Abstract

In this paper, we report the numerical simulation of an atom-cavity interaction within photonic crystal nano-cavities. The numerical model is based on a damping oscillator description of a dipole current and it is implemented with a finite-difference time-domain method. Using the method, we successfully simulate the atom-cavity mode field interactions of a two-level system embedded in a photonic crystal cavity under several coupling strength conditions. We show that enhancement and suppression of optical emission rate from a two-level system are also shown by this model.

© 2011 OSA

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  1. Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
    [CrossRef]
  2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
    [CrossRef]
  3. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  4. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
    [CrossRef] [PubMed]
  5. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
    [CrossRef]
  6. Kerry J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
    [CrossRef]
  7. M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
    [CrossRef]
  8. Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXive:0908.0788v1 [cond-mat.mes-hall].
  9. T. Tawara, H. Kamada, T. Tanabe, T. Sogawa, H. Okamoto, P. Yao, P. K. Pathak, and S. Hughes, “Cavity-QED assisted attraction between a cavity mode and an exciton mode in a planar photonic-crystal cavity,” Opt. Express 18, 2719–2728 (2010).
    [CrossRef] [PubMed]
  10. J. M. Raimond, M. Brune, and S. Haroche, “, “Manipulating quantum entanglement atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
    [CrossRef]
  11. T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
    [CrossRef]
  12. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
    [CrossRef]
  13. 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,” Nature (London) 445, 896–899 (2007).
    [CrossRef]
  14. G. S. Agarwal and R. R. Puri, “Exact quantum-electrodynamics results for scattering emission, and absorption from a Rydberg atom in a cavity with arbitrary Q,” Phys. Rev. A 33, 1757–1764 (1986).
    [CrossRef] [PubMed]
  15. 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. A 40,, 5516–5519 (1989).
    [CrossRef] [PubMed]
  16. F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
    [CrossRef] [PubMed]
  17. A. Taflove and S. C. Hagness, “Computational Electronics: The Finite-Difference Time-Domain Method,” 2nd ed (Artech House, Norwood2000).
  18. J. Vuckovic, O. Painter, Y. Xu, and A. Yariv, “Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quant. Electron. 35, 1168–1175 (1999).
    [CrossRef]
  19. G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, IEEE J. Select. Top. Quantum Electron. 10, 1052–1062 (2004).
    [CrossRef]
  20. D. Walls and G. Milburn, “Quantum Optics” (Springer-Verlag, Berlin, 1994).
  21. J. J. Childs, K. An, R. R. Dasari, and M. S. Feld, “Single Atom Emission in an Optical Resonator,” in Cavity Quantum Electrodynamics, P. R. Berman, Editor, Academic Press, San Diego (1994).
  22. J. D. Jackson, “Classical Electrodynamics,” 3rd ed, (Wiley, NY1999).
  23. E. M. Purcell, “Spontaneous Emission Probabilities at Radio Frequencies,” Phys. Rev. 69, 681 (1946).

2010 (2)

2009 (1)

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
[CrossRef]

2008 (1)

F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

2007 (1)

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

2006 (2)

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

2005 (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[CrossRef]

2004 (2)

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, IEEE J. Select. Top. Quantum Electron. 10, 1052–1062 (2004).
[CrossRef]

2003 (3)

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Kerry J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
[CrossRef]

2001 (1)

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

1999 (1)

J. Vuckovic, O. Painter, Y. Xu, and A. Yariv, “Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quant. Electron. 35, 1168–1175 (1999).
[CrossRef]

1989 (1)

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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

1986 (1)

G. S. Agarwal and R. R. Puri, “Exact quantum-electrodynamics results for scattering emission, and absorption from a Rydberg atom in a cavity with arbitrary Q,” Phys. Rev. A 33, 1757–1764 (1986).
[CrossRef] [PubMed]

1946 (1)

E. M. Purcell, “Spontaneous Emission Probabilities at Radio Frequencies,” Phys. Rev. 69, 681 (1946).

Agarwal, G. S.

G. S. Agarwal and R. R. Puri, “Exact quantum-electrodynamics results for scattering emission, and absorption from a Rydberg atom in a cavity with arbitrary Q,” Phys. Rev. A 33, 1757–1764 (1986).
[CrossRef] [PubMed]

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

An, K.

J. J. Childs, K. An, R. R. Dasari, and M. S. Feld, “Single Atom Emission in an Optical Resonator,” in Cavity Quantum Electrodynamics, P. R. Berman, Editor, Academic Press, San Diego (1994).

Arakawa, Y.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXive:0908.0788v1 [cond-mat.mes-hall].

