Abstract

We propose a nanogap structure composed of semiconductor nanoparticles forming an optical cavity. The resonant excitation of excitons in the nanoparticles can generate a localized strong light field in the gap region, also called “hot spot”. The spectral width of the hot spot is significantly narrow because of the small exciton damping and the dephasing at low temperature, so the semiconductor nanogap structure acts as a high-Q cavity. In addition, the interaction between light and matter at the nanogap is significantly larger than that in a conventional microcavity, because the former has a small cavity-mode volume beyond the diffraction limit. We theoretically demonstrate the large and well-defined vacuum-Rabi splitting of a two-level emitter placed inside the semiconductor nanogap cavity: the Rabi splitting energy of 1.7 meV for the transition dipole moment of the emitter (25 Debye) is about 6.3 times larger than the spectral width. An optical cavity providing such a large and well-defined Rabi splitting is highly suited for studying characteristic features of the cavity quantum electrodynamics and for the development of new applications.

© 2014 Optical Society of America

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  1. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
    [Crossref] [PubMed]
  2. T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004).
    [Crossref]
  3. E. Peter, P. Senellart, D. Martrou, a. Lemaître, J. Hours, J. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
    [Crossref] [PubMed]
  4. 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 445, 896–899 (2007).
    [Crossref] [PubMed]
  5. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).
    [Crossref]
  6. A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
    [Crossref]
  7. O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A 59, 4756 (1999).
    [Crossref]
  8. H. Ajiki and H. Ishihara, “Entangled-photon generation from a quantum dot in cavity QED,” Phys. Stat. Solidi C 6, 276–279 (2009).
    [Crossref]
  9. H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
    [Crossref]
  10. M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2010).
    [Crossref]
  11. G. Khitrova, H. Gibbs, M. Kira, S. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys. 2, 81–90 (2006).
    [Crossref]
  12. S. Rudin and T. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227 (1999).
    [Crossref]
  13. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  14. S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
    [Crossref] [PubMed]
  15. The complex eigenfrequency, whose imaginary part represents the spectral width, of the coupled states are given by Ω±=ω0−i(γcav+γ0)/4±g2−(γcav−γ0)2/16 at the zero detuning where the cavity-mode frequency agrees with that of material excitation. Although two real parts of Ω± appear for g > (γcav − γ0)/4, the splitting energy should be larger than the spectral width, i.e., g > (γcav + γ0)/4 for observing an evident energy splitting [14].
  16. A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
    [Crossref] [PubMed]
  17. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
    [Crossref]
  18. H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
    [Crossref]
  19. Y. Zeng, Y. Fu, M. Bengtsson, X. Chen, W. Lu, and H. Ågren, “Finite-difference time-domain simulations of exciton-polariton resonances in quantum-dot arrays,” Opt. Express 16, 4507–4519 (2008).
    [Crossref] [PubMed]
  20. S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).
  21. M. Uemoto and H. Ajiki, “Simulation method for resonant light scattering of exciton confined to arbitrary geometry,” Opt. Express 22, 9450–9464 (2014).
    [Crossref] [PubMed]
  22. K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I-Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
    [Crossref]
  23. M. Kalm and C. Uihlein, “Investigations on the temperature-dependent TPA linewidth of the Z3-exciton in CuCl,” Phys. Stat. Solidi B 87, 575 (1978).
    [Crossref]
  24. F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
    [Crossref] [PubMed]
  25. D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
    [Crossref]
  26. A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
    [Crossref] [PubMed]
  27. H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
    [Crossref]
  28. K. Shibata and H. Ajiki, “Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation,” Phys. Rev. A 89, 042319 (2014).
    [Crossref]

2014 (2)

M. Uemoto and H. Ajiki, “Simulation method for resonant light scattering of exciton confined to arbitrary geometry,” Opt. Express 22, 9450–9464 (2014).
[Crossref] [PubMed]

K. Shibata and H. Ajiki, “Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation,” Phys. Rev. A 89, 042319 (2014).
[Crossref]

2013 (2)

