Abstract

We theoretically study the dynamics of a strongly coupled quantum dot–bimodal microcavity system under an external magnetic field, where the nondegenerate excitonic spin states caused by the Zeeman effect are coupled to both orthogonal cavity modes. We develop an effective cavity quantum electrodynamics model, demonstrate the polarization-related nonlinear response under a linearly polarized pulse excitation by calculating the time-resolved intracavity photon number, and investigate the dependence of system parameters on the nonlinearity. In addition, we show that, when driven by two pulses with perpendicular polarization and a relative time delay, the coupled system suppresses the delayed one, which can be applied to polarized optical switching at a single-photon level.

© 2014 Optical Society of America

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  1. 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]
  2. J. P. Reithmaier, G. Sek, A. Loffler, 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]
  3. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
    [CrossRef]
  4. E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009).
    [CrossRef]
  5. J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
    [CrossRef]
  6. A. Majumdar, D. Englund, M. Bajcsy, and J. Vuckovic, “Nonlinear temporal dynamics of a strongly coupled quantum-dot-cavity system,” Phys. Rev. A 85, 033802 (2012).
  7. J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
    [CrossRef]
  8. 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]
  9. A. Faraon, A. Majumdar, and J. Vuckovic, “Generation of nonclassical states of light via photon blockade in optical nanocavities,” Phys. Rev. A 81, 033838 (2010).
    [CrossRef]
  10. A. Majumdar, M. Bajcsy, and J. Vuckovic, “Probing the ladder of dressed states and nonclassical light generation in quantum-dot-cavity QED,” Phys. Rev. A 85, 041801 (2012).
  11. T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
    [CrossRef]
  12. D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
    [CrossRef]
  13. E. del Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, “Two-photon lasing by a single quantum dot in a high-Q microcavity,” Phys. Rev. B 81, 035302 (2010).
    [CrossRef]
  14. Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett. 107, 233602 (2011).
    [CrossRef]
  15. P. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexciton–exciton cascade,” Phys. Rev. B 80, 155325 (2009).
  16. 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]
  17. C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006–15012 (2008).
    [CrossRef]
  18. A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
    [CrossRef]
  19. A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
    [CrossRef]
  20. M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).
  21. S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
    [CrossRef]
  22. H. Kim, T. C. Shen, D. Sridharan, G. S. Solomon, and E. Waks, “Magnetic field tuning of a quantum dot strongly coupled to a photonic crystal cavity,” Appl. Phys. Lett. 98, 091102 (2011).
    [CrossRef]
  23. Q. Ren, J. Lu, H. H. Tan, S. Wu, L. Sun, W. Zhou, W. Xie, Z. Sun, Y. Zhu, C. Jagadish, S. C. Shen, and Z. Chen, “Spin-resolved Purcell effect in a quantum dot microcavity system,” Nano Lett. 12, 3455–3459 (2012).
    [CrossRef]
  24. H. Kim, D. Sridharan, T. C. Shen, G. S. Solomon, and E. Waks, “Strong coupling between two quantum dots and a photonic crystal cavity using magnetic field tuning,” Opt. Express 19, 2589–2598 (2011).
    [CrossRef]
  25. A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
    [CrossRef]
  26. S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
    [CrossRef]
  27. K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
    [CrossRef]
  28. A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-Poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).
  29. S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
    [CrossRef]
  30. P. Machnikowski, “Theory of two-photon processes in quantum dots: coherent evolution and phonon-induced dephasing,” Phys. Rev. B 78, 195320 (2008).
    [CrossRef]
  31. E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
    [CrossRef]
  32. S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B 1, 424–432 (1999).
    [CrossRef]

2013

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
[CrossRef]

2012

A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-Poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).

Q. Ren, J. Lu, H. H. Tan, S. Wu, L. Sun, W. Zhou, W. Xie, Z. Sun, Y. Zhu, C. Jagadish, S. C. Shen, and Z. Chen, “Spin-resolved Purcell effect in a quantum dot microcavity system,” Nano Lett. 12, 3455–3459 (2012).
[CrossRef]

A. Majumdar, M. Bajcsy, and J. Vuckovic, “Probing the ladder of dressed states and nonclassical light generation in quantum-dot-cavity QED,” Phys. Rev. A 85, 041801 (2012).

