Abstract

We study the coupling between quantum dots through the dipole–dipole interaction in photonic nanofibers manufactured by embedding a dielectric material into a photonic crystal. The embedded dielectric material is doped with an ensemble of three-level quantum dots. A probe field is applied to monitor the absorption, and a control field is applied to induce dipole moments in quantum dots. Dipoles are induced in quantum dots due to the external fields, and they interact with each other via the dipole–dipole interaction. Quantum dots also interact with the nanofiber through the electron–bound photon interaction. The absorption coefficient has been calculated using the density matrix method, and the dipole–dipole interaction has been evaluated in the mean field approximation. It is found that the absorption spectrum splits from one peak to two peaks by the dipole–dipole interaction. The splitting of peaks can be controlled by either the resonance energy of quantum dots or bound photon states of the nanofiber.

© 2010 Optical Society of America

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  1. M. R. Singh, “Transparency in nanophotonic quantum wires,” J. Phys. B 42, 065503 (2009).
    [CrossRef]
  2. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006).
    [CrossRef]
  3. Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007).
    [CrossRef] [PubMed]
  4. D. Lauvernier, S. Garidel, M. Zegaoui, J. P. Vilcot, and D. Decoster, “GaAs/polymer optical nanowires: fabrication and characterisation,” Electron. Lett. 42, 217–219 (2006).
    [CrossRef]
  5. B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
    [CrossRef]
  6. M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. St. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
    [CrossRef]
  7. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals (Princeton U. Press, 2008).
  8. V. I. Rupasov and M. R. Singh, “Quantum gap solitons and many-polariton–atom bound states in dispersive medium and photonic bandgap,” Phys. Rev. Lett. 77, 338–341 (1996).
    [CrossRef] [PubMed]
  9. V. I. Rupasov and M. R. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996).
    [CrossRef] [PubMed]
  10. V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327–3330 (1996).
    [CrossRef] [PubMed]
  11. O. G. Calderón, M. A. Antón, and F. Carreño, “Near dipole-dipole effects in a V-type medium with vacuum induced coherence,” Eur. Phys. J. D 25, 77–87 (2003).
    [CrossRef]
  12. T. Pohl and P. R. Berman, “Breaking the dipole blockade: Nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
    [CrossRef] [PubMed]
  13. E. Paspalakis, A. Kalini, and A. F. Terzis, “Local field effects in excitonic population transfer in a driven quantum dot system,” Phys. Rev. B 73, 073305 (2006).
    [CrossRef]
  14. Ö. Çakir, A. A. Klyachko, and A. S. Shumovsky, “Steady-state entanglement of two atoms created by classical driving field,” Phys. Rev. A 71, 034303 (2005).
    [CrossRef]
  15. C. Skornia, J. von Zanthier, G. S. Agarwal, E. Werner, and H. Walther, “Monitoring the dipole-dipole interaction via quantum jumps of individual atoms,” Phys. Rev. A 64, 053803 (2001).
    [CrossRef]
  16. J. Evers, M. Kiffner, M. Macovei, and C. H. Keitel, “Geometry-dependent dynamics of two-type atoms via vacuum-induced coherences,” Phys. Rev. A 73, 023804 (2006).
    [CrossRef]
  17. S. Xie, Y. Yang, H. Chen, and S. Zhu, “Atom-atom interaction in an anisotropic photonic crystal,” J. Mod. Opt. 50, 83–112 (2003).