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
[Crossref] [PubMed]

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

2012 (1)

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[Crossref]

2011 (1)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

2010 (2)

A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
[Crossref]

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

2009 (2)

H. Ajiki and H. Ishihara, “Entangled-photon generation from a quantum dot in cavity QED,” Phys. Stat. Solidi C 6, 276–279 (2009).
[Crossref]

H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
[Crossref]

2008 (2)

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

Y. Zeng, Y. Fu, M. Bengtsson, X. Chen, W. Lu, and H. Ågren, “Finite-difference time-domain simulations of exciton-polariton resonances in quantum-dot arrays,” Opt. Express 16, 4507–4519 (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 445, 896–899 (2007).
[Crossref] [PubMed]

2006 (2)

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

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

2005 (1)

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

2004 (2)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004).
[Crossref]

2002 (1)

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

2000 (1)

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

1999 (2)

O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A 59, 4756 (1999).
[Crossref]

S. Rudin and T. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227 (1999).
[Crossref]

1985 (1)

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I-Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

1978 (1)

M. Kalm and C. Uihlein, “Investigations on the temperature-dependent TPA linewidth of the Z3-exciton in CuCl,” Phys. Stat. Solidi B 87, 575 (1978).
[Crossref]

1958 (1)

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Ågren, H.

Ajiki, H.

M. Uemoto and H. Ajiki, “Simulation method for resonant light scattering of exciton confined to arbitrary geometry,” Opt. Express 22, 9450–9464 (2014).
[Crossref] [PubMed]

K. Shibata and H. Ajiki, “Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation,” Phys. Rev. A 89, 042319 (2014).
[Crossref]

H. Ajiki and H. Ishihara, “Entangled-photon generation from a quantum dot in cavity QED,” Phys. Stat. Solidi C 6, 276–279 (2009).
[Crossref]

H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
[Crossref]

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[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 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. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Bengtsson, M.

Benson, O.

O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A 59, 4756 (1999).
[Crossref]

Bloch, J.

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

Bozhevolnyi, S. I.

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[Crossref]

Chen, X.

Cho, K.

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I-Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2010).
[Crossref]

Edamatsu, K.

H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
[Crossref]

Englund, D.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vučković, “Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade,” Nat. Phys. 4, 859–863 (2008).
[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 445, 896–899 (2007).
[Crossref] [PubMed]

Fan, S.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
[Crossref] [PubMed]

Faraon, A.

A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
[Crossref]

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

Forchel, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Fu, Y.

Fushman, I.

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

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 445, 896–899 (2007).
[Crossref] [PubMed]

Gérard, J.

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

Gibbs, H.

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

Gramotnev, D. K.

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[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 445, 896–899 (2007).
[Crossref] [PubMed]

Halas, N. J.

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

Hendrickson, J.

T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (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 445, 896–899 (2007).
[Crossref] [PubMed]

Hofmann, C.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Hours, J.

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

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, 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 445, 896–899 (2007).
[Crossref] [PubMed]

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 445, 896–899 (2007).
[Crossref] [PubMed]

Ishihara, H.

H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
[Crossref]

H. Ajiki and H. Ishihara, “Entangled-photon generation from a quantum dot in cavity QED,” Phys. Stat. Solidi C 6, 276–279 (2009).
[Crossref]

Kalm, M.

M. Kalm and C. Uihlein, “Investigations on the temperature-dependent TPA linewidth of the Z3-exciton in CuCl,” Phys. Stat. Solidi B 87, 575 (1978).
[Crossref]

Kawano, K.

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

Kawata, M.

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I-Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Khitrova, G.

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

Kira, M.

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

Koch, S.

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

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Large, N.

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

Lemaître, a.

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

Löffler, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Lu, W.

Majumdar, A.

A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
[Crossref]

Martrou, D.

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

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2010).
[Crossref]

Nordlander, P.

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

Pekar, S. I.

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).

Peter, E.

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

Petroff, P.

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

Pors, A.

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[Crossref]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Raman, A.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
[Crossref] [PubMed]

Reinecke, T.

