OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 2 — Feb. 1, 2012
  • pp: A138–A145

On the condensation of polaritons

Benoit Deveaud-Plédran  »View Author Affiliations


JOSA B, Vol. 29, Issue 2, pp. A138-A145 (2012)
http://dx.doi.org/10.1364/JOSAB.29.00A138


View Full Text Article

Enhanced HTML    Acrobat PDF (497 KB) Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Bose–Einstein condensates (BECs), the “fifth state of matter,” have in fact been discovered by chance both in liquid helium and in superconductors. Since these early encounters, BECs have been sought for, both in atom vapors and in solids. Here we report on the case of exciton polaritons. We discuss the experimental observation of macroscopically occupied polariton states and their possible attribution to a BEC. We also discuss the possible relation between a polariton condensate, a polariton laser, and a vertical surface-emitting laser (VCSEL). Vortices, superfluidity, Bogoliubov dispersion, half-vortices, and Josephson oscillations are then briefly summarized merrily for sake of discussion of the distinction between a polariton BEC and a VCSEL.

© 2012 Optical Society of America

OCIS Codes
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(270.6630) Quantum optics : Superradiance, superfluorescence
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
(020.1475) Atomic and molecular physics : Bose-Einstein condensates

History
Original Manuscript: October 18, 2011
Manuscript Accepted: November 23, 2011
Published: February 1, 2012

Citation
Benoit Deveaud-Plédran, "On the condensation of polaritons," J. Opt. Soc. Am. B 29, A138-A145 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-2-A138


