Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold |
Optics Express, Vol. 21, Issue 9, pp. 10792-10800 (2013)
http://dx.doi.org/10.1364/OE.21.010792
Acrobat PDF (1008 KB)
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.
© 2013 OSA
1. Introduction
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,” Nature 443, 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] .
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. Photonics 4, 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] .
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. B 62, R13298–13301 (2000) [CrossRef] .
12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [CrossRef] .
12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [CrossRef] .
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. A 62, 063809 (2000) [CrossRef] .
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. B 73, 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. B 80, 045317 (2009) [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,” Nature 443, 409–414 (2006) [CrossRef] [PubMed] .
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. B 80, 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] .
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] .
2. Sample and experimental setup
12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [CrossRef] .
3. Results
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,” Nature 443, 409–414 (2006) [CrossRef] [PubMed] .
12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [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. B 80, 045317 (2009) [CrossRef] .
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] .
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] .
27. M. Wouters and I. Carusotto, “Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime,” Phys. Rev. A 76, 043807 (2007) [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,” Nature 443, 409–414 (2006) [CrossRef] [PubMed] .
12. I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [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] .
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. B 73, 085306 (2006) [CrossRef] .
14. D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett. 87, 27002 (2009) [CrossRef] .
14. D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett. 87, 27002 (2009) [CrossRef] .
14. D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett. 87, 27002 (2009) [CrossRef] .
29. P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B 78, 035319 (2008) [CrossRef] .
14. D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett. 87, 27002 (2009) [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. B 80, 045317 (2009) [CrossRef] .
4. Conclusions
Acknowledgments
References and links
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,” Nature 443, 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. Photonics 4, 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. B 62, 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. B 62, R13298–13301 (2000) [CrossRef] . |
12. | I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005) [CrossRef] . |
13. | In this work we consider two kinds of threshold, associated with tuning the pump energy and power. They are denoted E_{Th}and P_{Th}respectively. |
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. A 62, 063809 (2000) [CrossRef] . |
16. | D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B 67, 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. B 73, 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. B 80, 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. A 76, 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. B 73, 085306 (2006) [CrossRef] . |
29. | P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B 78, 035319 (2008) [CrossRef] . |
OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(240.5420) Optics at surfaces : Polaritons
(020.1475) Atomic and molecular physics : Bose-Einstein condensates
(100.3175) Image processing : Interferometric imaging
(140.3945) Lasers and laser optics : Microcavities
ToC Category:
Optics at Surfaces
History
Original Manuscript: February 22, 2013
Revised Manuscript: April 15, 2013
Manuscript Accepted: April 17, 2013
Published: April 25, 2013
Citation
R. Spano, J. Cuadra, C. Lingg, D. Sanvitto, M. D. Martin, P. R. Eastham, M. van der Poel, J. M. Hvam, and L. Viña, "Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold," Opt. Express 21, 10792-10800 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10792
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References
- Physics of Semiconductor Microcavities, ed. B. Deveuad, (Wiley-VCH, Berlin, 2007).
- O. Penrose and L. Onsager, “Bose-Einstein Condensation and Liquid Helium,” Phys. Rev.104, 576–584 (1956). [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]
- 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]
- L. Pitaevskii and S. Stringari, Bose-Einstein condensation(Oxford University Press, Oxford, 2003).
- F. P. Laussy, G. Malpuech, A. Kavokin, and P. Bigenwald, “Spontaneous Coherence Buildup in a Polariton Laser,” Phys. Rev. Lett.93, 016402 (2004). [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]
- 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]
- I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B72, 125335 (2005). [CrossRef]
- In this work we consider two kinds of threshold, associated with tuning the pump energy and power. They are denoted EThand PThrespectively.
- D. M. Whittaker and P. R. Eastham, “Coherence properties of the microcavity polariton condensate,” Europhys. Lett.87, 27002 (2009). [CrossRef]
- F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A62, 063809 (2000). [CrossRef]
- D. Porras and C. Tejedor, “Linewidth of a polariton laser: Theoretical analysis of self-interaction effects,” Phys. Rev. B67, 161310(R)(2003). [CrossRef]
- 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]
- 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]
- 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]
- H. P. Baltes, “Coherence and the radiation laws,” Appl. Phys.12, 221–244 (1977). [CrossRef]
- 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.
- 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]
- 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]
- 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]
- 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]
- P.R. Eastham, “Mode locking and mode competition in a nonequilibrium solid-state condensate,” Phys. Rev. B78, 035319 (2008). [CrossRef]
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