Emission properties and photon statistics
of a single quantum dot laser

doi:10.1364/OE.18.009909

Emission properties and photon statistics of a single quantum dot laser

S. Ritter, P. Gartner, C. Gies, and F. Jahnke »View Author Affiliations

Optics Express, Vol. 18, Issue 10, pp. 9909-9921 (2010)
http://dx.doi.org/10.1364/OE.18.009909

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Abstract

A theoretical description for a single quantum-dot emitter in a microcavity is developed. We analyze for increasing steady-state pump rate the transition from the strong-coupling regime with photon antibunching to the weak-coupling regime with coherent emission. It is demonstrated how Coulomb interaction of excited carriers and excitation-induced dephasing can strongly modify the emission properties. Our theoretical investigations are based on a direct solution of the Liouville-von Neumann equation for the coupled carrier-photon system. We include multiple carrier excitations in the quantum dot, their Coulomb interaction, as well as excitation-induced dephasing and screening. Similarities and differences to atomic systems are discussed and results in the regime of recent experiments are interpreted.

OCIS Codes
(270.5290) Quantum optics : Photon statistics
(130.3990) Integrated optics : Micro-optical devices
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Optoelectronics

History
Original Manuscript: January 20, 2010
Revised Manuscript: March 12, 2010
Manuscript Accepted: March 25, 2010
Published: April 27, 2010

Citation
S. Ritter, P. Gartner, C. Gies, and F. Jahnke, "Emission properties and photon statistics of a single quantum dot laser," Opt. Express 18, 9909-9921 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-10-9909