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. Bose, “Plancks Gesetz und Lichtquantenhypothese,” Z. Phys. D 26, 178–181 (1924). [CrossRef]
  2. A. Einstein, “Quantentheorie des einatomigen idealen gases I,” Sitzungsber. Kgl. Preuss. Akad. Wiss., 1, 3–14 (1925).
  3. H. K. Onnes, “Further experiments with liquid helium. D. On the change of electric resistance of pure metals at very low temperatures, etc. V. The disappearance of the resistance of mercury,” Commun. Phys. Lab. Univ. Leiden 122b (1911).
  4. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Phys. Rev. 108, 1175–1204 (1957). [CrossRef]
  5. P. Kapitza, “Viscosity of liquid helium below the λ-point,” Nature 141, 74–75 (1938). [CrossRef]
  6. J. F. Allen and A. D. Misener, “Flow phenomena in liquid helium II,” Nature 142, 643–644 (1938). [CrossRef]
  7. F. London, “The λ-phenomenon of liquid helium and the Bose-Einstein degeneracy” Nature, 141, 643–644 (1938). [CrossRef]
  8. L. D. Landau, “Theory of the superfluidity of Helium II,” Phys. Rev. 60, 356–358 (1941). [CrossRef]
  9. N. N. Bogoliubov, “On the theory of superfluidity,” J. Phys. USSR 11, 23–32 (1947).
  10. S. A. Moskalenko, “Reversible optico-hydrodynamic phenomena in a nonideal. exciton gas,” Solid State Commun. 4, 199–204 (1962).
  11. J. M. Blatt, K. W. Böer, and W. Brandt, “Bose-Einstein condensation of excitons,” Phys. Rev. 126, 1691–1692 (1962). [CrossRef]
  12. L. V. Keldysh and A. N. Kozlov, “Collective properties of excitons on semiconductors,” Sov. Phys. JETP 27, 521–528 (1968).
  13. L. L. Chase, N. Peyghambarian, G. Grynberg, and A. Mysyrowicz, “Evidence for Bose-Einstein condensation of biexcitons in CuCl,” Phys. Rev. Lett. 42, 1231–1234 (1979). [CrossRef]
  14. D. Hulin, A. Mysyrowicz, and C. Benoit àl a Guillaume, “Evidence for Bose-Einstein statistics of an exciton gas,” Phys. Rev. Lett. 45, 1970–1973 (1980). [CrossRef]
  15. J. A. Kash, M. Zachau, E. E. Mendez, and J. M. Hong, “Fermi-Dirac distribution of excitons in coupled quantum wells,” Phys. Rev. Lett. 66, 2247–2250 (1991). [CrossRef]
  16. L. V. Butov and A. I. Filin, “Anomalous transport and luminescence of indirect excitons in AlAs/GaAs coupled quantum wells as evidence for exciton condensation,” Phys. Rev. B58, 1980–2000 (1998).
  17. L. V. Butov, C. W. Lai, A. L. Ivanov, A. C. Gossard, and D. S. Chemla, “Towards Bose–Einstein condensation of excitons in potential traps,” Nature 417, 47–52 (2002). [CrossRef]
  18. L. V. Butov, A. C. Gossard, and D. S. Chemla, “Macroscopically ordered state in an exciton system,” Nature 418, 751–754 (2002). [CrossRef]
  19. S. A. Moskalenko and D. W. Snoke, eds. Bose-Einstein Condensation of Excitons and Biexcitons and Coherent Nonlinear Optics with Excitons (Cambridge University, 2000).
  20. N. F. Mott, Metal Insulator Transitions, 2nd ed. (Taylor & Francis, 1990).
  21. L. Kappei, J. Szczytko, F. Morier-Genoud, and B. Deveaud, “Direct observation of the Mott transition in an optically excited semiconductor quantum well,” Phys. Rev. Lett. 94, 147403 (2005). [CrossRef]
  22. M. Stern, V. Garmider, V. Umansky, and I. Bar-Joseph, “Mott transition of excitons in coupled quantum wells,” Phys. Rev. Lett. 100, 256402 (2008). [CrossRef]
  23. D. Semkat, W.-D. Kraeft, G. Manzke, D. Krempe, and K. Henneberger, “Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation,” Phys. Rev. B81, 155201 (2009).
  24. V. V. Nikolaev and M. E. Portnoi, “Theory of excitonic Mott transition in double quantum wells,” Phys. Status Solidi C 1, 1357–1362 (2004). [CrossRef]
  25. D. Snoke, “Predicting the ionization threshold for carriers in excited semiconductors,” Solid State Commun. 146, 73–77 (2008). [CrossRef]
  26. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112, 1555–1567 (1958). [CrossRef]
  27. P. D. Lett, R. N. Watts, C I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988). [CrossRef]
  28. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995). [CrossRef]
  29. K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose-Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995). [CrossRef]
  30. D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543–1546 (1998). [CrossRef]
  31. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose condensates,” Science 275, 637–641 (1997). [CrossRef]
  32. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001). [CrossRef]
  33. C. Weisbuch, N. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992). [CrossRef]
  34. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon, 2003).