  18. M. R. Singh, “Transparency and spontaneous emission in a densely doped photonic band gap material,” J. Phys. B 39, 5131–5141 (2006).
    [CrossRef]
  19. M. R. Singh, “Switching mechanism due to the spontaneous emission cancellation in photonic bandgap materials doped with nano-particles,” Phys. Lett. A 363, 177–181 (2007).
    [CrossRef]
  20. M. R. Singh, “Dipole-dipole interaction in photonic-band-gap materials doped with nanoparticles,” Phys. Rev. A 75, 043809 (2007).
    [CrossRef]
  21. M. R. Singh, “Inhibition of two-photon absorption due to dipole–dipole interaction in nanoparticles,” Phys. Lett. A 372, 5083–5088 (2008).
    [CrossRef]
  22. M. R. Singh, “Controlling photon absorption in photonic nanowires via dipole–dipole interaction,” Opt. Lett. 34, 2909–2911 (2009).
    [CrossRef] [PubMed]
  23. P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
    [CrossRef] [PubMed]
  24. J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark splitting and quantum interference with intersubband transitions in quantum wells,” Phys. Rev. Lett. 94, 157403 (2005).
    [CrossRef] [PubMed]
  25. E. Hendry, M. Koeberg, F. Wang, H. Zhang, C. de Mello Donegá, D. Vanmaekelbergh, and M. Bonn, “Direct observation of electron-to-hole energy transfer in CdSe quantum dots,” Phys. Rev. Lett. 96, 057408 (2006).
    [CrossRef] [PubMed]
  26. S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
    [CrossRef]
  27. P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
    [CrossRef]
  28. K. B. Chung and S. H. Kim, “Defect modes in a two-dimensional square-lattice photonic crystal,” Opt. Commun. 209, 229–235 (2002).
    [CrossRef]
  29. S. John and M. Florescu, “Photonic bandgap materials: towards an all-optical micro-transistor,” J. Opt. A, Pure Appl. Opt. 3, S103–S120 (2001).
    [CrossRef]
  30. M. R. Singh and R. Lipson, “Optical switching in nonlinear photonic crystals lightly doped with nanostructures,” J. Phys. B 41, 015401 (2008).
    [CrossRef]
  31. D. Petrosyan and G. Kurizki, “Photon-photon correlations and entanglement in doped photonic crystals,” Phys. Rev. A 64, 023810 (2001).
    [CrossRef]
  32. K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006), Chap. 2.
  33. A. Ariv and P. Yeh, Photonics (Oxford U. Press, 2007).
  34. M. J. Adams, An Introduction to Optical Waveguides (Wiley, 1981).
  35. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  36. J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972–975 (1991).
    [CrossRef] [PubMed]
  37. M. R. Singh, Recent Research Activities in Chemical Physics: From Atomic Scale to Macroscale, E.Paspalakis and A.F.Terzis, eds. (Transworld Research Network, 2008), Chap. 5, pp. 101–165.
  38. D. G. Angelakis, E. Paspalakis, and P. L. Knight, “Transient properties of modified reservoir-induced transparency,” Phys. Rev. A 61, 055802 (2000).
    [CrossRef]
  39. M. R. Singh, “Anomalous electromagnetically induced transparency in photonic-band-gap materials,” Phys. Rev. A 70, 033813 (2004).
    [CrossRef]
  40. 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]
  41. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature 445, 896–899 (2007).
    [CrossRef] [PubMed]
  42. V. A. Sautenkov, Y. V. Rostovtsev, and E. R. Eliel, “Observation of narrow Autler–Townes components in the resonant response of a dense atomic gas” Phys. Rev. A 78, 013802 (2008).
    [CrossRef]

