Abstract

The build-up dynamics of quantum-optical correlations in a Jaynes–Cummings model for semiconductor quantum-dot systems is characterized using the cluster-expansion scheme. Assuming an excitation with a coherent state source under strong- and weak-coupling conditions, it is found that higher-order correlations are sequentially generated. Even though the influence of dephasing hinders their development, significant correlations build up even in the presence of strong dissipation showing that quantum-spectroscopy studies are possible even in interacting many-body systems like semiconductors.

© 2012 Optical Society of America

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  7. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
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    [CrossRef]
  32. C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
    [CrossRef]
  33. Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
    [CrossRef]
  34. M. Kira and S. W. Koch, “Quantum-optical spectroscopy of semiconductors,” Phys. Rev. A 73, 013813 (2006).
    [CrossRef]

2011 (1)

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

2009 (3)

L. Schneebeli, M. Kira, and S. W. Koch, “Microscopic theory of squeezed-light emission in strong-coupling semiconductor quantum-dot systems,” Phys. Rev. A 80, 033843 (2009).
[CrossRef]

M. Richter, A. Carmele, A. Sitek, and A. Knorr, “Few-photon model of the optical emission of semiconductor quantum dots,” Phys. Rev. Lett. 103, 087407 (2009).
[CrossRef]

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

2008 (3)

L. Schneebeli, M. Kira, and S. W. Koch, “Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities via photon-statistics spectroscopy,” Phys. Rev. Lett. 101, 097401 (2008).
[CrossRef]

M. Kira and S. W. Koch, “Cluster-expansion representation in quantum optics,” Phys. Rev. A 78, 022102 (2008).
[CrossRef]

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

2007 (1)

C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
[CrossRef]

2006 (5)

M. Kira and S. W. Koch, “Quantum-optical spectroscopy of semiconductors,” Phys. Rev. A 73, 013813 (2006).
[CrossRef]

M. Kira and S. W. Koch, “Many-body correlations and excitonic effects in semiconductor spectroscopy,” Prog. Quantum Electron. 30, 155–296 (2006).
[CrossRef]

S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, “Semiconductor excitons in new light,” Nature Mater. 5, 523–531 (2006).
[CrossRef]

T. Feldtmann, L. Schneebeli, M. Kira, and S. W. Koch, “Quantum theory of light emission from a semiconductor quantum dot,” Phys. Rev. B 73, 155319 (2006).

N. Baer, C. Gies, J. Wiersig, and F. Jahnke, “Luminescence of a semiconductor quantum dot system,” Eur. Phys. J. B 50, 411–418 (2006).
[CrossRef]

2005 (1)

K. J. Ahn, J. Förstner, and A. Knorr, “Resonance fluorescence of semiconductor quantum dots: signatures of the electron-phonon interaction,” Phys. Rev. B 71, 153309 (2005).

2004 (3)

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]

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]

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

2000 (2)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

1999 (1)

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

1996 (1)

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

1990 (1)

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

1987 (2)

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

1985 (1)

H. J. Carmichael, “Photon antibunching and squeezing for a single atom in a resonant cavity,” Phys. Rev. Lett. 55, 2790–2793 (1985).
[CrossRef]

1980 (2)

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695(1977).
[CrossRef]

1976 (1)

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
[CrossRef]

1963 (1)

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

Ahn, K. J.

K. J. Ahn, J. Förstner, and A. Knorr, “Resonance fluorescence of semiconductor quantum dots: signatures of the electron-phonon interaction,” Phys. Rev. B 71, 153309 (2005).

Aszmann, M.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Baer, N.

N. Baer, C. Gies, J. Wiersig, and F. Jahnke, “Luminescence of a semiconductor quantum dot system,” Eur. Phys. J. B 50, 411–418 (2006).
[CrossRef]

Bayer, M.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Berstermann, T.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Bertet, P.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Brune, M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Carmele, A.

