Abstract

We study the effect of pure dephasing on a two-level system in strong coupling in the nonlinear regime with the single mode of a cavity. The photoluminescence spectrum of the cavity has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies ±(n±n1) for integer n. We discuss recent experimental works that may already manifest signatures of single photon nonlinearities.

© 2010 Optical Society of America

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  5. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
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  6. 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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  18. I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
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  19. 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 (1990).
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  20. P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, "Quantum correlation among photons from a single quantum dot at room temperature," Nature 406, 968 (2000).
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  21. E. Jaynes and F. Cummings, "Comparison of quantum and semiclassical radiation theory with application to the beam maser," Proc. IEEE 51, 89 (1963).
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  22. 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 (1996).
    [CrossRef] [PubMed]
  23. 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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
    [CrossRef] [PubMed]
  24. A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
    [CrossRef]
  25. E. del Valle, F. P. Laussy, and C. Tejedor, "Luminescence spectra of quantum dots in microcavities. II. Fermions," Phys. Rev. B 79, 235326 (2009).
    [CrossRef]
  26. G. S. Agarwal and S. Dutta Gupta, "Steady states in cavity QED due to incoherent pumping," Phys. Rev. A 42, 1737 (1990).
    [CrossRef] [PubMed]
  27. F. P. Laussy and E. del Valle, "Optical spectra of the Jaynes-Cummings ladder," AIP Conference Proceedings 1147, 46 (2009).
    [CrossRef]
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    [CrossRef]
  29. M. Yamaguchi, T. Asano, K. Kojima, and S. Noda, "Quantum electrodynamics of a nanocavity coupled with exciton complexes in a quantum dot," Phys. Rev. B 80, 155326 (2009).
    [CrossRef]
  30. 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 (2009).
    [CrossRef] [PubMed]
  31. B. R. Mollow, "Power spectrum of light scattered by two-level systems," Phys. Rev. 188, 1969 (1969).
    [CrossRef]
  32. A. Auffèves, J.-M. Gérard, and J.-P. Poizat, "Pure emitter dephasing: A resource for advanced solid-state single photon sources," Phys. Rev. A 79, 053838 (2009).
    [CrossRef]
  33. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
    [CrossRef]
  34. 34. S. Strauf, "Lasing under strong coupling," Nat. Phys. (2010). AOP doi:10.1038/nphys1600.
    [CrossRef]
  35. D. Sanvitto, F. P. Laussy, F. Bello, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, "Single-photon nonlinearity of a semiconductor quantum dot in a cavity," arXiv:condmat/0612034 (2006).

2010 (2)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
[CrossRef]

34. S. Strauf, "Lasing under strong coupling," Nat. Phys. (2010). AOP doi:10.1038/nphys1600.
[CrossRef]

2009 (11)

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

A. Auffèves, J.-M. Gérard, and J.-P. Poizat, "Pure emitter dephasing: A resource for advanced solid-state single photon sources," Phys. Rev. A 79, 053838 (2009).
[CrossRef]

F. P. Laussy and E. del Valle, "Optical spectra of the Jaynes-Cummings ladder," AIP Conference Proceedings 1147, 46 (2009).
[CrossRef]

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

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

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 (2009).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724 (2009).
[CrossRef] [PubMed]

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
[CrossRef]

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[CrossRef]

A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, "Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities," Phys. Rev. Lett. 103, 087405 (2009).
[CrossRef] [PubMed]

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

2008 (7)

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, "Influence of pure dephasing on emission spectra from single photon sources," Phys. Rev. A 78, 045802 (2008).
[CrossRef]

M. Yamaguchi, T. Asano, and S. Noda, "Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics," Opt. Express 16, 118067 (2008).
[CrossRef]

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, "Large vacuum Rabi splitting in single self assembled quantum dot-nanocavity system," Appl. Phys. Express 1, 072102 (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 (2008).
[CrossRef] [PubMed]

F. P. Laussy, E. del Valle, and C. Tejedor, "Strong coupling of quantum dots in microcavities," Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
[CrossRef] [PubMed]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
[CrossRef]

2007 (3)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

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] [PubMed]

I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
[CrossRef]

2006 (1)

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

2005 (1)

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
[CrossRef]

2004 (1)

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

2000 (1)

P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, "Quantum correlation among photons from a single quantum dot at room temperature," Nature 406, 968 (2000).
[CrossRef] [PubMed]

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 (1996).
[CrossRef] [PubMed]

1990 (2)

G. S. Agarwal and S. Dutta Gupta, "Steady states in cavity QED due to incoherent pumping," Phys. Rev. A 42, 1737 (1990).
[CrossRef] [PubMed]

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 (1990).
[CrossRef] [PubMed]

1989 (1)

S. Haroche and D. Kleppner, "Cavity quantum electrodynamics," Phys. Today 42, 24 (1989).
[CrossRef]

1969 (1)

B. R. Mollow, "Power spectrum of light scattered by two-level systems," Phys. Rev. 188, 1969 (1969).
[CrossRef]

1963 (1)

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

Agarwal, G. S.