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References

D. Meschede, H. Walter, and G. Muller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985). [CrossRef] [PubMed]
K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: A laser with one atome in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994). [CrossRef] [PubMed]
J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, "Experimental realization of a one-atom laser in the regime of strong coupling," Nature 425, 268-271 (2003). [CrossRef] [PubMed]
H. Carmichael and L. A. Orozco, "Quantum optics: Single atom lases orderly light," Nature 425, 246-247 (2003). [CrossRef] [PubMed]
O. Benson and Y. Yamamoto, "Master-equation model of a single-quantum-dot microsphere laser," Phys. Rev. A 59, 4756-4763 (1999). [CrossRef]
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] [PubMed]
M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, "Efficient source of single photons: A single quantum dot in a micropost microcavity," Phys. Rev. Lett. 89, 233602 (2002). [CrossRef] [PubMed]
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] [PubMed]
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] [PubMed]
J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H.M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, "Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing," Phys. Rev. B 72, 193303 (2005). [CrossRef]
S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. M¨unch, A. L¨offler, M. Kamp, J. P. Reithmaier, V. D. Kulakovskii, and A. Forchel, "Lasing in high-q quantum-dot micropillar cavities," Appl. Phys. Lett. 89, 051107 (2006). [CrossRef]
S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Brouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers," Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]
S. M. Ulrich, C. Gies, J. Wiersig, S. Reitzenstein, C. Hofmann, A. L¨offler, A. Forchel, F. Jahnke, and P. Michler, "Photon statistics of semiconductor microcavity lasers," Phys. Rev. Lett. 98, 043906 (2007). [CrossRef] [PubMed]
Z. G. Xie, S. Gotzinger, W. Fang, H. Cao, and G. S. Solomon, "Influence of a single quantum dot state on the characteristics of a microdisk laser," Phys. Rev. Lett. 98, 117401 (2007). [CrossRef] [PubMed]
S. Reitzenstein, C. B¨ockler, A. Bazhenov, A. Gorbunov, A. Loffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, "Single quantum dot controlled lasing effects inhigh-q micropillar cavities," Opt. Express 16, 4848-4857 (2008). [CrossRef] [PubMed]
M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Photonic crystal nanocavity laser with a single quantum dot gain," Opt. Express 17, 15975-15982 (2009). [CrossRef] [PubMed]
Y. Mu and C. M. Savage, "One-atom lasers," Phys. Rev. A 46, 5944-5954 (1992). [CrossRef] [PubMed]
A. Wojs, P. Hawrylak, S. Fafard, and L. Jacak, "Electronic structure and magneto-optics of self-assembled quantum dots," Phys. Rev. B 54, 5604-5608 (1996). [CrossRef]
H. Kurtze, J. Seebeck, P. Gartner, D. R. Yakovlev, D. Reuter, A. D. Wieck, M. Bayer, and F. Jahnke, "Carrier relaxation dynamics in self-assembled semiconductor quantum dots," Phys. Rev. B 80, 235319 (2009). [CrossRef]
P. Hawrylak, "Excitonic artificial atoms: Engineering optical properties of quantum dots," Phys. Rev. B 60, 5597-5608 (1999). [CrossRef]
N. Baer, P. Gartner, and F. Jahnke, "Coulomb effects in semiconductor quantum dots," Eur. Phys. J. B 42, 231-237 (2004). [CrossRef]
S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Loffler, S. Hofling, A. Forchel, and P. Michler, "Non-resonant dotcavity coupling and its potential for resonant single-quantum-dot spectroscopy," Nat. Photonics 3, 724-728 (2009). [CrossRef]
E. Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, "Two-photon lasing by a single quantum dot in a high- q microcavity," Phys. Rev. B 81, 035302 (2010). [CrossRef]
H. J. Carmichael, Statistical Methods in Quantum Optics 1, (Springer, Berlin, 1998).
T. Pellizzari and H. Ritsch, "Photon statistics of the three-level one-atom laser," J. Modern Opt. 41, 609-623 (1994). [CrossRef]
A. D. Boozer, A. Boca, J. R. Buck, J. McKeever, and H. J. Kimble, "Comparison of theory and experiment for a one-atom laser in a regime of strong coupling," Phys. Rev. A 70, 023814 (2004). [CrossRef]
J. I. Perea, D. Porras, and C. Tejedor, "Dynamics of the excitations of a quantum dot in a microcavity," Phys. Rev. B 70, 115304 (2004). [CrossRef]
P. R. Rice and H. J. Carmichael, "Photon statistics of cavity-QED lasers," Phys. Rev. A 50, 4318-4329 (1994). [CrossRef] [PubMed]
W. A. Hugel, M. F. Heinrich, and M. Wegener, "Dephasing due to carrier-carrier scattering in 2d," Phys. Stat. Sol.(b) 221, 473-476 (2000). [CrossRef]
H. Haug, "Coulomb quantum kinetics for semiconductor femtosecond spectroscopy," Phys. Stat. Sol.(b) 221, 179-188 (2000). [CrossRef]
M. Lorke, J. Seebeck, T. R. Nielsen, P. Gartner, and F. Jahnke, "Excitation dependence of the homogeneous linewidths in quantum dots," Phys. Stat. Sol. (c) 3, 2393-2396 (2006). [CrossRef]
M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.6Ga0.4As/GaAs self-assembled quantum dots," Phys. Rev. B 65, 041308(R) (2002). [CrossRef]
M. Lorke, T. R. Nielsen, J. Seebeck, P. Gartner, and F. Jahnke, "Influence of carrier-carrier and electron-phonon correlations on optical absorption and gain in quantum-dot systems," Phys. Rev. B 73, 085324 (2006). [CrossRef]