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[CrossRef]

A. Majumdar, D. Englund, M. Bajcsy, and J. Vuckovic, “Nonlinear temporal dynamics of a strongly coupled quantum-dot-cavity system,” Phys. Rev. A 85, 033802 (2012).

2011

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett. 107, 233602 (2011).
[CrossRef]

H. Kim, D. Sridharan, T. C. Shen, G. S. Solomon, and E. Waks, “Strong coupling between two quantum dots and a photonic crystal cavity using magnetic field tuning,” Opt. Express 19, 2589–2598 (2011).
[CrossRef]

H. Kim, T. C. Shen, D. Sridharan, G. S. Solomon, and E. Waks, “Magnetic field tuning of a quantum dot strongly coupled to a photonic crystal cavity,” Appl. Phys. Lett. 98, 091102 (2011).
[CrossRef]

E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
[CrossRef]

2010

S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
[CrossRef]

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

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

E. del Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, “Two-photon lasing by a single quantum dot in a high-Q microcavity,” Phys. Rev. B 81, 035302 (2010).
[CrossRef]

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

2009

E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009).
[CrossRef]

P. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexciton–exciton cascade,” Phys. Rev. B 80, 155325 (2009).

S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
[CrossRef]

2008

P. Machnikowski, “Theory of two-photon processes in quantum dots: coherent evolution and phonon-induced dephasing,” Phys. Rev. B 78, 195320 (2008).
[CrossRef]

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[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]

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006–15012 (2008).
[CrossRef]

2007

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]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

2006

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

2004

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]

J. P. Reithmaier, G. Sek, A. Loffler, 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]

2002

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

1999

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B 1, 424–432 (1999).
[CrossRef]

1998

A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
[CrossRef]

1963

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Amann, M. C.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Arakawa, Y.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett. 107, 233602 (2011).
[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]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[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]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Bajcsy, M.

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
[CrossRef]

A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-Poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[CrossRef]

A. Majumdar, M. Bajcsy, and J. Vuckovic, “Probing the ladder of dressed states and nonclassical light generation in quantum-dot-cavity QED,” Phys. Rev. A 85, 041801 (2012).

A. Majumdar, D. Englund, M. Bajcsy, and J. Vuckovic, “Nonlinear temporal dynamics of a strongly coupled quantum-dot-cavity system,” Phys. Rev. A 85, 033802 (2012).

Baur, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Bayer, M.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
[CrossRef]

Bianchetti, R.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Blais, A.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Böhm, G.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Cancellieri, E.

E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
[CrossRef]

Chen, Z.

Q. Ren, J. Lu, H. H. Tan, S. Wu, L. Sun, W. Zhou, W. Xie, Z. Sun, Y. Zhu, C. Jagadish, S. C. Shen, and Z. Chen, “Spin-resolved Purcell effect in a quantum dot microcavity system,” Nano Lett. 12, 3455–3459 (2012).
[CrossRef]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

del Valle, E.

E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
[CrossRef]

E. del Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, “Two-photon lasing by a single quantum dot in a high-Q microcavity,” Phys. Rev. B 81, 035302 (2010).
[CrossRef]

E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009).
[CrossRef]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

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]

Englund, D.

A. Majumdar, D. Englund, M. Bajcsy, and J. Vuckovic, “Nonlinear temporal dynamics of a strongly coupled quantum-dot-cavity system,” Phys. Rev. A 85, 033802 (2012).

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[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]

Fafard, S.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

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]

Faraon, A.

D. Englund, A. Majumdar, M. Bajcsy, A. Faraon, P. Petroff, and J. Vučković, “Ultrafast photon-photon interaction in a strongly coupled quantum dot-cavity system,” Phys. Rev. Lett. 108, 093604 (2012).
[CrossRef]

A. Faraon, A. Majumdar, and J. Vuckovic, “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]

Fink, J. M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Finley, J. J.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Forchel, A.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
[CrossRef]

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006–15012 (2008).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

J. P. Reithmaier, G. Sek, A. Loffler, 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]

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
[CrossRef]

Franeck, P.