  35. A. Imamoglu, R. J. Ram, S. Pau, and Y. Yamamoto, “Nonequilibrium condensates and lasers without inversion: exciton-polariton lasers,” Phys. Rev. A53, 4250–4253 (1996).
  36. R. Houdre, J. L. Gibernon, P. Pellandini, R. P. Stanley, U. Oesterle, C. Weisbuch, J. O’Gorman, B. Roycroft, and M. Ilegems, “Saturation of the strong-coupling regime in a semiconductor microcavity: free-carrier bleaching of cavity polaritons,” Phys. Rev. B 52, 7810–7813 (1995). [CrossRef]
  37. P. G. Savvidis, J. J. Baumberg, R. M. Stevenson, M. S. Skolnick, D. M. Whittaker, and J. S. Roberts, “Angle-resonant stimulated polariton amplifier,” Phys. Rev. Lett. 84, 1547–1550 (2000). [CrossRef]
  38. M. Saba, C. Ciuti, J. Bloch, V. Thierry-Mieg, R. André, L. S. Dang, S. Kundermann, A. Mura, G. Bongiovanni, J. L. Staehli, and B. Deveaud, “High-temperature ultrafast polariton parametric amplification in semiconductor microcavities,” Nature, 414, 731–735 (2001). [CrossRef]
  39. G. Malpuech, A. Di Carlo, A. Kavokin, J. J. Baumberg, A. Zamfirescu, and P. Lugli, “Room-temperature polariton lasers based on GaN microcavities,” Appl. Phys. Lett. 81, 412–414 (2002). [CrossRef]
  40. J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. B. H. von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, “Spontaneous polarization buildup in a room-temperature polariton laser,” Phys. Rev. Lett. 101, 136409 (2008). [CrossRef]
  41. O. Penrose and L. Onsager, “Bose-Einstein condensation and liquid helium,” Phys. Rev. 104, 576–584 (1956). [CrossRef]
  42. L. S. Dang, H. Heger, R. André, F. Boeuf, and R. Romestain, “Stimulation of polariton photoluminescence in semiconductor microcavity,” Phys. Rev. Lett. 81, 3920–3923 (1998). [CrossRef]
  43. P. Senellart and J. Bloch, “Nonlinear emission of microcavity polaritons in the low density regime,” Phys. Rev. Lett.1233–1236 (1999). [CrossRef]
  44. J. Kasprzak, “Condensation of exciton polaritons,” PhD thesis (Université Joseph Fourier—Genoble 1, 2006).
  45. A. Amo, D. Sanvitto, F. P. Laussi, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009). [CrossRef]
  46. M. Richard,“Quasi-condensation de polaritons sous excitation incoherente dans les microcavities II-VI a base de CdTe,” PhD thesis (Université Joseph Fourier—Genoble 1, 2004).
  47. 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]
  48. P. Senellart, J. Bloch, B. Sermage, and J. Y. Marzin, “Microcavity polariton depopulation as evidence for stimulated scattering,” Phys. Rev. B63, R16263–16266 (2000).
  49. 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 (2008).
  50. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298, 199–202 (2002). [CrossRef]
  51. N. G. Vy, H. T. Cao, D. B. Tran Thoai, and H. Haug, “Time dependence of the ground-state population statistics of condensed microcavity polaritons,” Phys. Rev. B80, 195306 (2009).
  52. J. Kasprzak, M. Richard, A. Baas, B. Deveaud, R. Andre, J.-Ph. Poizat, and L. S. Dang, “Second-order time correlations within a polariton Bose-Einstein condensate in a CdTe microcavity,” Phys. Rev. Lett. 100, 067402 (2008). [CrossRef]
  53. M. Aßmann, J.-S. Tempel, F. Veit, M. Bayer, A. Rahimi-Iman, A. Löffler, S. Höfling, S. Reitzenstein, L. Worschech, and A. Forchel, “From polariton condensates to highly photonic quantum degenerate states of bosonic matter,” Proc. Natl. Acad. Sci. USA 108, 1804–1809 (2011). [CrossRef]
  54. P. Schwendimann and A. Quattropani, “Statistics of the polariton condensate,” Phys. Rev. 77, 085317 (2008). [CrossRef]
  55. 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]
  56. J. Scheuer and M. Orenstein, “Optical vortices crystals: spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999). [CrossRef]
  57. R. Ballili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007). [CrossRef]
  58. H. Deng, D. Press, S. Götzinger, G. S. Solomon, R. Hey, K. H. Ploog, and Y. Yamamoto, “Spatial coherence of a polariton condensate,” Phys. Rev. Lett. 99, 126403 (2007). [CrossRef]
  59. E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6, 860–864 (2010). [CrossRef]
  60. S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007). [CrossRef]
  61. G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, “Room temperature polariton lasing in a GaN/AlGaN multiple quantum well microcavity,” Appl. Phys. Lett. 93, 051102 (2008). [CrossRef]
  62. E. Wertz, L. Ferrier, D. D. Solnyshkov, P. Senellart, D. Bajoni, A. Miard, A. Lemaître, G. Malpuech, and J. Bloch, “Spontaneous formation of a polariton condensate in a planar GaAs microcavity,” Appl. Phys. Lett. 95, 051108 (2009). [CrossRef]