An, K.
Andreani, L. C.
Arakawa, Y.
Ates, S.
B¨ockler, C.
Badolato, A.
Baer, N.
Bayer, M.
Bazhenov, A.
Becher, C.
Benson, O.
Boca, A.
Boozer, A. D.
Brouwmeester, D.
Buck, J. R.
Cao, H.
Carmichael, H.
Carmichael, H. J.
Childs, J. J.
Choi, Y.-S.
Christenson, C.
Dasari, R. R.
Deppe, D. G.
Ell, C.
Fafard, S.
Fang, W.
Feld, M. S.
Forchel, A.
Gartner, P.
Gibbs, H. M.
Gibbs, H.M.
Gies, C.
Gonzalez-Tudela, A.
Gorbunov, A.
Gotzinger, S.
Haug, H.
Hawrylak, P.
Heinrich, M. F.
Hendrickson, J.
Hennessy, K.
Hofling, S.
Hofmann, C.
Hu, E.
Hu, E. L.
Hugel, W. A.
Imamoglu, A.
Iwamoto, S.
Jacak, L.
Jahnke, F.
Kamp, M.
Keldysh, L. V.
Khitrova, G.
Kimble, H. J.
Kiraz, A.
Kuhn, S.
Kulakovskii, V. D.
Kumagai, N.
Kurtze, H.
L¨offler, A.
Lam, D.
Laussy, F. P.
Loffler, A.
Lorke, M.
M¨unch, S.
McKeever, J.
Meschede, D.
Michler, P.
Morigi, G.
Mosor, S.
Mu, Y.
Muller, G.
Nielsen, T. R.
Nomura, M.
Orozco, L. A.
Ota, Y.
Pellizzari, T.
Pelton, M.
Perea, J. I.
Petroff, P. M.
Petroff, P.M.
Plant, J.
Porras, D.
Rakher, M. T.
Reinecke, T. L.
Reithmaier, J. P.
Reitzenstein, S.
Reuter, D.
Rice, P. R.
Richards, B. C.
Ritsch, H.
Rupper, G.
Santori, C.
Savage, C. M.
Scherer, A.
Schoenfeld, W. V.
Seebeck, J.
Sek, G.
Shchekin, O. B.
Solomon, G. S.
Strauf, S.
Sweet, J.
Tejedor, C.
Ulhaq, A.
Ulrich, S. M.
Valle, E.
Vuckovic, J.
Walter, H.
Wegener, M.
Wieck, A. D.
Wiersig, J.
Wojs, A.
Xie, Z. G.
Yakovlev, D. R.
Yamamoto, Y.
Yoshie, T.
Zhang, B.
Zhang, L.
Zippilli, S.

Appl. Phys. Lett.

S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. M¨unch, A. L¨offler, M. Kamp, J. P. Reithmaier, V. D. Kulakovskii, and A. Forchel, "Lasing in high-q quantum-dot micropillar cavities," Appl. Phys. Lett. 89, 051107 (2006). [CrossRef]

Eur. Phys. J. B

N. Baer, P. Gartner, and F. Jahnke, "Coulomb effects in semiconductor quantum dots," Eur. Phys. J. B 42, 231-237 (2004). [CrossRef]

J. Modern Opt.

T. Pellizzari and H. Ritsch, "Photon statistics of the three-level one-atom laser," J. Modern Opt. 41, 609-623 (1994). [CrossRef]

Nat. Photonics

S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Loffler, S. Hofling, A. Forchel, and P. Michler, "Non-resonant dotcavity coupling and its potential for resonant single-quantum-dot spectroscopy," Nat. Photonics 3, 724-728 (2009). [CrossRef]

Nature

J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, "Experimental realization of a one-atom laser in the regime of strong coupling," Nature 425, 268-271 (2003). [CrossRef] [PubMed]
H. Carmichael and L. A. Orozco, "Quantum optics: Single atom lases orderly light," Nature 425, 246-247 (2003). [CrossRef] [PubMed]
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] [PubMed]
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] [PubMed]

Opt. Express

Phys. Rev. A

Y. Mu and C. M. Savage, "One-atom lasers," Phys. Rev. A 46, 5944-5954 (1992). [CrossRef] [PubMed]
O. Benson and Y. Yamamoto, "Master-equation model of a single-quantum-dot microsphere laser," Phys. Rev. A 59, 4756-4763 (1999). [CrossRef]
P. R. Rice and H. J. Carmichael, "Photon statistics of cavity-QED lasers," Phys. Rev. A 50, 4318-4329 (1994). [CrossRef] [PubMed]
A. D. Boozer, A. Boca, J. R. Buck, J. McKeever, and H. J. Kimble, "Comparison of theory and experiment for a one-atom laser in a regime of strong coupling," Phys. Rev. A 70, 023814 (2004). [CrossRef]

