Abstract

We report an experimental study of the spontaneous spatial and temporal coherence of polariton condensates generated in the optical parametric oscillator configuration, below and at the parametric threshold, and as a function of condensate area. Above the threshold we obtain very long coherence times (up to 3 ns) and a spatial coherence extending over the entire condensate (40μm). The very long coherence time and its dependence on condensate area and pump power reflect the suppression of polariton-polariton interactions by an effect equivalent to motional narrowing.

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  1. Physics of Semiconductor Microcavities, ed. B. Deveuad, (Wiley-VCH, Berlin, 2007).
  2. O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Phys. Rev.104, 576–584 (1956).
    [CrossRef]
  3. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
    [CrossRef] [PubMed]
  4. E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
    [CrossRef]
  5. L. Pitaevskii and S. Stringari, Bose-Einstein condensation(Oxford University Press, Oxford, 2003).
  6. F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
    [CrossRef]
  7. K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
    [CrossRef] [PubMed]
  8. A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
    [CrossRef]
  9. R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
    [CrossRef] [PubMed]
  10. J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
    [CrossRef]
  11. A. I. Tartakovskii, D. N. Krizhanovskii, and V. D. Kulakovskii, “Polariton-polariton scattering in semiconductor microcavities: Distinctive features and similarities to the three-dimensional case,” Phys. Rev. B62, R13298–13301 (2000).
    [CrossRef]
  12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005).
    [CrossRef]
  13. In this work we consider two kinds of threshold, associated with tuning the pump energy and power. They are denoted EThand PThrespectively.
  14. D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett.87, 27002 (2009).
    [CrossRef]
  15. F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A62, 063809 (2000).
    [CrossRef]
  16. D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B67, 161310(R)(2003).
    [CrossRef]
  17. D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
    [CrossRef] [PubMed]
  18. F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
    [CrossRef]
  19. A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
    [CrossRef]
  20. D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
    [CrossRef]
  21. H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
    [CrossRef] [PubMed]
  22. H. P. Baltes, “Coherence and the radiation laws,” Appl. Phys.12, 221–244 (1977).
    [CrossRef]
  23. M. Richard, M. Wouters, and L. S. Dang, in Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures, NanoScience and Technology 146, eds. G. Slavcheva and P. Roussignol, (Springer-VerlagBerlin2010) Chap. 11 .
  24. The detuning δis defined as the difference between the bare cavity and exciton energies.
  25. A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
    [CrossRef] [PubMed]
  26. A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
    [CrossRef] [PubMed]
  27. M. Wouters and I. Carusotto, “Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A76, 043807 (2007).
    [CrossRef]
  28. P. R. Eastham and P. B. Littlewood, “Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity,” Phys. Rev. B73, 085306 (2006).
    [CrossRef]
  29. P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B78, 035319 (2008).
    [CrossRef]

2010

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
[CrossRef] [PubMed]

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

2009

D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett.87, 27002 (2009).
[CrossRef]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

2008

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B78, 035319 (2008).
[CrossRef]

2007

M. Wouters and I. Carusotto, “Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A76, 043807 (2007).
[CrossRef]

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

2006

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
[CrossRef]

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

P. R. Eastham and P. B. Littlewood, “Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity,” Phys. Rev. B73, 085306 (2006).
[CrossRef]

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

2005

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005).
[CrossRef]

2004

F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
[CrossRef]

2003

D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B67, 161310(R)(2003).
[CrossRef]

2000

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A62, 063809 (2000).
[CrossRef]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

A. I. Tartakovskii, D. N. Krizhanovskii, and V. D. Kulakovskii, “Polariton-polariton scattering in semiconductor microcavities: Distinctive features and similarities to the three-dimensional case,” Phys. Rev. B62, R13298–13301 (2000).
[CrossRef]

1977

H. P. Baltes, “Coherence and the radiation laws,” Appl. Phys.12, 221–244 (1977).
[CrossRef]

1956

O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Phys. Rev.104, 576–584 (1956).
[CrossRef]

Adrados, C.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

Al Rizeiqi, S.

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

Amo, A.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

André, R.

K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Astratov, V. N.

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

Baas, A.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

Baltes, H. P.

H. P. Baltes, “Coherence and the radiation laws,” Appl. Phys.12, 221–244 (1977).
[CrossRef]

Baumberg, J. J.

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

Berthelot, A.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Bigenwald, P.

F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
[CrossRef]

Bloch, J.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Bouchekioua, R.

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

Bradley, R.

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

Bradley, R. A.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

Bramati, A.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

Carusotto, I.

M. Wouters and I. Carusotto, “Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A76, 043807 (2007).
[CrossRef]

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005).
[CrossRef]

Cassabois, G.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Ciuti, C.

I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005).
[CrossRef]

Dang, L. S.