2009

M. R. Singh, “Transparency in nanophotonic quantum wires,” J. Phys. B 42, 065503 (2009).
[CrossRef]

T. Pohl and P. R. Berman, “Breaking the dipole blockade: Nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[CrossRef] [PubMed]

M. R. Singh, “Controlling photon absorption in photonic nanowires via dipole–dipole interaction,” Opt. Lett. 34, 2909–2911 (2009).
[CrossRef] [PubMed]

2008

M. R. Singh, “Inhibition of two-photon absorption due to dipole–dipole interaction in nanoparticles,” Phys. Lett. A 372, 5083–5088 (2008).
[CrossRef]

M. R. Singh and R. Lipson, “Optical switching in nonlinear photonic crystals lightly doped with nanostructures,” J. Phys. B 41, 015401 (2008).
[CrossRef]

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. St. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals (Princeton U. Press, 2008).

M. R. Singh, Recent Research Activities in Chemical Physics: From Atomic Scale to Macroscale, E.Paspalakis and A.F.Terzis, eds. (Transworld Research Network, 2008), Chap. 5, pp. 101–165.

V. A. Sautenkov, Y. V. Rostovtsev, and E. R. Eliel, “Observation of narrow Autler–Townes components in the resonant response of a dense atomic gas” Phys. Rev. A 78, 013802 (2008).
[CrossRef]

2007

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

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007).
[CrossRef] [PubMed]

A. Ariv and P. Yeh, Photonics (Oxford U. Press, 2007).

M. R. Singh, “Switching mechanism due to the spontaneous emission cancellation in photonic bandgap materials doped with nano-particles,” Phys. Lett. A 363, 177–181 (2007).
[CrossRef]

M. R. Singh, “Dipole-dipole interaction in photonic-band-gap materials doped with nanoparticles,” Phys. Rev. A 75, 043809 (2007).
[CrossRef]

2006

E. Hendry, M. Koeberg, F. Wang, H. Zhang, C. de Mello Donegá, D. Vanmaekelbergh, and M. Bonn, “Direct observation of electron-to-hole energy transfer in CdSe quantum dots,” Phys. Rev. Lett. 96, 057408 (2006).
[CrossRef] [PubMed]

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006), Chap. 2.

D. Lauvernier, S. Garidel, M. Zegaoui, J. P. Vilcot, and D. Decoster, “GaAs/polymer optical nanowires: fabrication and characterisation,” Electron. Lett. 42, 217–219 (2006).
[CrossRef]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78, 455–481 (2006).
[CrossRef]

E. Paspalakis, A. Kalini, and A. F. Terzis, “Local field effects in excitonic population transfer in a driven quantum dot system,” Phys. Rev. B 73, 073305 (2006).
[CrossRef]

J. Evers, M. Kiffner, M. Macovei, and C. H. Keitel, “Geometry-dependent dynamics of two-type atoms via vacuum-induced coherences,” Phys. Rev. A 73, 023804 (2006).
[CrossRef]

M. R. Singh, “Transparency and spontaneous emission in a densely doped photonic band gap material,” J. Phys. B 39, 5131–5141 (2006).
[CrossRef]

2005

Ö. Çakir, A. A. Klyachko, and A. S. Shumovsky, “Steady-state entanglement of two atoms created by classical driving field,” Phys. Rev. A 71, 034303 (2005).
[CrossRef]

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark splitting and quantum interference with intersubband transitions in quantum wells,” Phys. Rev. Lett. 94, 157403 (2005).
[CrossRef] [PubMed]

2004

P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004).
[CrossRef] [PubMed]

M. R. Singh, “Anomalous electromagnetically induced transparency in photonic-band-gap materials,” Phys. Rev. A 70, 033813 (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, 200–203 (2004).
[CrossRef] [PubMed]

2003

O. G. Calderón, M. A. Antón, and F. Carreño, “Near dipole-dipole effects in a V-type medium with vacuum induced coherence,” Eur. Phys. J. D 25, 77–87 (2003).
[CrossRef]

S. Xie, Y. Yang, H. Chen, and S. Zhu, “Atom-atom interaction in an anisotropic photonic crystal,” J. Mod. Opt. 50, 83–112 (2003).

2002

K. B. Chung and S. H. Kim, “Defect modes in a two-dimensional square-lattice photonic crystal,” Opt. Commun. 209, 229–235 (2002).
[CrossRef]

2001

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

D. Petrosyan and G. Kurizki, “Photon-photon correlations and entanglement in doped photonic crystals,” Phys. Rev. A 64, 023810 (2001).
[CrossRef]

C. Skornia, J. von Zanthier, G. S. Agarwal, E. Werner, and H. Walther, “Monitoring the dipole-dipole interaction via quantum jumps of individual atoms,” Phys. Rev. A 64, 053803 (2001).
[CrossRef]

2000

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

D. G. Angelakis, E. Paspalakis, and P. L. Knight, “Transient properties of modified reservoir-induced transparency,” Phys. Rev. A 61, 055802 (2000).
[CrossRef]