Phys. Rev. B

J. I. Perea, D. Porras, and C. Tejedor, "Dynamics of the excitations of a quantum dot in a microcavity," Phys. Rev. B 70, 115304 (2004). [CrossRef]
M. Lorke, T. R. Nielsen, J. Seebeck, P. Gartner, and F. Jahnke, "Influence of carrier-carrier and electron-phonon correlations on optical absorption and gain in quantum-dot systems," Phys. Rev. B 73, 085324 (2006). [CrossRef]
E. Valle, S. Zippilli, F. P. Laussy, A. Gonzalez-Tudela, G. Morigi, and C. Tejedor, "Two-photon lasing by a single quantum dot in a high- q microcavity," Phys. Rev. B 81, 035302 (2010). [CrossRef]
J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H.M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, "Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing," Phys. Rev. B 72, 193303 (2005). [CrossRef]
A. Wojs, P. Hawrylak, S. Fafard, and L. Jacak, "Electronic structure and magneto-optics of self-assembled quantum dots," Phys. Rev. B 54, 5604-5608 (1996). [CrossRef]
H. Kurtze, J. Seebeck, P. Gartner, D. R. Yakovlev, D. Reuter, A. D. Wieck, M. Bayer, and F. Jahnke, "Carrier relaxation dynamics in self-assembled semiconductor quantum dots," Phys. Rev. B 80, 235319 (2009). [CrossRef]
P. Hawrylak, "Excitonic artificial atoms: Engineering optical properties of quantum dots," Phys. Rev. B 60, 5597-5608 (1999). [CrossRef]

Phys. Rev. Lett.

S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Brouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers," Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]
S. M. Ulrich, C. Gies, J. Wiersig, S. Reitzenstein, C. Hofmann, A. L¨offler, A. Forchel, F. Jahnke, and P. Michler, "Photon statistics of semiconductor microcavity lasers," Phys. Rev. Lett. 98, 043906 (2007). [CrossRef] [PubMed]
Z. G. Xie, S. Gotzinger, W. Fang, H. Cao, and G. S. Solomon, "Influence of a single quantum dot state on the characteristics of a microdisk laser," Phys. Rev. Lett. 98, 117401 (2007). [CrossRef] [PubMed]
D. Meschede, H. Walter, and G. Muller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985). [CrossRef] [PubMed]
K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: A laser with one atome in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994). [CrossRef] [PubMed]
M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, "Efficient source of single photons: A single quantum dot in a micropost microcavity," Phys. Rev. Lett. 89, 233602 (2002). [CrossRef] [PubMed]

Phys. Stat. Sol.

W. A. Hugel, M. F. Heinrich, and M. Wegener, "Dephasing due to carrier-carrier scattering in 2d," Phys. Stat. Sol.(b) 221, 473-476 (2000). [CrossRef]
H. Haug, "Coulomb quantum kinetics for semiconductor femtosecond spectroscopy," Phys. Stat. Sol.(b) 221, 179-188 (2000). [CrossRef]
M. Lorke, J. Seebeck, T. R. Nielsen, P. Gartner, and F. Jahnke, "Excitation dependence of the homogeneous linewidths in quantum dots," Phys. Stat. Sol. (c) 3, 2393-2396 (2006). [CrossRef]

Science

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] [PubMed]

Other

M. Bayer and A. Forchel, "Temperature dependence of the exciton homogeneous linewidth in In0.6Ga0.4As/GaAs self-assembled quantum dots," Phys. Rev. B 65, 041308(R) (2002). [CrossRef]
H. J. Carmichael, Statistical Methods in Quantum Optics 1, (Springer, Berlin, 1998).

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[1] D. Meschede, H. Walter, and G. Muller, "One-atom maser," Phys. Rev. Lett. 54, 551-554 (1985). [CrossRef] [PubMed]

[2] K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, "Microlaser: A laser with one atome in an optical resonator," Phys. Rev. Lett. 73, 3375-3378 (1994). [CrossRef] [PubMed]

[3] J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, "Experimental realization of a one-atom laser in the regime of strong coupling," Nature 425, 268-271 (2003). [CrossRef] [PubMed]

[4] H. Carmichael and L. A. Orozco, "Quantum optics: Single atom lases orderly light," Nature 425, 246-247 (2003). [CrossRef] [PubMed]

[5] O. Benson and Y. Yamamoto, "Master-equation model of a single-quantum-dot microsphere laser," Phys. Rev. A 59, 4756-4763 (1999). [CrossRef]

[6] 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] [PubMed]

[7] M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, "Efficient source of single photons: A single quantum dot in a micropost microcavity," Phys. Rev. Lett. 89, 233602 (2002). [CrossRef] [PubMed]

[8] 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] [PubMed]

[9] 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] [PubMed]