S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
[CrossRef]

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]

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]

Gonzalez-Tudela, A.

E. del Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, “Two-photon lasing by a single quantum dot in a high-Q microcavity,” Phys. Rev. B 81, 035302 (2010).
[CrossRef]

Gonzalez–Tudela, A.

E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
[CrossRef]

Göppl, M.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Gorbunov, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
[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]

Hauke, N.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Hawrylak, P.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

Heindel, T.

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]

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]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Hennessy, K. J.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Hinzer, K.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

Hofbauer, F.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Höfling, S.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
[CrossRef]

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006–15012 (2008).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Hofmann, C.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

J. P. Reithmaier, G. Sek, A. Loffler, 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]

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K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Hu, E.

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Hu, E. L.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[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).
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P. Pathak and S. Hughes, “Cavity-assisted fast generation of entangled photon pairs through the biexciton–exciton cascade,” Phys. Rev. B 80, 155325 (2009).

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T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 605–609 (2012).
[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]

K. Hennessy, C. Högerle, E. Hu, A. Badolato, and A. Imamoglu, “Tuning photonic nanocavities by atomic force microscope nano-oxidation,” Appl. Phys. Lett. 89, 041118 (2006).
[CrossRef]

Iwamoto, S.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett. 107, 233602 (2011).
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Jagadish, C.

Q. Ren, J. Lu, H. H. Tan, S. Wu, L. Sun, W. Zhou, W. Xie, Z. Sun, Y. Zhu, C. Jagadish, S. C. Shen, and Z. Chen, “Spin-resolved Purcell effect in a quantum dot microcavity system,” Nano Lett. 12, 3455–3459 (2012).
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E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
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Kaer, P.

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
[CrossRef]

Kamp, M.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Kaniber, M.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Kasprzak, J.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Loffler, 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]

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]

Kim, E. D.

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
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H. Kim, D. Sridharan, T. C. Shen, G. S. Solomon, and E. Waks, “Strong coupling between two quantum dots and a photonic crystal cavity using magnetic field tuning,” Opt. Express 19, 2589–2598 (2011).
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H. Kim, T. C. Shen, D. Sridharan, G. S. Solomon, and E. Waks, “Magnetic field tuning of a quantum dot strongly coupled to a photonic crystal cavity,” Appl. Phys. Lett. 98, 091102 (2011).
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Kistner, C.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

C. Kistner, T. Heindel, C. Schneider, A. Rahimi-Iman, S. Reitzenstein, S. Höfling, and A. Forchel, “Demonstration of strong coupling via electro-optical tuning in high-quality QD-micropillar systems,” Opt. Express 16, 15006–15012 (2008).
[CrossRef]

Klopf, F.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Loffler, 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]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Loffler, 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]

Kumagai, N.

Y. Ota, S. Iwamoto, N. Kumagai, and Y. Arakawa, “Spontaneous two-photon emission from a single quantum dot,” Phys. Rev. Lett. 107, 233602 (2011).
[CrossRef]

Kuther, A.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaier, F. Klopf, and F. Schäfer, “Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots,” Phys. Rev. B 65, 195315 (2002).

A. Kuther, M. Bayer, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, and J. P. Reithmaier, “Zeeman splitting of excitons and biexcitons in single In_{0.60}Ga_{0.40}As/GaAs self-assembled quantum dots,” Phys. Rev. B 58, R7508–R7511 (1998).
[CrossRef]

Kwon, S. H.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Lagoudakis, K. G.

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
[CrossRef]

Langbein, W.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system,” Nat. Mater. 9, 304–308 (2010).
[CrossRef]

Laucht, A.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
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E. del Valle, F. Laussy, and C. Tejedor, “Luminescence spectra of quantum dots in microcavities. II. Fermions,” Phys. Rev. B 79, 235326 (2009).
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Laussy, F. P.