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Arnold, J. M.

G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, IEEE J. Select. Top. Quantum Electron. 10, 1052–1062 (2004).
[CrossRef]

Asano, T.

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Badolato, A.

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “, “Manipulating quantum entanglement atoms and photons in a cavity,” Rev. Mod. Phys. 73, 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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

Childs, J. J.

J. J. Childs, K. An, R. R. Dasari, and M. S. Feld, “Single Atom Emission in an Optical Resonator,” in Cavity Quantum Electrodynamics, P. R. Berman, Editor, Academic Press, San Diego (1994).

Dasari, R. R.

J. J. Childs, K. An, R. R. Dasari, and M. S. Feld, “Single Atom Emission in an Optical Resonator,” in Cavity Quantum Electrodynamics, P. R. Berman, Editor, Academic Press, San Diego (1994).

del Valle, E.

F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

Deppe, D. G.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Ell, C.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Feld, M. S.

J. J. Childs, K. An, R. R. Dasari, and M. S. Feld, “Single Atom Emission in an Optical Resonator,” in Cavity Quantum Electrodynamics, P. R. Berman, Editor, Academic Press, San Diego (1994).

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, “Computational Electronics: The Finite-Difference Time-Domain Method,” 2nd ed (Artech House, Norwood2000).

Haroche, S.

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

Hendrickson, J.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Hennessy, K.

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Hu, E. L.

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Hughes, S.

Imamoglu, A.

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

Iwamoto, S.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXive:0908.0788v1 [cond-mat.mes-hall].

Jackson, J. D.

J. D. Jackson, “Classical Electrodynamics,” 3rd ed, (Wiley, NY1999).

Kamada, H.

Kawasaki, K.

Khitrova, G.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

Khitroya, G.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Kimble, 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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Kira, M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

Kojima, K.

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
[CrossRef]

Kumagai, N.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXive:0908.0788v1 [cond-mat.mes-hall].

Kuramochi, E.

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Laussy, F. P.

F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

Milburn, G.

D. Walls and G. Milburn, “Quantum Optics” (Springer-Verlag, Berlin, 1994).

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Noda, S.

M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

Notomi, M.

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Okamoto, H.

Ota, Y.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Impact of electron-phonon interactions on quantum-dot cavity quantum electrodynamics,” arXive:0908.0788v1 [cond-mat.mes-hall].

Painter, O.

J. Vuckovic, O. Painter, Y. Xu, and A. Yariv, “Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quant. Electron. 35, 1168–1175 (1999).
[CrossRef]

Pathak, P. K.

Purcell, E. M.

E. M. Purcell, “Spontaneous Emission Probabilities at Radio Frequencies,” Phys. Rev. 69, 681 (1946).

Puri, R. R.

G. S. Agarwal and R. R. Puri, “Exact quantum-electrodynamics results for scattering emission, and absorption from a Rydberg atom in a cavity with arbitrary Q,” Phys. Rev. A 33, 1757–1764 (1986).
[CrossRef] [PubMed]

Raimond, J. M.

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

Raizen, M. G.

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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

Rice, P. R.

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. A 40,, 5516–5519 (1989).
[CrossRef] [PubMed]

Roh, Y.

Rupper, G.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Scherer,

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Scherer, A.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[CrossRef]

Shchekin, O. B.

T. Yoshie, Scherer, J. Hendrickson, G. Khitroya, 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 (London) 432, 200–203 (2004).
[CrossRef]

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Slavcheva, G. M.

G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, IEEE J. Select. Top. Quantum Electron. 10, 1052–1062 (2004).
[CrossRef]

Sogawa, T.

Song, B.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[CrossRef]

Spillane, S. M.

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F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
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D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature (London) 421, 925–928 (2003).
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Kerry J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).
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J. Vuckovic, O. Painter, Y. Xu, and A. Yariv, “Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quant. Electron. 35, 1168–1175 (1999).
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M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, “Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot,” Phys. Rev. B 80, 155326 (2009).
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Appl. Phys. Lett. (1)

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IEEE J. Quant. Electron. (1)

J. Vuckovic, O. Painter, Y. Xu, and A. Yariv, “Finite-Difference Time-Domain Calculation of the Spontaneous Emission Coupling Factor in Optical Microcavities,” IEEE J. Quant. Electron. 35, 1168–1175 (1999).
[CrossRef]

IEEE J. Select. Top. Quantum Electron. (1)

G. M. Slavcheva, J. M. Arnold, and R. W. Ziolkowski, IEEE J. Select. Top. Quantum Electron. 10, 1052–1062 (2004).
[CrossRef]

Nature (London) (5)

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,” Nature (London) 445, 896–899 (2007).
[CrossRef]

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Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425, 944–947 (2003).
[CrossRef]

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B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
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F. P. Laussy, E. del Valle, and C. Tejedor, “Strong Coupling of Quantum Dots in Microcavities,” Phys. Rev. Lett. 101, 083601 (2008).
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D. Walls and G. Milburn, “Quantum Optics” (Springer-Verlag, Berlin, 1994).