M. Richter, A. Carmele, A. Sitek, and A. Knorr, “Few-photon model of the optical emission of semiconductor quantum dots,” Phys. Rev. Lett. 103, 087407 (2009).
[CrossRef]

Carmichael, H. J.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

H. J. Carmichael, “Photon antibunching and squeezing for a single atom in a resonant cavity,” Phys. Rev. Lett. 55, 2790–2793 (1985).
[CrossRef]

Cummings, F.

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

Cundiff, S. T.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695(1977).
[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]

Dreyer, J.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Eberly, J. H.

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Ell, C.

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

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

Feldtmann, T.

T. Feldtmann, L. Schneebeli, M. Kira, and S. W. Koch, “Quantum theory of light emission from a semiconductor quantum dot,” Phys. Rev. B 73, 155319 (2006).

Forchel, A.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[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]

Förstner, J.

K. J. Ahn, J. Förstner, and A. Knorr, “Resonance fluorescence of semiconductor quantum dots: signatures of the electron-phonon interaction,” Phys. Rev. B 71, 153309 (2005).

Fuhrmanek, A.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

Gauthier, D. J.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

Gibbs, H. M.

S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, “Semiconductor excitons in new light,” Nature Mater. 5, 523–531 (2006).
[CrossRef]

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

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

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Gies, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
[CrossRef]

N. Baer, C. Gies, J. Wiersig, and F. Jahnke, “Luminescence of a semiconductor quantum dot system,” Eur. Phys. J. B 50, 411–418 (2006).
[CrossRef]

Hagley, E.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Haroche, S.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

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]

Hofling, S.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Hofmann, C.

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]

Hommel, D.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Hoyer, W.

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

Hu, E.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Hunter, A. E.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Jahnke, F.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
[CrossRef]

N. Baer, C. Gies, J. Wiersig, and F. Jahnke, “Luminescence of a semiconductor quantum dot system,” Eur. Phys. J. B 50, 411–418 (2006).
[CrossRef]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Jaynes, E.

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

Kalden, J.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[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.

S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, “Semiconductor excitons in new light,” Nature Mater. 5, 523–531 (2006).
[CrossRef]

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

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

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Kimble, H. J.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695(1977).
[CrossRef]

Kira, M.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

L. Schneebeli, M. Kira, and S. W. Koch, “Microscopic theory of squeezed-light emission in strong-coupling semiconductor quantum-dot systems,” Phys. Rev. A 80, 033843 (2009).
[CrossRef]

L. Schneebeli, M. Kira, and S. W. Koch, “Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities via photon-statistics spectroscopy,” Phys. Rev. Lett. 101, 097401 (2008).
[CrossRef]

M. Kira and S. W. Koch, “Cluster-expansion representation in quantum optics,” Phys. Rev. A 78, 022102 (2008).
[CrossRef]

S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, “Semiconductor excitons in new light,” Nature Mater. 5, 523–531 (2006).
[CrossRef]

T. Feldtmann, L. Schneebeli, M. Kira, and S. W. Koch, “Quantum theory of light emission from a semiconductor quantum dot,” Phys. Rev. B 73, 155319 (2006).

M. Kira and S. W. Koch, “Many-body correlations and excitonic effects in semiconductor spectroscopy,” Prog. Quantum Electron. 30, 155–296 (2006).
[CrossRef]

M. Kira and S. W. Koch, “Quantum-optical spectroscopy of semiconductors,” Phys. Rev. A 73, 013813 (2006).
[CrossRef]

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

M. Kira and S. W. Koch, Semiconductor Quantum Optics, 1st ed. (Cambridge University, 2011).

Kiraz, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Kistner, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Klein, N.

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

Knorr, A.

M. Richter, A. Carmele, A. Sitek, and A. Knorr, “Few-photon model of the optical emission of semiconductor quantum dots,” Phys. Rev. Lett. 103, 087407 (2009).
[CrossRef]

K. J. Ahn, J. Förstner, and A. Knorr, “Resonance fluorescence of semiconductor quantum dots: signatures of the electron-phonon interaction,” Phys. Rev. B 71, 153309 (2005).