E. del Valle, A. Gonzalez–Tudela, E. Cancellieri, F. P. Laussy, and C. Tejedor, “Generation of a two-photon state from a quantum dot in a microcavity,” New J. Phys. 13, 113014 (2011).
[CrossRef]

E. del Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, “Two-photon lasing by a single quantum dot in a high-Q microcavity,” Phys. Rev. B 81, 035302 (2010).
[CrossRef]

Leek, P. J.

J. M. Fink, M. Göppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, and A. Wallraff, “Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system,” Nature 454, 315–318 (2008).
[CrossRef]

Lodahl, P.

A. Laucht, J. M. Villas-Bôas, S. Stobbe, N. Hauke, F. Hofbauer, G. Böhm, P. Lodahl, M. C. Amann, M. Kaniber, and J. J. Finley, “Mutual coupling of two semiconductor quantum dots via an optical nanocavity,” Phys. Rev. B 82, 075305 (2010).
[CrossRef]

Loffler, A.

J. P. Reithmaier, G. Sek, A. Loffler, 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]

Löffler, A.

S. Reitzenstein, S. Münch, P. Franeck, A. Löffler, S. Höfling, L. Worschech, A. Forchel, I. V. Ponomarev, and T. L. Reinecke, “Exciton spin state mediated photon-photon coupling in a strongly coupled quantum dot microcavity system,” Phys. Rev. B 82, 121306 (2010).
[CrossRef]

S. Reitzenstein, S. Münch, P. Franeck, A. Rahimi-Iman, A. Löffler, S. Höfling, L. Worschech, and A. Forchel, “Control of the strong light-matter interaction between an elongated In0.3Ga0.7 As quantum dot and a micropillar cavity using external magnetic fields,” Phys. Rev. Lett. 103, 127401 (2009).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs∕GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Lu, J.

Q. Ren, J. Lu, H. H. Tan, S. Wu, L. Sun, W. Zhou, W. Xie, Z. Sun, Y. Zhu, C. Jagadish, S. C. Shen, and Z. Chen, “Spin-resolved Purcell effect in a quantum dot microcavity system,” Nano Lett. 12, 3455–3459 (2012).
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P. Machnikowski, “Theory of two-photon processes in quantum dots: coherent evolution and phonon-induced dephasing,” Phys. Rev. B 78, 195320 (2008).
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Majumdar, A.

A. Majumdar, P. Kaer, M. Bajcsy, E. D. Kim, K. G. Lagoudakis, A. Rundquist, and J. Vučković, “Proposed coupling of an electron spin in a semiconductor quantum dot to a nanosize optical cavity,” Phys. Rev. Lett. 111, 027402 (2013).
[CrossRef]

A. Majumdar, M. Bajcsy, A. Rundquist, and J. Vučković, “Loss-enabled sub-Poissonian light generation in a bimodal nanocavity,” Phys. Rev. Lett. 108, 183601 (2012).

A. Majumdar, D. Englund, M. Bajcsy, and J. Vuckovic, “Nonlinear temporal dynamics of a strongly coupled quantum-dot-cavity system,” Phys. Rev. A 85, 033802 (2012).

A. Majumdar, M. Bajcsy, and J. Vuckovic, “Probing the ladder of dressed states and nonclassical light generation in quantum-dot-cavity QED,” Phys. Rev. A 85, 041801 (2012).

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Nat. Phys.

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Opt. Express

Phys. Rev. A

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Figures (7)

Fig. 1.
Fig. 1.

Dressed state energies (solid lines) and QD excitonic eigenstate energies (dashed lines) as functions of magnetic field. The system parameters are ωc=ω0, Δs=0, and g/2π=20GHz.

Fig. 2.
Fig. 2.

Time-resolved intracavity photon number driven by a single X-polarized laser pulse as a function of magnetic field. Parameters are Δxl=Δcl=Δs=0 κ/2π=20GHz, γ/2π=1GHz, Ω0/2π=2GHz, τ=5ps, and (a) g/2π=10GHz, (b) g/2π=20GHz, and (c) g/2π=30GHz. All of the g values satisfy the strong coupling condition 2g/κ1. The insets extract the time and photon number value of the peak of Y-polarized oscillation as functions of magnetic field for g/2π=10GHz (red solid squares), 20 GHz (blue open squares), and 30 GHz (black crosses).