1997

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

1996

V. I. Rupasov and M. R. Singh, “Quantum gap solitons and many-polariton–atom bound states in dispersive medium and photonic bandgap,” Phys. Rev. Lett. 77, 338–341 (1996).
[CrossRef] [PubMed]

V. I. Rupasov and M. R. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996).
[CrossRef] [PubMed]

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327–3330 (1996).
[CrossRef] [PubMed]

1991

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
[CrossRef]

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972–975 (1991).
[CrossRef] [PubMed]

1981

M. J. Adams, An Introduction to Optical Waveguides (Wiley, 1981).

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, 1981).

Agarwal, G. S.

C. Skornia, J. von Zanthier, G. S. Agarwal, E. Werner, and H. Walther, “Monitoring the dipole-dipole interaction via quantum jumps of individual atoms,” Phys. Rev. A 64, 053803 (2001).
[CrossRef]

Angelakis, D. G.

D. G. Angelakis, E. Paspalakis, and P. L. Knight, “Transient properties of modified reservoir-induced transparency,” Phys. Rev. A 61, 055802 (2000).
[CrossRef]

Antón, M. A.

O. G. Calderón, M. A. Antón, and F. Carreño, “Near dipole-dipole effects in a V-type medium with vacuum induced coherence,” Eur. Phys. J. D 25, 77–87 (2003).
[CrossRef]

Ariv, A.

A. Ariv and P. Yeh, Photonics (Oxford U. Press, 2007).

Atatüre, M.

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

Bay, S.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Beck, M.

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark splitting and quantum interference with intersubband transitions in quantum wells,” Phys. Rev. Lett. 94, 157403 (2005).
[CrossRef] [PubMed]

Bergman, K.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

Berman, P. R.

T. Pohl and P. R. Berman, “Breaking the dipole blockade: Nearly resonant dipole interactions in few-atom systems,” Phys. Rev. Lett. 102, 013004 (2009).
[CrossRef] [PubMed]

Biberman, A.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

Bonn, M.

E. Hendry, M. Koeberg, F. Wang, H. Zhang, C. de Mello Donegá, D. Vanmaekelbergh, and M. Bonn, “Direct observation of electron-to-hole energy transfer in CdSe quantum dots,” Phys. Rev. Lett. 96, 057408 (2006).
[CrossRef] [PubMed]

Boyd, R. W.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67, 972–975 (1991).
[CrossRef] [PubMed]

Çakir, Ö.

Ö. Çakir, A. A. Klyachko, and A. S. Shumovsky, “Steady-state entanglement of two atoms created by classical driving field,” Phys. Rev. A 71, 034303 (2005).
[CrossRef]

Calderón, O. G.

O. G. Calderón, M. A. Antón, and F. Carreño, “Near dipole-dipole effects in a V-type medium with vacuum induced coherence,” Eur. Phys. J. D 25, 77–87 (2003).
[CrossRef]

Carreño, F.

O. G. Calderón, M. A. Antón, and F. Carreño, “Near dipole-dipole effects in a V-type medium with vacuum induced coherence,” Eur. Phys. J. D 25, 77–87 (2003).
[CrossRef]

Chen, H.

S. Xie, Y. Yang, H. Chen, and S. Zhu, “Atom-atom interaction in an anisotropic photonic crystal,” J. Mod. Opt. 50, 83–112 (2003).

Chen, X.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

Chou, C.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

Chung, K. B.

K. B. Chung and S. H. Kim, “Defect modes in a two-dimensional square-lattice photonic crystal,” Opt. Commun. 209, 229–235 (2002).
[CrossRef]

Dadap, J. I.

B. G. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. I. Dadap, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, R. M. Osgood, Jr., and K. Bergman, “Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks,” IEEE Photon. Technol. Lett. 20, 398–400 (2008).
[CrossRef]

de Mello Donegá, C.