Koch, S. W.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

L. Schneebeli, M. Kira, and S. W. Koch, “Microscopic theory of squeezed-light emission in strong-coupling semiconductor quantum-dot systems,” Phys. Rev. A 80, 033843 (2009).
[CrossRef]

L. Schneebeli, M. Kira, and S. W. Koch, “Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities via photon-statistics spectroscopy,” Phys. Rev. Lett. 101, 097401 (2008).
[CrossRef]

M. Kira and S. W. Koch, “Cluster-expansion representation in quantum optics,” Phys. Rev. A 78, 022102 (2008).
[CrossRef]

M. Kira and S. W. Koch, “Many-body correlations and excitonic effects in semiconductor spectroscopy,” Prog. Quantum Electron. 30, 155–296 (2006).
[CrossRef]

T. Feldtmann, L. Schneebeli, M. Kira, and S. W. Koch, “Quantum theory of light emission from a semiconductor quantum dot,” Phys. Rev. B 73, 155319 (2006).

S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, “Semiconductor excitons in new light,” Nature Mater. 5, 523–531 (2006).
[CrossRef]

M. Kira and S. W. Koch, “Quantum-optical spectroscopy of semiconductors,” Phys. Rev. A 73, 013813 (2006).
[CrossRef]

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

M. Kira and S. W. Koch, Semiconductor Quantum Optics, 1st ed. (Cambridge University, 2011).

Kruse, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Kubanek, A.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

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]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Lindblad, G.

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
[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]

Lorke, M.

C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
[CrossRef]

Maali, A.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Mandel, L.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695(1977).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Michler, P.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Milburn, G.

D. Walls and G. Milburn, Quantum Optics, 2nd ed. (Springer-Verlag, 2008).

Morin, S. E.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

Mosor, S.

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

Mossberg, T. W.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

Murr, K.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

Narozhny, N. B.

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Nogues, G.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Osnaghi, S.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Petroff, P. M.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Pinkse, P. W. H.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

Puppe, T.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

Raimond, J. M.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Raimond, J.-M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Rauschenbeutel, A.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J.-M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Reinecke, T. L.

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]

Reithmaier, J. P.

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]

Reitzenstein, S.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[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]

Rempe, G.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

Richter, M.

M. Richter, A. Carmele, A. Sitek, and A. Knorr, “Few-photon model of the optical emission of semiconductor quantum dots,” Phys. Rev. Lett. 103, 087407 (2009).
[CrossRef]

Rupper, G.

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

Sanchez-Mondragon, J. J.

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Scherer, A.

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

Schmidt-Kaler, F.

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, “Quantum Rabi oscillation: A direct test of field quantization in a cavity,” Phys. Rev. Lett. 76, 1800–1803 (1996).
[CrossRef]

Schneebeli, L.

L. Schneebeli, M. Kira, and S. W. Koch, “Microscopic theory of squeezed-light emission in strong-coupling semiconductor quantum-dot systems,” Phys. Rev. A 80, 033843 (2009).
[CrossRef]

L. Schneebeli, M. Kira, and S. W. Koch, “Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities via photon-statistics spectroscopy,” Phys. Rev. Lett. 101, 097401 (2008).
[CrossRef]

T. Feldtmann, L. Schneebeli, M. Kira, and S. W. Koch, “Quantum theory of light emission from a semiconductor quantum dot,” Phys. Rev. B 73, 155319 (2006).

Schneider, C.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

Schoenfeld, W. V.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000).
[CrossRef]

Schuster, I.

I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P. W. H. Pinkse, K. Murr, and G. Rempe, “Nonlinear spectroscopy of photons bound to one atom,” Nature Mater. 4, 382–385 (2008).
[CrossRef]

Schwabl, F.

F. Schwabl, Statistical Mechanics, 2nd ed. (Springer-Verlag, 2006).

Sek, G.

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]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Shchekin, O. B.

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

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Sitek, A.

M. Richter, A. Carmele, A. Sitek, and A. Knorr, “Few-photon model of the optical emission of semiconductor quantum dots,” Phys. Rev. Lett. 103, 087407 (2009).
[CrossRef]

Smith, R. P.

M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, “Quantum spectroscopy with Schrödinger-cat states,” Nature Phys. 7, 799–804 (2011).
[CrossRef]

Stolz, H.