G. S. Agarwal and S. Dutta Gupta, "Steady states in cavity QED due to incoherent pumping," Phys. Rev. A 42, 1737 (1990).
[CrossRef] [PubMed]

Amann, M.-C.

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
[CrossRef]

Angele, J.

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
[CrossRef]

Arakawa, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
[CrossRef]

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, "Large vacuum Rabi splitting in single self assembled quantum dot-nanocavity system," Appl. Phys. Express 1, 072102 (2008).
[CrossRef]

Asano, T.

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

M. Yamaguchi, T. Asano, and S. Noda, "Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics," Opt. Express 16, 118067 (2008).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724 (2009).
[CrossRef] [PubMed]

Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

Auffèves, A.

A. Auffèves, J.-M. Gérard, and J.-P. Poizat, "Pure emitter dephasing: A resource for advanced solid-state single photon sources," Phys. Rev. A 79, 053838 (2009).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
[CrossRef] [PubMed]

Berthelot, A.

I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
[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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
[CrossRef] [PubMed]

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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
[CrossRef] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

Bloch, J.

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[CrossRef]

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

Böhm, G.

A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, "Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities," Phys. Rev. Lett. 103, 087405 (2009).
[CrossRef] [PubMed]

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
[CrossRef]

Borri, P.

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
[CrossRef]

Braive, R.

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[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 (1996).
[CrossRef] [PubMed]

Buratto, S. K.

P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, "Quantum correlation among photons from a single quantum dot at room temperature," Nature 406, 968 (2000).
[CrossRef] [PubMed]

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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 (1990).
[CrossRef] [PubMed]

Mork, J.

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, "Influence of pure dephasing on emission spectra from single photon sources," Phys. Rev. A 78, 045802 (2008).
[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 (1990).
[CrossRef] [PubMed]

Naesby, A.

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, "Influence of pure dephasing on emission spectra from single photon sources," Phys. Rev. A 78, 045802 (2008).
[CrossRef]

Noda, S.

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

M. Yamaguchi, T. Asano, and S. Noda, "Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics," Opt. Express 16, 118067 (2008).
[CrossRef]

Nomura, M.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
[CrossRef]

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, "Large vacuum Rabi splitting in single self assembled quantum dot-nanocavity system," Appl. Phys. Express 1, 072102 (2008).
[CrossRef]

Ohkouchi, S.

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

Ota, Y.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
[CrossRef]

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, "Large vacuum Rabi splitting in single self assembled quantum dot-nanocavity system," Appl. Phys. Express 1, 072102 (2008).
[CrossRef]

Petroff, P.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
[CrossRef]

Poizat, J.-P.

A. Auffèves, J.-M. Gérard, and J.-P. Poizat, "Pure emitter dephasing: A resource for advanced solid-state single photon sources," Phys. Rev. A 79, 053838 (2009).
[CrossRef]

Press, D.

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] [PubMed]

Rahimi-Iman, A.

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 (1996).
[CrossRef] [PubMed]

Raymer, M. G.

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

Reitzenstein, S.

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 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Reuter, D.

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
[CrossRef]

Roussignol, P.

I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
[CrossRef]

Sagnes, I.

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[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 (1996).
[CrossRef] [PubMed]

Schneider, C.

Schoelkopf, R. J.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

Schuster, D. I.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

Senellart, P.

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[CrossRef]

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

Shirane, M.

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

Stavarache, V.

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
[CrossRef]

Stobbe, S.

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
[CrossRef]

Stoltz, N.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
[CrossRef]

Strauf, S.

34. S. Strauf, "Lasing under strong coupling," Nat. Phys. (2010). AOP doi:10.1038/nphys1600.
[CrossRef]

Strouse, G. F.

P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, "Quantum correlation among photons from a single quantum dot at room temperature," Nature 406, 968 (2000).
[CrossRef] [PubMed]

Suffczynski, J.