  63. D. Bajoni, P. Senellart, A. Lemaître, and J. Bloch, “Photon lasing in GaAs microcavity: similarities with a polariton condensate,” Phys. Rev. B76, 201305 (2007).
  64. M. G. A. Bernard and G. Duraffourg, “Laser conditions in semiconductors,” Phys. Status Solidi 1, 699–703 (1961). [CrossRef]
  65. S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007). [CrossRef]
  66. D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, and J. Bloch, “Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities,” Phys. Rev. Lett. 100, 047401 (2008). [CrossRef]
  67. B. Nelsen, R. Balili, D. W. Snoke, L. Pfeiffer, and K. West, “Lasing and polariton condensation: two distinct transitions in GaAs microcavities with stress traps,” J. Appl. Phys. 105, 122414 (2009). [CrossRef]
  68. S. Azzini, D. Gerace, M. Galli, I. Sagnes, R. Braive, A. Lemaître, J. Bloch, and D. Bajoni, “Ultra-low threshold polariton lasing in photonic crystal cavities,” Appl. Phys. Lett. 99, 111106 (2011). [CrossRef]
  69. H. Deng, G. Weihs, D. Snoke, J. Bloch, and Y. Yamamoto, “Polariton lasing vs. photon lasing in a semiconductor microcavity,” Proc. Natl. Acad. Sci. USA 100, 15318–15323 (2003). [CrossRef]
  70. D. Sarchi, M. Wouters, and V. Savona, “Polariton parametric photoluminescence in spatially inhomogeneous systems,” Phys. Rev., B79, 165315 (2009).
  71. Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006). [CrossRef]
  72. L. Onsager, “Statistical hydrodynamics,” Il Nuevo Cimento 6, 279–287 (1949). [CrossRef]
  73. F. Dalfovo, S. Giorgini, L. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999). [CrossRef]
  74. M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wiemann, and E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999). [CrossRef]
  75. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001). [CrossRef]
  76. K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000). [CrossRef]
  77. Y. F. Chen and Y. P. Lan, “Formation of optical vortex lattices in solid-state microchip lasers: spontaneous transverse mode locking,” Phys. Rev. A64, 063807 (2001).
  78. Y. F. Chen, K. F. Huang, H. C. Lai, and Y. P. Lan, “Observation of vector vortex lattices in polarization states of an isotropic microcavity laser,” Phys. Rev. Lett. 90, 053904 (2003). [CrossRef]
  79. K. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L. S. Dang, and B. Deveaud-Plédran, “Quantized vortices in an exciton–polariton condensate,” Nat. Phys. 4, 706–710 (2008). [CrossRef]
  80. A. Amo, J. Lefrére, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nature 457, 291–295 (2009). [CrossRef]
  81. D. Sanvitto, S. Pigeon, A. Amo, D. Ballarini, M. De Giorgi, I. Carusotto, R. Hivet, F. Pisanello, V. G. Sala, P. S. S. Guimaraes, R. Houdré, E. Giacobino, C. Ciuti, A. Bramati, and G. Gigli, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010). [CrossRef]
  82. G.E. Volovik and V. P. Mineev, “Hydrodynamics of the A phase of superfluid He3,” Sov. Phys. JETP 44, 591–599 (1976).
  83. W. F. Brinkman, “Textural singularities in the superfluid A phase of 3He,” J. Low Temp. Phys. B 26, 165–191 (1977). [CrossRef]
  84. Y. G. Rubo, “Half vortices in exciton polariton condensates,” Phys. Rev. Lett. 99, 106401 (2007). [CrossRef]
  85. K. Lagoudakis, T. Ostatnick, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009). [CrossRef]
  86. N. N. Bogoliubov, “On a new method in the theory of superconductivity,” Il Nuevo Cimento 7, 794–805 (1958). [CrossRef]
  87. J. M. Vogels, K. Xu, C. Raman, J. R. Abo-Shaeer, and W. Ketterle, “Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas,” Phys. Rev. Lett. 88, 060402 (2002). [CrossRef]
  88. V. Kohnle, Y. Léger, M. Wouters, M. Richard, M. T. Portela-Oberli, and B. Deveaud-Plédran, “From single particle to superfluid excitations in a dissipative polariton gas,” Phys. Rev. Lett. 106, 255302 (2011). [CrossRef]
  89. B. D. Josephson, “Coupled superconductors,” Rev. Mod. Phys. 36, 216–220 (1964). [CrossRef]
  90. Y. Mahklin, G. Schön, and A. Schnirman, “Quantum-state engineering with Josephson-junction devices,” Rev. Mod. Phys. 73, 357–400 (2001). [CrossRef]
  91. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev., A59, 620–633 (1999).
  92. K. 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]
  93. E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6, 860–864 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited