Abstract

The Jaynes–Cummings (JC) model has been the theoretical workhorse for understanding cavity quantum electrodynamics (QED) and for exploring multiphoton effects caused by the quantization of light. Today, it is an indispensable tool used to describe a variety of quantum optical systems, including semiconductor quantum-dot (QD) cavities, atoms in cavities, and superconducting circuits. Unfortunately, dissipation in many cavity-QED systems, especially QD structures, can strongly inhibit any direct spectral features of higher lying photon states and their spectral anharmonicities. In this work, we introduce a strategy to directly access and probe these multiphoton states and show that they can be directly observed even in the presence of a significant amount of dissipation. Our excitation scheme employs off-resonant excitation of a coupled QD cavity system using a nonlinear coherent drive, and the computed fluorescence spectra demonstrate the feasibility of the direct spectroscopic observation of higher rungs of the JC ladder using realistic QD cavity systems.

© 2015 Optical Society of America

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2015 (2)

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

S. Hughes and H. J. Carmichael, “Viewpoint: crystal vibrations invert quantum dot exciton,” Physics 8, 29 (2015).

2013 (3)

S. Hughes and H. J. Carmichael, “Phonon-mediated population inversion in a semiconductor quantum-dot cavity system,” New. J. Phys. 15, 053039 (2013).

A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, “Charge noise and spin noise in a semiconductor quantum device,” Nat. Phys. 9, 570–575 (2013).
[Crossref]

A. Ulhaq, S. Weiler, S. M. Ulrich, M. Jetter, P. Michler, C. Roy, and S. Hughes, “Detuning-dependent Mollow triplet of a coherently-driven single quantum dot,” Opt. Express 21, 4382–4395 (2013).
[Crossref]

2012 (5)

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetteri, P. Michler, C. Roy, and S. Hughes, “Phonon-assisted incoherent excitation of a quantum dot and its emission properties,” Phys. Rev. B 86, 241304 (2012).
[Crossref]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 607–611 (2012).
[Crossref]

A. Majumdar, M. Bajcsy, and J. Vučković, “Ultrafast all-optical switching by single photons,” Phys. Rev. A 85, 041801 (2012).
[Crossref]

F. P. Laussy, E. del Valle, M. Schrapp, A. Laucht, and J. J. Finley, “Climbing the Jaynes–Cummings ladder by photon counting,” J. Nanophoton. 6, 061803 (2012).
[Crossref]

E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved N-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
[Crossref]

2011 (6)

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
[Crossref]

R. Bose, D. Sridharan, G. S. Solomon, and E. Waks, “Observation of strong coupling through transmission modification of a cavity-coupled photonic crystal waveguide,” Opt. Express 19, 5398–5409 (2011).
[Crossref]

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Conditional phase shift from a quantum dot in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
[Crossref]

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

C. Roy and S. Hughes, “Phonon-dressed Mollow triplet in the regime of cavity quantum electrodynamics: excitation-induced dephasing and nonperturbative cavity feeding effects,” Phys. Rev. Lett. 106, 247403 (2011).
[Crossref]

A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2011).
[Crossref]

2010 (8)

P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
[Crossref]

V. Loo, L. Lanco, A. Lemaitre, I. Sagnes, O. Krebs, P. Voisin, and P. Senellart, “Quantum dot-cavity strong-coupling regime measured through coherent reflection spectroscopy in a very high-Q micropillar,” Appl. Phys. Lett. 97, 241110 (2010).
[Crossref]

J. Kasprazak, 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]

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vuckovic, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104, 073904 (2010).
[Crossref]

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
[Crossref]

D. P. S. McCutcheon and A. Nazir, “Quantum dot Rabi rotations beyond the weak exciton-phonon coupling regime,” New. J. Phys. 12, 113042 (2010).