[10] J. Hendrickson, B. C. Richards, J. Sweet, S. Mosor, C. Christenson, D. Lam, G. Khitrova, H.M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, "Quantum dot photonic-crystal-slab nanocavities: Quality factors and lasing," Phys. Rev. B 72, 193303 (2005). [CrossRef]

[11] S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. M¨unch, A. L¨offler, M. Kamp, J. P. Reithmaier, V. D. Kulakovskii, and A. Forchel, "Lasing in high-q quantum-dot micropillar cavities," Appl. Phys. Lett. 89, 051107 (2006). [CrossRef]

[12] S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Brouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers," Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]

[13] S. M. Ulrich, C. Gies, J. Wiersig, S. Reitzenstein, C. Hofmann, A. L¨offler, A. Forchel, F. Jahnke, and P. Michler, "Photon statistics of semiconductor microcavity lasers," Phys. Rev. Lett. 98, 043906 (2007). [CrossRef] [PubMed]

[14] Z. G. Xie, S. Gotzinger, W. Fang, H. Cao, and G. S. Solomon, "Influence of a single quantum dot state on the characteristics of a microdisk laser," Phys. Rev. Lett. 98, 117401 (2007). [CrossRef] [PubMed]

[15] S. Reitzenstein, C. B¨ockler, A. Bazhenov, A. Gorbunov, A. Loffler, M. Kamp, V. D. Kulakovskii, and A. Forchel, "Single quantum dot controlled lasing effects inhigh-q micropillar cavities," Opt. Express 16, 4848-4857 (2008). [CrossRef] [PubMed]

[16] M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, "Photonic crystal nanocavity laser with a single quantum dot gain," Opt. Express 17, 15975-15982 (2009). [CrossRef] [PubMed]

[17] Y. Mu and C. M. Savage, "One-atom lasers," Phys. Rev. A 46, 5944-5954 (1992). [CrossRef] [PubMed]

[18] A. Wojs, P. Hawrylak, S. Fafard, and L. Jacak, "Electronic structure and magneto-optics of self-assembled quantum dots," Phys. Rev. B 54, 5604-5608 (1996). [CrossRef]

[19] H. Kurtze, J. Seebeck, P. Gartner, D. R. Yakovlev, D. Reuter, A. D. Wieck, M. Bayer, and F. Jahnke, "Carrier relaxation dynamics in self-assembled semiconductor quantum dots," Phys. Rev. B 80, 235319 (2009). [CrossRef]

[20] P. Hawrylak, "Excitonic artificial atoms: Engineering optical properties of quantum dots," Phys. Rev. B 60, 5597-5608 (1999). [CrossRef]

[21] N. Baer, P. Gartner, and F. Jahnke, "Coulomb effects in semiconductor quantum dots," Eur. Phys. J. B 42, 231-237 (2004). [CrossRef]

[22] S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Loffler, S. Hofling, A. Forchel, and P. Michler, "Non-resonant dotcavity coupling and its potential for resonant single-quantum-dot spectroscopy," Nat. Photonics 3, 724-728 (2009). [CrossRef]

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

[24] H. J. Carmichael, Statistical Methods in Quantum Optics 1, (Springer, Berlin, 1998).

[25] T. Pellizzari and H. Ritsch, "Photon statistics of the three-level one-atom laser," J. Modern Opt. 41, 609-623 (1994). [CrossRef]

[26] A. D. Boozer, A. Boca, J. R. Buck, J. McKeever, and H. J. Kimble, "Comparison of theory and experiment for a one-atom laser in a regime of strong coupling," Phys. Rev. A 70, 023814 (2004). [CrossRef]

[27] J. I. Perea, D. Porras, and C. Tejedor, "Dynamics of the excitations of a quantum dot in a microcavity," Phys. Rev. B 70, 115304 (2004). [CrossRef]

[28] P. R. Rice and H. J. Carmichael, "Photon statistics of cavity-QED lasers," Phys. Rev. A 50, 4318-4329 (1994). [CrossRef] [PubMed]

[29] W. A. Hugel, M. F. Heinrich, and M. Wegener, "Dephasing due to carrier-carrier scattering in 2d," Phys. Stat. Sol.(b) 221, 473-476 (2000). [CrossRef]

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