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[CrossRef]

Suhr, T.

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, "Influence of pure dephasing on emission spectra from single photon sources," Phys. Rev. A 78, 045802 (2008).
[CrossRef]

Tejedor, C.

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

F. P. Laussy, E. del Valle, and C. Tejedor, "Strong coupling of quantum dots in microcavities," Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724 (2009).
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Villas-Bôas, J. M.

A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, "Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities," Phys. Rev. Lett. 103, 087405 (2009).
[CrossRef] [PubMed]

Voisin, C.

I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
[CrossRef]

Voisin, P.

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
[CrossRef]

Vuckovic, J.

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
[CrossRef]

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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

Wieck, A. D.

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
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Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
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Woggon, U.

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
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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 (1990).
[CrossRef] [PubMed]

Yamaguchi, M.

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

M. Yamaguchi, T. Asano, and S. Noda, "Photon emission by nanocavity-enhanced quantum anti-Zeno effect in solid-state cavity quantum-electrodynamics," Opt. Express 16, 118067 (2008).
[CrossRef]

Yamamoto, Y.

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] [PubMed]

Yao, P.

Yorozu, S.

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

Zhu, Y.

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 (1990).
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AIP Conference Proceedings (1)

F. P. Laussy and E. del Valle, "Optical spectra of the Jaynes-Cummings ladder," AIP Conference Proceedings 1147, 46 (2009).
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Appl. Phys. Express (2)

Y. Ota, N. Kumagai, S. Ohkouchi, M. Shirane, M. Nomura, S. Ishida, S. Iwamoto, S. Yorozu, and Y. Arakawa, "Investigation of the spectral triplet in strongly coupled quantum dot-nanocavity system," Appl. Phys. Express 2, 122301 (2009).
[CrossRef]

M. Nomura, Y. Ota, N. Kumagai, S. Iwamoto, and Y. Arakawa, "Large vacuum Rabi splitting in single self assembled quantum dot-nanocavity system," Appl. Phys. Express 1, 072102 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

A. Dousse, J. Suffczyński, R. Braive, A. Miard, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Scalable implementation of strongly coupled cavity-quantum dot devices," Appl. Phys. Lett. 94, 121102 (2009).
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Nat. Phys. (3)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Laser oscillation in a strongly coupled single quantum-dot-nanocavity system," Nat. Phys. (2010). AOP doi:10.1038/nphys1518.
[CrossRef]

34. S. Strauf, "Lasing under strong coupling," Nat. Phys. (2010). AOP doi:10.1038/nphys1600.
[CrossRef]

A. Faraon, I. Fushman, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, "Coherent generation of non-classical light on a chip via photon-induced tunneling and blockade," Nat. Phys. 4, 859 (2008).
[CrossRef]

Nature (5)

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 √ n nonlinearity in a cavity QED system," Nature 454, 315 (2008).
[CrossRef] [PubMed]

P. Michler, A. Imamoglu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, "Quantum correlation among photons from a single quantum dot at room temperature," Nature 406, 968 (2000).
[CrossRef] [PubMed]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature 431, 162 (2004).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724 (2009).
[CrossRef] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fǎlt, E. L. Hu, and A. Ǐmamoglu, "Quantum nature of a strongly coupled single quantum dot-cavity system," Nature 445, 896 (2007).
[CrossRef] [PubMed]

New J. Phys. (1)

A. Laucht, F. Hofbauer, N. Hauke, J. Angele, S. Stobbe, M. Kaniber, G. Böhm, P. Lodahl, M.-C. Amann, and J. J. Finley, "Electrical control of spontaneous emission and strong coupling for a single quantum dot," New J. Phys. 11, 023034 (2009).
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A. Auffèves, J.-M. Gérard, and J.-P. Poizat, "Pure emitter dephasing: A resource for advanced solid-state single photon sources," Phys. Rev. A 79, 053838 (2009).
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A. Naesby, T. Suhr, P. T. Kristensen, and J. Mork, "Influence of pure dephasing on emission spectra from single photon sources," Phys. Rev. A 78, 045802 (2008).
[CrossRef]

G. Cui and M. G. Raymer, "Emission spectra and quantum efficiency of single-photon sources in the cavity-QED strong-coupling regime," Phys. Rev. A 73, 053807 (2006).
[CrossRef]

Phys. Rev. B (4)

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

P. Borri, W. Langbein, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Exciton dephasing via phonon interactions in InAs quantum dots: Dependence on quantum confinement," Phys. Rev. B 71, 115328 (2005).
[CrossRef]