2009 (3)

S. Ates, S. M. Ulrich, S. Reitzenstein, A. Loffler, A. Forchel, and P. Michler, “Post-selected indistinguishable photons from the resonance fluorescence of a single quantum dot in a microcavity,” Phys. Rev. Lett. 103, 167402 (2009).
[Crossref]

S. Hughes and P. Yao, “Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system,” Opt. Express 17, 3322–3330 (2009).
[Crossref]

E. B. Flagg, A. Muller, J. W. Ronbertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, and G. J. Salamo, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
[Crossref]

2008 (3)

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,” Nat. Phys. 4, 382–385 (2008).
[Crossref]

L. S. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance,” Nat. Phys. 5, 105–109 (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]

2007 (6)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
[Crossref]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref]

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007).
[Crossref]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauss, S. H. Kwon, C. Scneider, A. Löffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150,000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

2005 (1)

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. 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]

2004 (2)

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. Seogonk, 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]

2003 (1)

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, “Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots,” Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

2002 (4)

B. Krummheuer, V. M. Axt, and T. Kuhn, “Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots,” Phys. Rev. B 65, 195313 (2002).
[Crossref]

I. Wilson-Rae and A. Imamoglŭ, “Quantum dot cavity-QED in the presence of strong electron–phonon interactions,” Phys. Rev. B 65, 235311 (2002).
[Crossref]

A. Kuhn, M. Hennrich, and G. Rempe, “Deterministic single-photon source for distributed quantum networking,” Phys. Rev. Lett. 89, 067901 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

2001 (1)

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87, 133603 (2001).
[Crossref]

2000 (1)

C. H. Bennett and D. P. Divincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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1999 (1)

S. M. Tan, “A computational toolbox for quantum and atomic optics,” J. Opt. B. 1, 424–432 (1999).
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1998 (1)

P. Zhou and S. Swain, “Dynamics of a driven two-level atom coupled to a frequency-tunable cavity,” Phys. Rev. A. 58, 1515–1530 (1998).
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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).
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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).
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1989 (1)

H. J. Carmichael, R. J. Brecha, M. G. Raizen, and H. J. Kimble, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
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1969 (1)

B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969–1975 (1969).
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1963 (1)

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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Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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Ates, S.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
[Crossref]

S. Ates, S. M. Ulrich, S. Reitzenstein, A. Loffler, A. Forchel, and P. Michler, “Post-selected indistinguishable photons from the resonance fluorescence of a single quantum dot in a microcavity,” Phys. Rev. Lett. 103, 167402 (2009).
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Axt, V. M.

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

B. Krummheuer, V. M. Axt, and T. Kuhn, “Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots,” Phys. Rev. B 65, 195313 (2002).
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Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6, 607–611 (2012).
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A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2011).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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Bajcsy, M.

A. Majumdar, M. Bajcsy, and J. Vučković, “Ultrafast all-optical switching by single photons,” Phys. Rev. A 85, 041801 (2012).
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Barth, A. M.

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

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).
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Bennett, C. H.

C. H. Bennett and D. P. Divincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
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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]

Bianucci, P.

A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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Bishop, L. S.

L. S. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance,” Nat. Phys. 5, 105–109 (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).
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Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton–photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 067401 (2005).
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Bose, R.

Boyle, S. J.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Brash, A. J.

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

Brecha, R. J.

H. J. Carmichael, R. J. Brecha, M. G. Raizen, and H. J. Kimble, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[Crossref]

Brune, 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).
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Carmichael, H. J.

S. Hughes and H. J. Carmichael, “Viewpoint: crystal vibrations invert quantum dot exciton,” Physics 8, 29 (2015).

S. Hughes and H. J. Carmichael, “Phonon-mediated population inversion in a semiconductor quantum-dot cavity system,” New. J. Phys. 15, 053039 (2013).

S. Hughes and H. J. Carmichael, “Stationary inversion of a two level system coupled to an off-resonant cavity with strong dissipation,” Phys. Rev. Lett. 107, 193601 (2011).
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S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
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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, R. J. Brecha, M. G. Raizen, and H. J. Kimble, “Subnatural linewidth averaging for coupled atomic and cavity-mode oscillators,” Phys. Rev. A 40, 5516–5519 (1989).
[Crossref]

For a textbook discussion, e.g., see H. J. Carmichael, Statistical Methods in Quantum Optics 1 (Springer-Verlag, 2002).

For a textbook discussion, e.g., see H. J. Carmichael, Statistical Methods in Quantum Optics 2 (Springer-Verlag, 2008).

Chow, J. M.

L. S. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance,” Nat. Phys. 5, 105–109 (2008).
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Collett, M. J.