Fig. 3.
Fig. 3.

Time-resolved intracavity photon number as a function of (a) cavity-laser detuning Δcl, (b) exciton-laser detuning Δxl, and (c) mode splitting Δs. Parameters are B=3T; g/2π=20GHz; κ/2π=20GHz; γ/2π=1GHz; Ω0/2π=2GHz; τ=5ps; and (a) Δxl=0, Δs=0; (b) Δcl=0, Δs=0; (c) Δcl=Δxl=0. The insets extract the time and photon number value of the peak of Y-polarized oscillation as functions of Δcl (red solid squares), Δxl (blue open squares), and Δs (black crosses).

Fig. 4.
Fig. 4.

Time-resolved intracavity photon number as a function of (a) laser pulse magnitude Ω0 and (b) laser pulse duration τ. Parameters are B=3T, Δxl=Δcl=Δs=0, g/2π=20GHz, κ/2π=20GHz, γ/2π=1GHz, and (a) τ=5ps and (b) Ω0/2π=2GHz. Photon number curves are normalized by the maximum of total photon number in each chart. The curves in each row correspond to the same pulse area. The insets of (a) and (b) show the photon number value of the X- (red solid squares) and Y-polarized (blue open squares) photon as functions of Ω0 and τ, respectively, indicating their different influences on the nonlinear response.

Fig. 5.
Fig. 5.

Time-resolved intracavity photon number as a function of laser polarization. Parameters are B=3T, Δxl=Δcl=Δs=0, g/2π=20GHz, κ/2π=20GHz, γ/2π=1GHz, τ=5ps, and Ω0/2π=2GHz.

Fig. 6.
Fig. 6.

Time-resolved intracavity photon number driven by two orthogonally polarized laser pulses as a function of pulse time delay. Parameters are B=3T; Δxl=Δcl=Δs=0; κ/2π=20GHz; γ/2π=1GHz; Ω0/2π=2GHz; and τ=5ps for both pulses; and (a) g/2π=10GHz, (b) g/2π=20GHz, and (c) g/2π=30GHz. We set the peak of the pre pulse (i.e., Y-polarized) at 0 ps, and the peak of the postpulse (i.e., X-polarized) at t=Δt. The insets show the areas under time-resolved intracavity photon number curves with X and Y polarization for g/2π=10GHz (red solid squares), g/2π=20GHz (blue open squares), and g/2π=30GHz (black crosses).

Fig. 7.
Fig. 7.

Time-resolved intracavity photon number driven by two orthogonally polarized laser pulses as a function of prepulse magnitude. Parameters are B=3T, Δxl=Δcl=0, α=0, g/2π=20GHz, κ/2π=20GHz, γ/2π=1GHz, ΩY0/2π=2GHz, Δt=20ps, and τ=5ps for both pulses. The inset shows the area under time-resolved intracavity photon number curves with X-polarization.

Equations (5)

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Hsys=ωσ±(|σ±σ±|)+(ωc+Δs2)aa+(ωcΔs2)bb+ga(aσX+aσX)+gb(bσY+bσY).
Hsys=[ω0iΔBg0iΔBω00gg0ωC+Δs200g0ωCΔs2],
H=(ΔxlΔB)|σ±σ±|+(Δcl+Δs2)aa+(ΔclΔs2)bb+g(aσX+aσX+bσY+bσY)+ΩX(t)(a+a)+ΩY(t)(b+b),
Lρ=κ2L(a)ρ+κ2L(b)ρ+γ2L(|σ+G|)ρ+γ2L(|σG|)ρ,
H=Δxl(|AA|+|BB|)iΔB|AB|+iΔB|BA|+Δcl(αα+ββ)+g(α|GA|+β|GB|+H.C.)+2Ω(t)(α+α),

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