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

Sweet, J.

W. Hoyer, M. Kira, S. W. Koch, H. Stolz, S. Mosor, J. Sweet, C. Ell, G. Khitrova, and H. M. Gibbs, “Entanglement between a photon and a quantum well,” Phys. Rev. Lett. 93, 067401 (2004).
[CrossRef]

Walls, D.

D. Walls and G. Milburn, Quantum Optics, 2nd ed. (Springer-Verlag, 2008).

Walther, H.

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

G. Rempe, H. Walther, and N. Klein, “Observation of quantum collapse and revival in a one-atom maser,” Phys. Rev. Lett. 58, 353–356 (1987).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Wiersig, J.

J. Wiersig, C. Gies, F. Jahnke, M. Aszmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Hofling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[CrossRef]

C. Gies, J. Wiersig, M. Lorke, and F. Jahnke, “Semiconductor model for quantum-dot-based microcavity lasers,” Phys. Rev. A 75, 013803 (2007).
[CrossRef]

N. Baer, C. Gies, J. Wiersig, and F. Jahnke, “Luminescence of a semiconductor quantum dot system,” Eur. Phys. J. B 50, 411–418 (2006).
[CrossRef]

Wu, Q.

Y. Zhu, D. J. Gauthier, S. E. Morin, Q. Wu, H. J. Carmichael, and T. W. Mossberg, “Vacuum Rabi splitting as a feature of linear-dispersion theory: analysis and experimental observations,” Phys. Rev. Lett. 64, 2499–2502 (1990).
[CrossRef]

Yoshie, T.

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

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
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Zhang, L.

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Figures (4)

Fig. 1.
Fig. 1.

Dynamics of quantum statistics without dissipation. The time-evolution of the population inversion σ z is presented in (a) linear and (b) semilogarithmic time scale. The corresponding dynamics of the collective C -particle correlations Δ I C all is shown for C = 1 up to C = 4 in (c) semilogarithmic and (d) double-logarithmic scale. The times of interest are marked with vertical dashed and solid lines. The shaded area displays the collapse region.

Fig. 2.
Fig. 2.

Dynamics of quantum statistics with dissipation. Same plots as in Fig. 1(b–d) but now with a dephasing of γ = g .

Fig. 3.
Fig. 3.

Effect of dissipation on build-up of correlations. (a) The maximum of correlations up to the first revival time Δ I C max is plotted as function of the cluster number C for the even ( 2 C ) -particle correlations without dephasing (squares) and a dephasing of γ = g (circles). The dashed lines are a guide to the eye. (b) The same quantity is presented as function of γ for C = 2 (solid line), C = 3 (dashed line), and C = 4 (dotted line). The shaded area indicates the weak-coupling regime.

Fig. 4.
Fig. 4.

Evolution of light’s quantum statistics toward the steady state. The Wigner function of light is shown at (a) the initial time, (b) an intermediate time ( t = T rev ), and (c) the final time. The contour lines are defined at 0.05, 0.2, and 0.8 normalized to the peak height of W ( x , y ) . A dephasing of γ = g has been used. (d) The corresponding scaled marginal distributions P ¯ ( x ) = P ( x ) / max [ P ( x ) ] .

Equations (51)