M. Richard, M. Wouters, and L. S. Dang, in Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures, NanoScience and Technology 146, eds. G. Slavcheva and P. Roussignol, (Springer-VerlagBerlin2010) Chap. 11 .

Dang, Le Si

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Delalande, C.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Deng, H.

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

Deveaud, B.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Deveaud-Plédran, B.

K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

Eastham, P. R.

D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett.87, 27002 (2009).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

P. R. Eastham and P. B. Littlewood, “Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity,” Phys. Rev. B73, 085306 (2006).
[CrossRef]

Eastham, P.R.

P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B78, 035319 (2008).
[CrossRef]

Emam-Ismail, M.

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

Favero, I.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Ferreira, R.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Ferrier, L.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Gérard, J. M.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Giacobino, E.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

Grousson, R.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Guda, K.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

Hey, R.

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

Houdré, R.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

Jeambrun, P.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Johne, R.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Karr, J.-Ph.

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

Kasprzak, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Kavokin, A.

F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
[CrossRef]

F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
[CrossRef]

Kavokin, A. V.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Keeling, J. M. J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Krizhanovskii, D. N.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

A. I. Tartakovskii, D. N. Krizhanovskii, and V. D. Kulakovskii, “Polariton-polariton scattering in semiconductor microcavities: Distinctive features and similarities to the three-dimensional case,” Phys. Rev. B62, R13298–13301 (2000).
[CrossRef]

Kulakovskii, V. D.

A. I. Tartakovskii, D. N. Krizhanovskii, and V. D. Kulakovskii, “Polariton-polariton scattering in semiconductor microcavities: Distinctive features and similarities to the three-dimensional case,” Phys. Rev. B62, R13298–13301 (2000).
[CrossRef]

Kundermann, S.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Lagoudakis, K. G.

K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

Laussy, F. P.

F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
[CrossRef]

F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
[CrossRef]

Lemaitre, A.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Liew, T. C. H.

A. Amo, T. C. H. Liew, C. Adrados, R. Houdré, E. Giacobino, A. V. Kavokin, and A. Bramati, “Exciton-polariton spin switches,” Nat. Photonics4, 361–366 (2010).
[CrossRef]

Littlewood, P. B.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

P. R. Eastham and P. B. Littlewood, “Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity,” Phys. Rev. B73, 085306 (2006).
[CrossRef]

Love, A. P. D.

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

Malpuech, G.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
[CrossRef]

F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004).
[CrossRef]

Marchetti, F. M.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Onsager, L.

O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Phys. Rev.104, 576–584 (1956).
[CrossRef]

Penrose, O.

O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Phys. Rev.104, 576–584 (1956).
[CrossRef]

Pietka, B.

K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, “Coherent Oscillations in an Exciton-Polariton Josephson Junction,” Phys. Rev. Lett.105, 120403 (2010).
[CrossRef] [PubMed]

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

Pitaevskii, L.

L. Pitaevskii and S. Stringari, Bose-Einstein condensation(Oxford University Press, Oxford, 2003).

Ploog, K. H.

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

Porras, D.

D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B67, 161310(R)(2003).
[CrossRef]

Richard, M.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

M. Richard, M. Wouters, and L. S. Dang, in Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures, NanoScience and Technology 146, eds. G. Slavcheva and P. Roussignol, (Springer-VerlagBerlin2010) Chap. 11 .

Roberts, J. S.

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

Romanelli, M.

A. Baas, J.-Ph. Karr, M. Romanelli, A. Bramati, and E. Giacobino, “Quantum Degeneracy of Microcavity Polaritons,” Phys. Rev. Lett.96, 176401 (2006).
[CrossRef] [PubMed]

Roussignol, Ph.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
[CrossRef]

Sagnes, I.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Sanvitto, D.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

Savona, V.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Savvidis, P. G.

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

Senellart, P.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Shelykh, I. A.

F. P. Laussy, I. A. Shelykh, G. Malpuech, and A. Kavokin, “Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light,” Phys. Rev. B73, 035315 (2006).
[CrossRef]

Skolnick, M. S.

D. N. Krizhanovskii, K. G. Lagoudakis, M. Wouters, B. Pietka, R. A. Bradley, K. Guda, D. M. Whittaker, M. S. Skolnick, B. Deveaud-Plédran, M. Richard, R. André, and Le Si Dang, “Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities,” Phys. Rev. B80, 045317 (2009).
[CrossRef]

A. P. D. Love, D. N. Krizhanovskii, D. M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R. Bradley, M. S. Skolnick, P. R. Eastham, R. André, and Le Si Dang, “Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate,” Phys. Rev. Lett.101, 067404 (2008).
[CrossRef] [PubMed]

D. N. Krizhanovskii, D. Sanvitto, A. P. D. Love, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Dominant Effect of Polariton-Polariton Interactions on the Coherence of the Microcavity Optical Parametric Oscillator,” Phys. Rev. Lett.97, 097402 (2006).
[CrossRef] [PubMed]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

Solnyshkov, D. D.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaitre, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nature Phys.6, 860–864 (2010).
[CrossRef]

Solomon, G. S.