E. Hendry, M. Koeberg, F. Wang, H. Zhang, C. de Mello Donegá, D. Vanmaekelbergh, and M. Bonn, “Direct observation of electron-to-hole energy transfer in CdSe quantum dots,” Phys. Rev. Lett. 96, 057408 (2006).
[CrossRef] [PubMed]

Decoster, D.

D. Lauvernier, S. Garidel, M. Zegaoui, J. P. Vilcot, and D. Decoster, “GaAs/polymer optical nanowires: fabrication and characterisation,” Electron. Lett. 42, 217–219 (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]

Dynes, J. F.

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark splitting and quantum interference with intersubband transitions in quantum wells,” Phys. Rev. Lett. 94, 157403 (2005).
[CrossRef] [PubMed]

Eliel, E. R.

V. A. Sautenkov, Y. V. Rostovtsev, and E. R. Eliel, “Observation of narrow Autler–Townes components in the resonant response of a dense atomic gas” Phys. Rev. A 78, 013802 (2008).
[CrossRef]

V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P. Woerdman, “Dipole-dipole broadened line shape in a partially excited dense atomic gas,” Phys. Rev. Lett. 77, 3327–3330 (1996).
[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,” Nature 432, 200–203 (2004).
[CrossRef] [PubMed]

Evers, J.

J. Evers, M. Kiffner, M. Macovei, and C. H. Keitel, “Geometry-dependent dynamics of two-type atoms via vacuum-induced coherences,” Phys. Rev. A 73, 023804 (2006).
[CrossRef]

Faist, J.

J. F. Dynes, M. D. Frogley, M. Beck, J. Faist, and C. C. Phillips, “ac Stark splitting and quantum interference with intersubband transitions in quantum wells,” Phys. Rev. Lett. 94, 157403 (2005).
[CrossRef] [PubMed]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, 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.

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

Frogley, M. D.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram is shown for a photonic nanofiber (top view). The nanofiber is made from embedding a dielectric material into a photonic crystal A. Quantum dots are doped into the embedded material.

Fig. 2
Fig. 2

Schematic diagram of a three-level quantum dot. The levels are denoted by | 1 , | 2 , and | 3 . A control laser couples | 3 and | 1 , whereas a probe laser couples | 2 and | 1 . Levels | 3 and | 2 decay to the level | 1 due to the electron–bound photon interaction.

Fig. 3
Fig. 3

Absorption coefficient Im ( χ d d / χ 0 ) is plotted as a function of the normalized probe detuning δ 21 when the control field is absent. The solid and dashed lines correspond to C 21 = 0 and C 21 = 2 , respectively. Note that the absorption peak shifts to the right due to the DD interaction. Linewidths are calculated when both resonance energies ε 21 and ε 31 lie far away from ε 00 .

Fig. 4
Fig. 4

Absorption coefficient Im ( χ d d / χ 0 ) is plotted as a function of the normalized probe detuning δ 21 when the control field is present. The solid and dashed lines correspond to C 31 = 0 and C 31 = 5 , respectively. Note that the absorption peak splits into two peaks due to the DD coupling C 31 . The C 21 coupling is taken as C 21 = 2 . Linewidths are calculated when both resonance energies ε 21 and ε 31 lie far away from ε 00 .

Fig. 5
Fig. 5

In this figure, the effect of the EBP interaction due to linewidth Γ 31 is presented. The absorption coefficient Im ( χ d d / χ 0 ) is plotted as a function of the normalized probe detuning δ 21 when the control field is present. Parameters are taken as C 31 = 5 and C 21 = 2 . The solid, dotted, and dashed-dotted lines are calculated when resonance energy ε 31 lies at 1330, 1260, and 1256, respectively.

Fig. 6
Fig. 6

The normalized DOS is plotted as function of energy near the photon bound state ε 00 .