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Figures (8)

Fig. 1
Fig. 1

Standard representation of a cavity quantum electrodynamic system comprising a single mode of the electromagnetic field in a cavity with decay rate κ coupled with a coupling strength g to a two-level system with spontaneous decay rate γ. Schematic representing a two-level system in an optical cavity. The QD mode is coupled to a cavity mode with coupling strength g. The excited state of the dot decays incoherently with the decay rate γ.

Fig. 2
Fig. 2

(a) Silicon photonic crystal cavity structure with three missing holes (L3) and (b) Hy field profile of fundamental mode. The two-level system is located in the middle of the cavity, where the horizontal component of the electric field of the fundamental mode has its maximum values.

Fig. 3
Fig. 3

Calculated g-factor as a function of Δɛ. Theoretical results are obtained using Eq. (6).

Fig. 4
Fig. 4

Calculated cavity field spectra for a two-level system located in a photonic crystal nanocavity. The Q-factor is 8.3 × 104 and Δɛ = 0.5(g = 3.56GHz).

Fig. 5
Fig. 5

Time evolution of Jx and Hy. The two-level system is located in the center of the cavity(Q = 8.3 × 104). The coupling parameter is (a) and (b) Δɛ = 5 × 10−6(g = 11GHz), (c) and (d) Δɛ = 5 × 10−3(g = 360GHz), (e) and (f) Δɛ = 5 × 10−2(g = 1.1THz)

Fig. 6
Fig. 6

Enhancement ratio of radiation from a two-level system is calculated as the dacay ratio versus that in a vacuum. The Q-factor of the cavity is 1.1 × 104 (low-Q) and the damping factor is δ = 0.0GHz.

Fig. 7
Fig. 7

Enhancement ratio of radiation from a two-level system located in a photonic crystal cavity. The Q-factor is 1.1×104 (κ = 109GHz), the damping factor is δ = 3.0GHz, and the coupling strength are (a) Δɛ = 0.005 (g = 356GHz) and (b) Δɛ = 0.0005 (g = 113GHz).

Fig. 8
Fig. 8

Inverse damping time of J2(t) and E2. The Q-factor is 8.3 × 104(κ = 14GHz), the damping factor is δ = 3.0×102GHz, and Δɛ = 0.5(g = 3.56THz). Under the zero detuning condition, the dipole current decay becomes slow and the field mode decay becomes fast and their decay rates coincide.

Equations (13)

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H = h ¯ ω p ( a a + 1 2 ) + h ¯ Ω 2 σ z + h ¯ g ( a σ + σ + a ) + H κ + H r .
d 2 dt 2 J ( t ) + 2 δ d dt J ( t ) + ω p 2 J ( t ) = ɛ 0 Δ ɛ ω p 2 E ( t ) ,
χ ( ω ) = Δ ɛ p ω p 2 ω p 2 + 2 i ω δ ω 2 .
χ ( ω ) = 2 N ɛ ω p V eff V g 2 ω p ω + i δ ,
V eff = ɛ ( r ) | E ( r ) | 2 d 3 r max [ ɛ ( r ) | E ( r ) | 2 ] ,
2 g = ω p Δ ɛ p V ɛ V eff .
× H ( t ) = ɛ d dt E ( t ) + J ( t )
× E ( t ) = μ d dt H ( t )
J n + 1 = α J n + ξ J n 1 + η [ E n + 1 E n 1 2 Δ t ] ,
α = 2 ω p 2 Δ t 2 1 + δ Δ t , ξ = δ Δ t 1 δ Δ t + 1 , η = ɛ 0 Δ ɛ ω p 2 Δ t 2 1 + δ Δ t .
E n + 1 = E 0 n + 1 + Δ E n + 1 ,
Δ E n + 1 = C 1 ( E 0 n + 1 E n + 1 ) 1 2 C 2 Δ t ɛ 0 ɛ [ ( 1 + α ) J n + ξ J n 1 ] .
C 1 = 1 2 η 2 ɛ 0 ɛ + 1 2 η , C 2 = 2 ɛ 0 ɛ 2 ɛ 0 ɛ + 1 2 η .

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