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H ^ JC = ω B B + ω 21 σ z g ( σ B + σ + B ) ,
[ σ , σ ] + = [ σ , σ + ] + = 1.
[ σ , σ + ] = 2 σ z .
i t ρ ^ = [ H ^ JC , ρ ^ ] .
i t ρ ^ = [ H ^ JC , ρ ^ ] + i γ [ 2 L ^ ρ ^ L ^ L ^ L ^ ρ ^ ρ ^ L ^ L ^ ] ,
i t σ z | deph = 0 , i t σ | deph = i γ σ .
ρ ^ = n 1 , n 2 = 0 N σ 1 , σ 2 = ± | σ 1 | n 1 ρ n 2 , σ 2 n 1 , σ 1 n 2 | σ 2 | ,
H ^ = g ( P ^ B ^ + P ^ B ^ ) .
i t B ^ = g P ^ ,
i t P ^ = g B ^ [ P ^ , P ^ ] .
i t B ^ = g P ^ ,
i t P ^ = 2 g P ^ z B ^ ,
i t N = F [ N ] + Hi [ N + 1 ] ,
I K J ( t ) [ B ^ ( t ) ] J [ B ^ ( t ) ] K = [ c ( t ) ] J + K I K J ( 0 ) , c ( t ) cos ( ω g t ) ,
I ˜ K J ( t ) [ P ^ ( t ) ] J [ P ^ ( t ) ] K = e i π 2 ( K J ) [ s ( t ) ] J + K I K J ( 0 ) , s ( t ) sin ( ω g t ) ,
| I K J ( t ) | 2 J + K + | I ˜ K J ( t ) | 2 J + K = | I K J ( 0 ) | 2 J + K ,
| β = n = 0 e | β | 2 2 β n n ! | n .
I K J ( 0 ) = [ β ] J β K ,
I K J ( B + ) J B K = Tr [ ρ ^ ( B + ) J B K ] = n = 0 σ = ± ( n + J ) ! ( n + K ) ! n ! ρ n + J , σ n + K , σ .
χ N ( β ) e β B + e β B = J , K = 0 β J ( β ) K J ! K ! I K J ,
ξ N ( β ) = J , K = 0 β J ( β ) K J ! K ! Δ I K J = ln [ χ N ( β ) ] .
Δ I K J = [ ( 1 ) K J + K β J ( β ) K ξ N ( β ) ] β = 0 .
T Rabi = π g | β | .
T rev = 2 π | β | g .
Δ I ¯ K J Δ I K J J ! K ! | β | J + K ,
Δ I C all = J = 0 C | Δ I ¯ C J J | ,
Δ I C max max t [ 0 , T rev ] [ Δ I C all ( t ) ] .
ρ ^ steady = 1 2 n = 0 ( | n | ρ n , n ini | n | + | n | + ρ n + 1 , n + 1 ini + | n | ) ,
ρ ^ steady light Tr 2 LS [ ρ ^ steady ] = n = 0 | n S n n | , S n 1 2 ( ρ n , n ini + ρ n + 1 , n + 1 ini ) ,
ρ ^ steady light = n = 0 | n S n | β n | , S n | β = 1 2 ( 1 + | β | 2 n + 1 ) | β | 2 n n ! e | β | 2 ,
ρ ^ rand light = n = 0 | n S n rand n | , S n rand = | β | 2 n n ! e | β | 2 .
Δ I 0 1 = I 0 1 , Δ I 1 0 = [ Δ I 0 1 ] ,
Δ I 0 2 = I 0 2 ( I 0 1 ) 2 , Δ I 2 0 = [ Δ I 0 2 ] ,
Δ I 1 1 = I 1 1 I 0 1 I 1 0 ,
Δ I 0 3 = I 3 0 3 I 1 0 I 2 0 + 2 ( I 1 0 ) 3 , Δ I 3 0 = [ Δ I 0 3 ] ,
Δ I 1 2 = I 1 2 I 1 0 I 0 2 2 I 0 1 I 1 1 + 2 I 1 0 ( I 0 1 ) 2 , Δ I 2 1 = [ Δ I 1 2 ] .
t ρ n 2 , n 1 , = i g ( n 1 ρ n 2 , n 1 1 , + n 2 ρ n 2 1 , + n 1 , ) ,