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

Staehli, J. L.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Stevenson, R. M.

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

Stringari, S.

L. Pitaevskii and S. Stringari, Bose-Einstein condensation(Oxford University Press, Oxford, 2003).

Szymanska, M. H.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, “Bose-Einstein condensation of exciton polaritons,” Nature443, 409–414 (2006).
[CrossRef] [PubMed]

Tartakovskii, A. I.

A. I. Tartakovskii, D. N. Krizhanovskii, and V. D. Kulakovskii, “Polariton-polariton scattering in semiconductor microcavities: Distinctive features and similarities to the three-dimensional case,” Phys. Rev. B62, R13298–13301 (2000).
[CrossRef]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
[CrossRef] [PubMed]

J. J. Baumberg, P. G. Savvidis, R. M. Stevenson, A. I. Tartakovskii, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical parametric oscillation,” Phys. Rev. B62, R16247–16250 (2000).
[CrossRef]

Tassone, F.

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A62, 063809 (2000).
[CrossRef]

Tejedor, C.

D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B67, 161310(R)(2003).
[CrossRef]

Voisin, C.

A. Berthelot, I. Favero, G. Cassabois, C. Voisin, C. Delalande, Ph. Roussignol, R. Ferreira, and J. M. Gérard, “Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot,” Nat. Phys.2, 759–764 (2006).
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[CrossRef] [PubMed]

R. M. Stevenson, V. N. Astratov, M. S. Skolnick, D. M. Whittaker, M. Emam-Ismail, A. I. Tartakovskii, P. G. Savvidis, J. J. Baumberg, and J. S. Roberts, “Continuous wave observation of massive polariton redistribution by stimulated scattering in semiconductor microcavities,” Phys. Rev. Lett.85, 3680–3683 (2000).
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[CrossRef]

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[CrossRef] [PubMed]

H. Deng, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial Coherence of a Polariton Condensate,” Phys. Rev. Lett.99, 126403 (2007).
[CrossRef] [PubMed]

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Other

M. Richard, M. Wouters, and L. S. Dang, in Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures, NanoScience and Technology 146, eds. G. Slavcheva and P. Roussignol, (Springer-VerlagBerlin2010) Chap. 11 .

The detuning δis defined as the difference between the bare cavity and exciton energies.

Physics of Semiconductor Microcavities, ed. B. Deveuad, (Wiley-VCH, Berlin, 2007).

L. Pitaevskii and S. Stringari, Bose-Einstein condensation(Oxford University Press, Oxford, 2003).

In this work we consider two kinds of threshold, associated with tuning the pump energy and power. They are denoted EThand PThrespectively.

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Figures (4)

Fig. 1
Fig. 1

Interference pattern (a/d) and corresponding coherence (b/e) of the condensate generated at/below the parametric threshold, ETh, corresponding to a pump energy E1 = 1552.574 meV/ E2 = 1552.567 meV and power density P = 15.8kW/cm2. Horizontal profiles at the center (c/f) showing the constant coherence along the entire condensate for E1, and an exponentially decaying one for E2.The red line is the Lorentzian fit.

Fig. 2
Fig. 2

Coherence length Lc as a function of the energy distance from the threshold δEEThE. Red line is a guide to the eye.

Fig. 3
Fig. 3

(a) Temporal coherence decay above parametric threshold for condensate area 2.7 × 103μm2 at a pump power density Pd = 10kW/cm2, the central line is a fit to Eq. (1), side bands define the confidence range in which the experimental points fall within a probability of 95%. (b) Temporal coherence decay for Pd = 5.4kW/cm2 (black squares) and 10kW/cm2 (blue dots) at A = 70μm2. Lines are fits to Eq. (1); (c) τc as a function of the condensate area A, the line is a fit to τcAx, with x = 0.41 ± 0.05; (d) τr as a function of condensate area A, the line is a fit to τrAx with x = 0.41 ± 0.17.

Fig. 4
Fig. 4

Temporal coherence Tc as obtained from Eq. (2) as a function of the condensate area A. Red solid line is a fit to square root dependence on area A, dashed line corresponds to the best fit to a linear dependence.

Equations (2)

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| g ( 1 ) ( τ ) | = exp [ 2 τ r 2 τ c 2 ( e τ / τ r + τ τ r 1 ) ] ,
| g ( 1 ) ( τ ) | = exp [ τ r T c ( e τ / τ r + τ τ r 1 ) ] .

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