Equations (25)

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ε k p = c 4 n p r arccos ( 4 n p   cos ( k p L ) ( n p 1 ) 2 ( n p + 1 ) 2 ) ,
ε k d = c n d k d ,
k n   tan ( k n d x / 2 n π 2 ) = k d 2 ( ε n m k z ) k p 2 ( ε n m k z ) k n 2 ,
k m   tan ( k m d y / 2 m π 2 ) = k d 2 ( ε n m k z ) k p 2 ( ε n m k z ) k m 2 ,
k p ( ε n m k z ) = 1 L arccos [ ( n p + 1 ) 2 4 n p cos ( 4 ε n m k z n p r c ) ( n p 1 ) 2 4 n p ] ,
k d ( ε n m k z ) = n d c ε n m k z .
n . m k z = n , m D ( ε n m k z ) d ε ε n m k z ,
D ( ε n m k z ) = d z π d k z d ε n m k z .
k z = ( n d c ε n m k z ) 2 k n 2 k m 2 .
D ( ε n m k z ) = ( n d d z 2 π c ) ε n m ε n m k z ε n m ,
H d d = 2 γ 0 [ C 21 ρ 21 + C 23 ρ 31 ] σ 21 + e i ( ε p ε 21 ) t / 2 γ 0 [ C 31 ρ 31 + C 23 ρ 21 ] σ 31 + e i ( ε c ε 31 ) t / + H .c . ,
H EBP = i = 2 , 3 ε i 1 σ i 1 z + n , m , k z ε n m k z p n m k z + p n m k z i = 2 , 3 n , m , k z ( ε n m k z μ i 1 2 / 2 ϵ 0 2 V ) ( ε n m k z ) p n m k z σ i 1 + e i ( ε i 1 ε n m k z ) t / + H .c . ,
χ = N 0 μ 21 2 γ 0 ρ 21 2 ϵ 0 x p ,
χ d d = χ 0 ( ξ 1 ξ 2 + ξ 3 d 13 ( d 21 d 23 + | x c + C 31 ξ 4 | 2 ) C 21 ( ξ 1 ξ 2 + ξ 2 ) ) .
ξ 1 = i ( 2 | x c + C 31 ξ 4 | 2 d 23 d 13 ) ,
ξ 2 = | x c | 2 ( d 31 + d 13 ) γ 31 d 31 d 13 + 2 | x c | 2 ( d 31 + d 13 ) ,
ξ 3 = i ( d 23 d 13 | x c + C 31 ξ 4 | 2 ) ,     ξ 4 = i x c d 31 ( 1 2 ξ 2 ) ,
Ξ i 1 = ( ε i 1 μ i 1 2 2 ϵ 0 V ) n m D ( ε n m k z ) d ε n m k z ( 1 ( ε n m k z ε i 1 ) i γ i 1 ) ,     i = 2 , 3 ,
Δ i 1 = ( ε i 1 3 / 2 μ i 1 2 n d 2 2 c ϵ 0 d x d y ) n m cos ( ϕ i 1 / 2 ) [ ( ε n m ε i 1 ) 2 + γ i 1 2 ] 1 / 4 ,     i = 2 , 3.
Γ i 1 = n m η i 1 [ ( ε n m ε i 1 ) 2 + γ i 1 2 ] 1 / 4 ,     i = 2 , 3 ,
η i 1 = ( ε i 1 3 / 2 μ i 1 2 n d   sin   ϕ i 1 / 2 2 2 c ϵ 0 d x d y ) ,
ϕ i 1 = arctan ( γ i 1 ε n m ε i 1 ) ,     i = 2 , 3.
χ d d = χ 0 i [ | x c + C 31 ξ 4 | 2 ( 2 ξ 2 1 ) + d 23 d 13 ( 1 ξ 2 ) ] d 13 ( d 21 d 23 + | x c + C 31 ξ 4 | 2 ) C 21 [ | x c + C 31 ξ 4 | 2 ( 2 ξ 2 1 ) + d 23 d 13 ( 1 ξ 2 ) ] .
χ d d = χ 0 ( i i ( δ 21 + C 21 ) + ( Γ 21 ) / 2 ) .
χ d d = χ 0 ( i [ | x c | 2 ( 2 ξ 2 1 ) + d 23 d 13 ( 1 ξ 2 ) ] d 13 ( d 21 d 23 + | x c | 2 ) ) .

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