S. S. Shamailov, A. S. Parkins, M. J. Collett, and H. J. Carmichael, “Multi-photon blockade and dressing of the dressed states,” Opt. Commun. 283, 766–772 (2010).
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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).
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Danckwerts, J.

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, “Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots,” Phys. Rev. Lett. 91, 127401 (2003).
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del Valle, E.

F. P. Laussy, E. del Valle, M. Schrapp, A. Laucht, and J. J. Finley, “Climbing the Jaynes–Cummings ladder by photon counting,” J. Nanophoton. 6, 061803 (2012).
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E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved N-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
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Deppe, D. G.

E. B. Flagg, A. Muller, J. W. Ronbertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, and G. J. Salamo, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
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A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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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).
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Devoret, M. H.

L. S. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance,” Nat. Phys. 5, 105–109 (2008).
[Crossref]

Divincenzo, D. P.

C. H. Bennett and D. P. Divincenzo, “Quantum information and computation,” Nature 404, 247–255 (2000).
[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).
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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).
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Englund, D.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vuckovic, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104, 073904 (2010).
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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
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Falt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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Faraon, A.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vuckovic, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104, 073904 (2010).
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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[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.

F. P. Laussy, E. del Valle, M. Schrapp, A. Laucht, and J. J. Finley, “Climbing the Jaynes–Cummings ladder by photon counting,” J. Nanophoton. 6, 061803 (2012).
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Flagg, E. B.

E. B. Flagg, A. Muller, J. W. Ronbertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, and G. J. Salamo, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
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A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
[Crossref]

Forchel, A.

S. M. Ulrich, S. Ates, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, “Dephasing of triplet-sideband optical emission of a resonantly driven InAs/GaAs quantum dot inside a microcavity,” Phys. Rev. Lett. 106, 247402 (2011).
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A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Conditional phase shift from a quantum dot in a pillar microcavity,” Phys. Rev. A 84, 011803(R) (2011).
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J. Kasprazak, 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).
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P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
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S. Ates, S. M. Ulrich, S. Reitzenstein, A. Loffler, A. Forchel, and P. Michler, “Post-selected indistinguishable photons from the resonance fluorescence of a single quantum dot in a microcavity,” Phys. Rev. Lett. 103, 167402 (2009).
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D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007).
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S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauss, S. H. Kwon, C. Scneider, A. Löffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150,000,” Appl. Phys. Lett. 90, 251109 (2007).
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J. P. Reithmaier, G. Seogonk, 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).
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Förstner, J.

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, “Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots,” Phys. Rev. Lett. 91, 127401 (2003).
[Crossref]

Founta, S.

E. B. Flagg, A. Muller, J. W. Ronbertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, and G. J. Salamo, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
[Crossref]

Fox, A. M.

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Franeck, P.

P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
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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,” Nat. Phys. 4, 382–385 (2008).
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Fushman, I.

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
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Gammon, D.

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87, 133603 (2001).
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Gauger, E. M.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 105, 177402 (2010).
[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]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref]

Gérard, J. M.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. 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]

Gerry, C.

For a textbook discussion, e.g., see C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

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]

Girvin, S. M.

L. S. Bishop, J. M. Chow, J. Koch, A. A. Houck, M. H. Devoret, E. Thuneberg, S. M. Girvin, and R. J. Schoelkopf, “Nonlinear response of the vacuum Rabi resonance,” Nat. Phys. 5, 105–109 (2008).
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Gisin, N.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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Glässl, M.

J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, “Phonon-assisted population inversion of a single InGaAs/GaAs quantum dot by pulsed laser excitation,” Phys. Rev. Lett. 114, 137401 (2015).

Godden, T. M.

A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 105, 177402 (2010).
[Crossref]

Gonzalez-Tudela, A.

E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved N-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
[Crossref]

Gopal, A. V.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotations by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[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. Scneider, A. Löffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150,000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

Götzinger, S.

D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007).
[Crossref]

Greuter, L.

A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, “Charge noise and spin noise in a semiconductor quantum device,” Nat. Phys. 9, 570–575 (2013).
[Crossref]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[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.