I. Favero, A. Berthelot, G. Cassabois, C. Voisin, C. Delalande, P. Roussignol, R. Ferreira, and J. M. Gérard, "Temperature dependence of the zero-phonon linewidth in quantum dots: An effect of the fluctuating environment," Phys. Rev. B 75, 073308 (2007).
[CrossRef]

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

Phys. Rev. Lett. (6)

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 (1996).
[CrossRef] [PubMed]

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 (1990).
[CrossRef] [PubMed]

F. P. Laussy, E. del Valle, and C. Tejedor, "Strong coupling of quantum dots in microcavities," Phys. Rev. Lett. 101, 083601 (2008).
[CrossRef] [PubMed]

A. Laucht, N. Hauke, J. M. Villas-Bôas, F. Hofbauer, G. Böhm, M. Kaniber, and J. J. Finley, "Dephasing of exciton polaritons in photoexcited InGaAs quantum dots in GaAs nanocavities," Phys. Rev. Lett. 103, 087405 (2009).
[CrossRef] [PubMed]

J. Suffczyński, A. Dousse, K. Gauthron, A. Lemaître, I. Sagnes, L. Lanco, J. Bloch, P. Voisin, and P. Senellart, "Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems," Phys. Rev. Lett. 103, 027401 (2009).
[CrossRef] [PubMed]

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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Other (2)

D. Sanvitto, F. P. Laussy, F. Bello, D. M. Whittaker, A. M. Fox, M. S. Skolnick, A. Tahraoui, P. W. Fry, and M. Hopkinson, "Single-photon nonlinearity of a semiconductor quantum dot in a cavity," arXiv:condmat/0612034 (2006).

E. del Valle, Microcavity Quantum Electrodynamics (VDM Verlag, 2009).

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Figures (3)

Fig. 1.
Fig. 1.

(Colour online) Loss of the Jaynes-Cummings quadruplet and emergence of a triplet with dephasing, for a system well into strong coupling (γa /g = 0.1 and γσ /g = 0.001). Values of dephasing are γϕ σ /g = 0 (dotted), 0.75 (dashed) and 1.5 (solid). Panel (a) [resp., (b)] is for Pσ /g = 0.02 [resp., 0.1]. In inset (c), the level structure (Jaynes-Cummings ladder) at γϕ σ = 0, from the vacuum up to 5 excitations, and the transitions between its rungs that give rise to the dressed states resonances ωp /g. These appear below for the parameters of (b) and show the impact of dephasing on strong coupling: inner transitions (blue) melt into a common line while outer transitions (red) remain well apart.

Fig. 2.
Fig. 2.

Evolution of strong-coupling with increasing electronic pumping. Parameters are those of state of the art systems from the literature [7,9,28]: g = 120μeV, γa = 38μeV, γσ = 1μeV, γϕ σ = g, at resonance, Pσ varying as indicated, without cavity pumping and with detector resolution of 46μeV. (a) The system evolves from the vacuum Rabi doublet into a triplet, similarly to the experiment of Ota et al. [28]. (b) At much higher pumpings, the system goes to lasing then to quenching. These transitions are shown in (c) cavity and (d) dot population, and (e) g (2) (0).

Fig. 3.
Fig. 3.

Strong-coupling in the nonlinear regime in presence of dephasing as detuning is varied. Parameters are γσ /g - 0.001 and Pa /g = 0.011 for both panels, and for (a) [resp., (b)], γϕ σ /g = 1 [resp., sigmoid function of Δ], γa /g - 0.35 [resp., 0.5] and Pσ /g = 0.1 [resp., 0.3]. Instead of the usual anticrossing, triplets are observed in slightly varying configurations: (a) A triplet is grown as the dot enters in resonance similarly to the experiment of Hennessy et al. [5]. (b) As detuning varies with temperature, a triplet is observed out of resonance with an asymmetry with detuning caused by the temperature-dependent dephasing similarly to the experiment of Sanvitto et al. [35].

Equations (2)

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ρ = i [ ρ , H ] + c = a , σ γ c 2 ( 2 c c ρ c c ) + c = a , σ P c 2 ( 2 c ρc c c ρ ρc c ) + γ σ ϕ ρ .
M mnμν mnμν = i ω a ( m n ) + i ω σ ( μ ν ) γ a P a 2 ( m + n ) γ σ + P σ 2 ( μ + ν ) γ σ ϕ 2 ( μ ν ) 2 .

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