S. Rudin and T. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227 (1999).
[Crossref]

Reinecke, T. L.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Reitzenstein, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Ridolfo, A.

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

Rudin, S.

S. Rudin and T. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227 (1999).
[Crossref]

Saija, R.

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

Savasta, S.

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

Scherer, A.

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

T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004).
[Crossref]

Schlather, A. E.

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

Sek, G.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

Senellart, P.

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

Shen, Y. R.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

Shibata, K.

K. Shibata and H. Ajiki, “Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation,” Phys. Rev. A 89, 042319 (2014).
[Crossref]

Shin, W.

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
[Crossref] [PubMed]

Stefano, O. D.

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

Stoltz, N.

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

Tsuji, T.

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

Uemoto, M.

Uihlein, C.

M. Kalm and C. Uihlein, “Investigations on the temperature-dependent TPA linewidth of the Z3-exciton in CuCl,” Phys. Stat. Solidi B 87, 575 (1978).
[Crossref]

Urban, A. S.

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

Vuckovic, J.

A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
[Crossref]

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

Wang, F.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

Willatzen, M.

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[Crossref]

Winger, 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 445, 896–899 (2007).
[Crossref] [PubMed]

Yamamoto, Y.

O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A 59, 4756 (1999).
[Crossref]

Yoshie, T.

T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004).
[Crossref]

Zeng, Y.

ACS Nano (1)

S. Savasta, R. Saija, A. Ridolfo, and O. D. Stefano, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano 4, 6369–6376 (2010).
[Crossref] [PubMed]

J. Phys. Soc. Jpn. (1)

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I-Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[Crossref]

Nano Lett. (1)

A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. 13, 3281–3286 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[Crossref]

Nat. Phys. (2)

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

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

Nature (3)

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432, 197–200 (2004).
[Crossref] [PubMed]

T. Yoshie, A. Scherer, and J. Hendrickson, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 9–12 (2004).
[Crossref]

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 445, 896–899 (2007).
[Crossref] [PubMed]

New J. Phys. (1)

H. Ajiki, H. Ishihara, and K. Edamatsu, “Cavity-assisted generation of entangled photons from a V-type three-level system,” New J. Phys. 11, 033033 (2009).
[Crossref]

Opt. Express (2)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (3)

A. Faraon, A. Majumdar, and J. Vučković, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
[Crossref]

O. Benson and Y. Yamamoto, “Master-equation model of a single-quantum-dot microsphere laser,” Phys. Rev. A 59, 4756 (1999).
[Crossref]

K. Shibata and H. Ajiki, “Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation,” Phys. Rev. A 89, 042319 (2014).
[Crossref]

Phys. Rev. B (4)

H. Ajiki, T. Tsuji, K. Kawano, and K. Cho, “Optical spectra and exciton-light coupled modes of a spherical semiconductor nanocrystal,” Phys. Rev. B 66, 245322 (2002).
[Crossref]

D. K. Gramotnev, A. Pors, M. Willatzen, and S. I. Bozhevolnyi, “Gap-plasmon nanoantennas and bowtie resonators,” Phys. Rev. B 85, 045434 (2012).
[Crossref]

S. Rudin and T. Reinecke, “Oscillator model for vacuum Rabi splitting in microcavities,” Phys. Rev. B 59, 10227 (1999).
[Crossref]

H. Ajiki and K. Cho, “Longitudinal and transverse components of excitons in a spherical quantum dot,” Phys. Rev. B 62, 7402–7412 (2000).
[Crossref]

Phys. Rev. Lett. (3)

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

A. Raman, W. Shin, and S. Fan, “Upper bound on the modal material loss rate in plasmonic and metamaterial systems,” Phys. Rev. Lett. 110, 183901 (2013).
[Crossref] [PubMed]

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[Crossref] [PubMed]

Phys. Stat. Solidi B (1)

M. Kalm and C. Uihlein, “Investigations on the temperature-dependent TPA linewidth of the Z3-exciton in CuCl,” Phys. Stat. Solidi B 87, 575 (1978).
[Crossref]

Phys. Stat. Solidi C (1)

H. Ajiki and H. Ishihara, “Entangled-photon generation from a quantum dot in cavity QED,” Phys. Stat. Solidi C 6, 276–279 (2009).
[Crossref]

Sov. Phys. JETP (1)

S. I. Pekar, “The theory of electromagnetic waves in a crystal in which excitons are produced,” Sov. Phys. JETP 6, 785–796 (1958).