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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A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2011).
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A. Majumdar, M. Bajcsy, and J. Vučković, “Ultrafast all-optical switching by single photons,” Phys. Rev. A 85, 041801 (2012).
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D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vuckovic, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104, 073904 (2010).
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Wallraff, 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).
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A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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I. Wilson-Rae and A. Imamoglŭ, “Quantum dot cavity-QED in the presence of strong electron–phonon interactions,” Phys. Rev. B 65, 235311 (2002).
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A. Reinhard, T. Volz, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglŭ, “Strongly correlated photons on a chip,” Nat. Photonics 6, 93–96 (2011).
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K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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E. B. Flagg, A. Muller, J. W. Ronbertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, and G. J. Salamo, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
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A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007).
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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).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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A. V. Kuhlmann, J. Houel, A. Ludwig, L. Greuter, D. Reuter, A. D. Wieck, M. Poggio, and R. J. Warburton, “Charge noise and spin noise in a semiconductor quantum device,” Nat. Phys. 9, 570–575 (2013).
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Nature (6)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, L. Hu, and A. Imamoglŭ, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
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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).
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D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
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Phys. Rev. A. (1)

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Phys. Rev. B (4)

S. Weiler, A. Ulhaq, S. M. Ulrich, D. Richter, M. Jetteri, P. Michler, C. Roy, and S. Hughes, “Phonon-assisted incoherent excitation of a quantum dot and its emission properties,” Phys. Rev. B 86, 241304 (2012).
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I. Wilson-Rae and A. Imamoglŭ, “Quantum dot cavity-QED in the presence of strong electron–phonon interactions,” Phys. Rev. B 65, 235311 (2002).
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P. Yao, P. K. Pathak, E. Illes, S. Hughes, S. Münch, S. Reitzenstein, P. Franeck, A. Löffler, T. Heindel, S. Höfling, L. Worschech, and A. Forchel, “Nonlinear photoluminescence spectra from a quantum-dot-cavity system: interplay of pump-induced stimulated emission and anharmonic cavity QED,” Phys. Rev. B 81, 033309 (2010).
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D. Press, S. Götzinger, S. Reitzenstein, C. Hofmann, A. Löffler, M. Kamp, A. Forchel, and Y. Yamamoto, “Photon antibunching from a single quantum-dot-microcavity system in the strong coupling regime,” Phys. Rev. Lett. 98, 117402 (2007).
[Crossref]

J. Förstner, C. Weber, J. Danckwerts, and A. Knorr, “Phonon-assisted damping of Rabi oscillations in semiconductor quantum dots,” Phys. Rev. Lett. 91, 127401 (2003).
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Physics (1)

S. Hughes and H. J. Carmichael, “Viewpoint: crystal vibrations invert quantum dot exciton,” Physics 8, 29 (2015).

Proc. IEEE (1)

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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Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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Other (4)

For a textbook discussion, e.g., see C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2005).

For a textbook discussion, e.g., see H. J. Carmichael, Statistical Methods in Quantum Optics 1 (Springer-Verlag, 2002).

For a textbook discussion, e.g., see H. J. Carmichael, Statistical Methods in Quantum Optics 2 (Springer-Verlag, 2008).

D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Books, 2006).

Supplementary Material (1)

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Figures (11)