t ρ n 2 , n 1 1 , + = i g ( n 1 ρ n 2 , n 1 , n 2 ρ n 2 1 , + n 1 1 , + ) γ ρ n 2 , n 1 1 , + ,
t ρ n 2 1 , + n 1 , = i g ( n 1 ρ n 2 1 , + n 1 1 , + n 2 ρ n 2 , n 1 , ) γ ρ n 2 1 , + n 1 , ,
t ρ n 2 1 , + n 1 1 , + = i g ( n 1 ρ n 2 1 , + n 1 , n 2 ρ n 2 , n 1 1 , + ) .
ρ n 2 , n 1 , ( t = 0 ) = ρ n 1 , n 2 ini , ρ n 2 , + n 1 , + ( t = 0 ) = ρ n 2 , + n 1 , ( t = 0 ) = ρ n 2 , n 1 , + ( t = 0 ) = 0.
ρ n 2 , n 1 , ( t ) = e γ t 2 4 Γ n 1 , n 2 Γ n 1 , n 2 + ρ n 1 , n 2 ini × { Γ n 1 , n 2 [ ( γ + Γ n 1 , n 2 + ) e Γ n 1 , n 2 + t 2 ( γ Γ n 1 , n 2 + ) e Γ n 1 , n 2 + t 2 ] + Γ n 1 , n 2 + [ ( γ + Γ n 1 , n 2 ) e Γ n 1 , n 2 t 2 ( γ Γ n 1 , n 2 ) e Γ n 1 , n 2 t 2 ] } ,
ρ n 2 , n 1 , + ( t ) = i g e γ t 2 2 Γ n 1 + 1 , n 2 Γ n 1 + 1 , n 2 + ρ n 1 + 1 , n 2 ini × { Γ n 1 + 1 , n 2 [ ( n 1 + 1 n 2 ) e Γ n 1 + 1 , n 2 + t 2 ( n 1 + 1 n 2 ) e Γ n 1 + 1 , n 2 + t 2 ] + Γ n 1 + 1 , n 2 + [ ( n 1 + 1 + n 2 ) e Γ n 1 + 1 , n 2 t 2 ( n 1 + 1 + n 2 ) e Γ n 1 + 1 , n 2 t 2 ] } ,
ρ n 2 , + n 1 , ( t ) = i g e γ t 2 2 Γ n 1 , n 2 + 1 Γ n 1 , n 2 + 1 + ρ n 1 , n 2 + 1 ini × { Γ n 1 , n 2 + 1 [ ( n 1 n 2 + 1 ) e Γ n 1 , n 2 + 1 + t 2 ( n 1 n 2 + 1 ) e Γ n 1 , n 2 + 1 + t 2 ] Γ n 1 , n 2 + 1 + [ ( n 1 + n 2 + 1 ) e Γ n 1 , n 2 + 1 t 2 ( n 1 + n 2 + 1 ) e Γ n 1 , n 2 + 1 t 2 ] } ,
ρ n 2 , + n 1 , + ( t ) = e γ t 2 4 Γ n 1 + 1 , n 2 + 1 Γ n 1 + 1 , n 2 + 1 + ρ n 1 + 1 , n 2 + 1 ini × { Γ n 1 + 1 , n 2 + 1 [ ( γ + Γ n 1 + 1 , n 2 + 1 + ) e Γ n 1 + 1 , n 2 + 1 + t 2 ( γ Γ n 1 + 1 , n 2 + 1 + ) e Γ n 1 + 1 , n 2 + 1 + t 2 ] + Γ n 1 + 1 , n 2 + 1 + [ ( γ Γ n 1 + 1 , n 2 + 1 ) e Γ n 1 + 1 , n 2 + 1 t 2 ( γ + Γ n 1 + 1 , n 2 + 1 ) e Γ n 1 + 1 , n 2 + 1 t 2 ] } ,
Γ n 1 , n 2 ± [ γ 2 4 g 2 ( n 1 n 2 ) 2 ] 1 / 2 .
lim t ρ n 2 , n 1 , ( t ) = δ n 1 , n 2 2 ρ n 1 , n 2 ini ,
lim t ρ n 2 , n 1 , + ( t ) = lim t ρ n 2 , + n 1 , ( t ) = 0 ,
lim t ρ n 2 , + n 1 , + ( t ) = δ n 1 , n 2 2 ρ n 1 + 1 , n 2 + 1 ini .
ρ ^ steady = 1 2 n = 0 ( | n | ρ n , n ini | n | + | n | + ρ n + 1 , n + 1 ini + | n | ) .
ρ ^ steady light Tr 2 LS [ ρ ^ steady ] = n = 0 | n S n n | , S n 1 2 ( ρ n , n ini + ρ n + 1 , n + 1 ini ) .

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