Other (2)

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2010).
[Crossref]

The complex eigenfrequency, whose imaginary part represents the spectral width, of the coupled states are given by Ω±=ω0−i(γcav+γ0)/4±g2−(γcav−γ0)2/16 at the zero detuning where the cavity-mode frequency agrees with that of material excitation. Although two real parts of Ω± appear for g > (γcav − γ0)/4, the splitting energy should be larger than the spectral width, i.e., g > (γcav + γ0)/4 for observing an evident energy splitting [14].

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Figures (5)

Fig. 1
Fig. 1

Schematic illustrations of (a) the empty semiconductor nanogap cavity and (b) the nanogap cavity with a spherical two-level emitter (a QD or a cluster of molecules) placed at r0. The polarization direction of an incident electromagnetic field Einc is also depicted.

Fig. 2
Fig. 2

Calculated near-field enhancement |E/Einc|2 at r0 (see Fig. 1) for (a) the empty semiconductor nanogap cavity and (b) the semiconductor nanogap cavity with the two-level emitter under zero detuning condition. The transition dipole moment of the emitter is μ = 10 Debye.

Fig. 3
Fig. 3

The near-field enhancement distributions for the empty semiconductor nanogap cavity in resonant condition (h̄ω = 3.2086 eV) (a), the semiconductor nanogap cavity with the two-level emitter at h̄ω = 3.2083 eV (b), h̄ω = 3.2086 eV (c), and h̄ω = 3.2088 eV (d). The energies in (b) and (d) correspond, respectively, to the lower and the higher peak energies in Fig. 2(b).

Fig. 4
Fig. 4

(a) The near-field spectra of the semiconductor nanogap cavity with two-level emitter at r0. From the bottom to the top, the detuning changed from negative (Eex < Ecav) to positive (Eex > Ecav) values. (b) The peak energies in (a) are plotted with triangles as a function of the detuning. The solid curves are obtained from Eq. (6) with Ω R = 580 μeV.

Fig. 5
Fig. 5

The Rabi splitting energy Ω R as a function of the transition dipole moment μ of the emitter. The red points are obtained by fitting the calculated energy curves using Eq. (6), and the dashed line indicates Ω R = 64.6 (μeV/Debye)×μ. R denotes the radius of CuCl spherical QDs, with the transition dipole moment indicated by the vertical dotted lines.

Tables (1)

Tables Icon

Table 1 Parameters of previously reported zero-dimensional cavity-emitter systems, and those of the proposed semiconductor-nanogap system (“Emitter, SC nanogap”). “MTL” and “SC” stand for metal and semiconductor, respectively. The dipole moment of the J-aggregates is estimated from the metal nanogap structure, by assuming a volume of 15 nm3.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

g = μ h ¯ ω 2 ε V m ,
μ = 1 2 χ ( k t μ , ω ) E ( t μ ) + χ ( k l , ω ) ( Φ ) = 0 .
ε ( k , ω ) = ε bg + ε bg Δ LT E G + ( h ¯ 2 / 2 M ) k 2 h ¯ ω i h ¯ γ ex ,
ε ( ω ) = ε bg em 2 E 0 μ 2 / V em ( h ¯ ω ) 2 E 0 2 + i ( h ¯ ω ) ( h ¯ γ 0 ) ,
^ = E cav a ^ a ^ + E ex 2 σ ^ z + h ¯ Ω R 2 ( a ^ σ ^ + a ^ σ ^ + ) ,
E = 1 2 ( E cav + E ex ) ± 1 2 ( E cav E ex ) 2 + ( h ¯ Ω R ) 2 .

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