Fig. 1.
Fig. 1. Left: schematic depicting the excitation scheme. Here the cavity ( c ) is on resonance with the exciton, which is represented as a two-level system with ground state | g and excited state | e . The transition frequencies of interest and the detuning of the laser are also depicted. Right: micropillar schematic, as an example of a semiconductor cavity-QED system, shows some example excitation and emission paths.
Fig. 2.
Fig. 2. Cavity mode and exciton populations for parameter sets- A , B , and C with cavity decay rates Γ c = g , g / 10 , and g / 500 , respectively, from bottom to top. The exciton and cavity are on resonance ( ω c = ω x ) . The laser is detuned by Δ L and excites the system with energy η x = 0.2 g . These populations are proportional to the PL intensity (integrated spectrum) and show almost no higher-order photon effects for parameter set- A .
Fig. 3.
Fig. 3. Log plots of the spectral maps calculated in the JC-WEA and using the full N -photon treatment (see text) are shown on the left and right, respectively, for parameter set- A (where Γ c = g ) and Δ L = 6 g . The top (bottom) panels contain the cavity (exciton)-emitted spectra. The dashed curves show the transitions expected within the JC-WEA.
Fig. 4.
Fig. 4. Energy level diagrams for a weak excitation in (a) the Floquet picture and (b) the interaction picture. Peaks associated with all seven possible transitions are labeled, with the exception of the transition with energy ω L , which is threefold degenerate and could take place between any of the two sets of levels separated by ω L .
Fig. 5.
Fig. 5. Example cavity-emitted spectra for parameter set- A in the JC-WEA with an excitation pump that is an order of magnitude larger in the bottom panel. The peak labels correspond to those in the energy level diagrams in Fig. 4, and again Δ L = 6 g .
Fig. 6.
Fig. 6. Enlarged region of the full N -photon spectral map (log scale) for a system that is excited via the exciton, and emission is collected via the cavity, for parameter set- A . The dashed curves show the transition energies calculated in the JC-WEA and the dotted curves show the transitions calculated for the two-photon excitation approximation.
Fig. 7.
Fig. 7. (a) Cavity-emitted spectrum for an exciton pump power of η x = 4 g and a detuning of Δ L = 6 g , using the first parameter set. (b) The associated energy level diagram, in the interaction picture, with the probabilities of being in a state with (0, 1, 2) excitations listed for each level, and a labeling of the transitions observed in the spectrum. The primed (unprimed) transitions occur in the upward (downward) direction and the peak at ω L is a fivefold degenerate transition associated with each level decaying to itself (in the interaction picture). (c) Multiphoton cavity correlations.
Fig. 8.
Fig. 8. Log plots of the spectral maps with cavity driving calculated in the JC-WEA and using the full N -photon treatment (see text) are shown on the left and right, respectively, for parameter set- A with Γ c = g , and again Δ L = 6 g . The top (bottom) panels contain the cavity (exciton)-emitted spectra. The dashed curves show the transitions expected within the JC-WEA.
Fig. 9.
Fig. 9. Cavity emission spectra of an exciton-driven system with pump power η x = 1.5 g that is excited via resonant two-photon driving, with a laser-exciton detuning of Δ L x 5.45 g and an exciton-cavity detuning of Δ x c = 10 g ; we again use parameter set- A . The red dashed curve is calculated in the JC-WEA and the blue solid curve shows the full N -photon result. The unfilled circles show peak locations expected in the JC-WEA. The N -photon spectra have been normalized to 1 and the JC-WEA spectra have been normalized by the same amount to preserve relative scaling.
Fig. 10.
Fig. 10. Cavity-emitted spectra with an exciton drive, demonstrating the effects of phonon scattering at 4 K for parameter set- A , with an excitation pump power of η x = 3 g with a detuning of Δ L = 6 g . All spectra have been normalized to 1.
Fig. 11.
Fig. 11. Cavity-emitted spectra for a cavity-driven system, demonstrating the effects of phonon scattering at 4 K, with an excitation pump power of η x = 6 g and Δ L = 6 g .

Equations (7)

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d ρ d t = i [ H , ρ ] + L ( ρ ) ,
H = Δ x L σ ^ + σ ^ + Δ c L a ^ a ^ + g ( a ^ σ ^ + σ ^ + a ^ ) + η x ( σ ^ + + σ ^ ) + η c ( a ^ + a ^ ) .
L = Γ c 2 ( 2 a ^ ρ a ^ a ^ a ^ ρ ρ a ^ a ^ ) + Γ x 2 ( 2 σ ^ ρ σ ^ + σ ^ + σ ^ ρ ρ σ ^ + σ ^ ) + Γ 4 ( σ ^ z ρ σ ^ z ρ ) ,
| g 0 , | 1 , = 1 2 ( | e 0 | g 1 ) , | 1 , + = 1 2 ( | e 0 + | g 1 ) ,
S c ( ω ) lim t Re { 0 d τ [ a ^ ( t + τ ) a ^ ( t ) a ^ ( t + τ ) a ^ ( t ) ] e i ( ω L ω ) τ }
S x ( ω ) lim t Re { 0 d τ [ σ ^ + ( t + τ ) σ ^ ( t ) σ ^ + ( t + τ ) σ ^ ( t ) ] e i ( ω L ω ) τ } .
E k = 2 3 [ Δ L + A cos ( 2 k π 3 + θ ) ] ,

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