 0 A 0 [ exp ( i ω L t ) σ 12 + exp ( i ω L t ) σ 21 + exp ( i ω L t ) σ 12 + exp ( i ω L t ) σ 21 ]
H ˜ = U ( t ) H U ( t ) i h ¯ d U ( t ) d t U ( t ) = h ¯ Δ A L σ 22 d 0 A 0 [ σ 12 + σ 21 + exp ( 2 i ω L t ) σ 12 + exp ( 2 i ω L t ) σ 21 ] h ¯ Δ A L σ 22 d 0 A 0 ( σ 12 + σ 21 ) ,
H ˜ = 2 h ¯ Ω R 22 ,
2 Ω = Δ A L 2 + ( 2 d 0 A 0 / h ¯ ) 2 | Δ A L |
σ 3 ( t ) = ( c 2 s 2 ) R 3 ( t ) + 2 s c [ R 12 ( t ) + R 21 ( t ) ] = ( c 2 s 2 ) R 3 ( 0 ) + 4 s c | R 12 ( 0 ) | cos ( 2 Ω t + θ 0 ) ,
σ 3 s t = Δ A L 2 Ω [ 2 ( 1 + 1 N p ) 1 1 η N p + 1 2 N p 1 1 η 1 ] ,

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