Coexisting Polariton Condensates and Their Temporal Coherence in Semiconductor Microcavities

  • D. N. Krizhanovskii
  • David M. Whittaker
  • M. S. Skolnick
  • K. G. Lagoudakis
  • M. Wouters
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 172)


In this chapter, we study macroscopically occupied condensates, which can be observed in semiconductor microcavities under conditions of resonant or non-resonant excitation. In the case of resonant excitation, polariton condensates form due to optical parametric oscillation (OPO) and are strongly non-equilibrium states. In case of non-resonantly incoherently pumped system, the distribution of the higher energy polaritons shows some thermalisation, but the resultant polariton condensates are also far from thermodynamic equilibrium due to finite polariton lifetime. In this chapter, we show that both systems have very similar properties. We reveal the effects of polariton–polariton interactions and non-equilibrium character on the condensate properties. Above threshold condensation into several polariton levels with different energies and k-vectors is observed, which arises from the non-equilibrium character of the polariton system. The specific k-vectors at which condensation is triggered are determined by the local disorder potential landscape. We also investigate the coherence of a single condensed mode by measuring the first (g (1))- and second (g (2))-order correlation functions. We find that the decay times of these functions are \(\sim 100\mbox{ \textendash }150\,\mathrm{ps}\), much longer than the 1.5 ps polariton lifetime. Even though the polariton condensate is a non-equilibrium system, the strong slowing down of the decay allows coherence decay processes characteristic of an equilibrium, interacting BEC to be observed. The signature of the interactions is a Gaussian form for the g (1)-function and a saturation of coherence time with increasing number of particles in the condensate, as observed experimentally and confirmed theoretically. Although predicted, these effects have not been observed for atom BECs.


Optical Parametric Oscillation Coherence Time Temporal Coherence Disorder Potential Polariton Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work was supported by the EU ITN Clermont 2 and Clermont 4 projects and EPSRC grants GR/S09838/01, GR/S76076/01. D. Krizhanovskii is an EPSRC Advanced Fellow (grant EP/E051448/1).


  1. [1].
    J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymanska, R. Andre, J.L. Staehli, V. Savona, P.B. Littlewood, B. Deveaud, Le Si Dang, Nature 443, 409–414 (2006)ADSCrossRefGoogle Scholar
  2. [2].
    M. Richard, J. Kasprzak, R. Andr, R. Romestain, G. Le Si Dang Malpuech, A. Kavokin, Phys. Rev. B 72, 201301 (2005)Google Scholar
  3. [3].
    R. Balili, V. Hartwell, D. Snoke, L. Pfei_er, K. West, Science 316, 1007–1010 (2007)Google Scholar
  4. [4].
    D.N. Krizhanovskii, A.P. Love, D. Sanvitto, D.M. Whittaker, M.S. Skolnick, J.S. Roberts, Phys. Rev. B 75, 233307 (2007)ADSCrossRefGoogle Scholar
  5. [5].
    S. Christopoulos, G. Baldassarri von Hogersthal, A.J. Grundy, P.G. Lagoudakis, A.V. Kavokin, J.J. Baumberg, G. Christmann, R. Butte, E. Feltin, J.-F. Carlin, N. Grandjean, Phys. Rev. Lett. 98, 126405 (2007).ADSCrossRefGoogle Scholar
  6. [6].
    G. Christmann, R. Butte, E. Feltin, J.F. Carlin, N. Grandjean, Appl. Phys. Lett. 93, 051102 (2008)ADSCrossRefGoogle Scholar
  7. [7].
    H. Deng et al., Phys. Rev. Lett. 97, 146402 (2006)ADSCrossRefGoogle Scholar
  8. [8].
    R.M. Stevenson, V.N. Astratov, M.S. Skolnick, D.M. Whittaker, M. Emam-Ismail, A.I. Tartakovskii, P.G. Savvidis, J.J. Baumberg, J.S. Roberts, Phys. Rev. Lett. 85, 3680 (2000)ADSCrossRefGoogle Scholar
  9. [9].
    M. Wouters, I. Carussoto, Phys. Rev. Lett. 99, 140402 (2007)ADSCrossRefGoogle Scholar
  10. [10].
    D.N. Krizhanovskii, D.M. Whittaker, R.A. Bradley, K. Guda, D. Sarkar, D. Sanvitto, L. Vina, E. Cerda, P. Santos, K. Biermann, R. Hey, M.S. Skolnick, Phys. Rev. Lett. 104, 126402 (2010)ADSCrossRefGoogle Scholar
  11. [11].
    M.H. Szymanska, J. Keeling, P.B. Littlewood, Phys. Rev. Lett. 96, 230602 (2006)ADSCrossRefGoogle Scholar
  12. [12].
    J. Keeling, N.G. Berlo, Phys. Rev. Lett. 100, 250401 (2008)ADSCrossRefGoogle Scholar
  13. [13].
    D. Sarchi, V. Savona, Phys. Rev. B 75, 115326 (2007)ADSCrossRefGoogle Scholar
  14. [14].
    D. Sanvitto, D.N. Krizhanovskii, D.M. Whittaker, S. Ceccarelli, M.S. Skolnick, J.S. Roberts, Phys. Rev. B 73, 241308 (2006)ADSCrossRefGoogle Scholar
  15. [15].
    D.N. Krizhanovskii, D. Sanvitto, A.P. Love, M.S. Skolnick, D.M. Whittaker, J.S. Roberts, Phys. Rev. Lett. 97, 097402 (2006)ADSCrossRefGoogle Scholar
  16. [16].
    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, Le Si Dang, Phys. Rev. Lett. 101, 067404 (2008)ADSCrossRefGoogle Scholar
  17. [17].
    K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. Andre, B. Le Si Dang Deveaud-Pledran, Nat. Phys. 4, 706 (2008)Google Scholar
  18. [18].
    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, Le Si Dang, Phys. Rev. B 80, 045317 (2009)ADSCrossRefGoogle Scholar
  19. [19].
    F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani, P. Schwendimann, Phys. Rev. B 56, 7554 (1997)ADSCrossRefGoogle Scholar
  20. [20].
    A.I. Tartakovskii, M. Emam-Ismail, R.M. Stevenson, M.S. Skolnick, V.N. Astratov, D.M. Whittaker, J.J. Baumberg, J.S. Roberts, Phys. Rev. B 62, R2283 (2000)ADSCrossRefGoogle Scholar
  21. [21].
    M. Wouters, I. Carusotto, C. Ciuti, Phys. Rev. B 77, 115340 (2008)ADSCrossRefGoogle Scholar
  22. [22].
    P.R. Eastham, Phys. Rev. B 78, 035319 (2008)ADSCrossRefGoogle Scholar
  23. [23].
    R. Loudon, The Quantum Theory of Light (Oxford University Press, Oxford, 2000)zbMATHGoogle Scholar
  24. [24].
    L.K. Thomsen, H.M. Wiseman, Phys. Rev. A 65, 063607 and reference there in (2002)Google Scholar
  25. [25].
    M. Kohl, T.W. Hansch, T. Esslinger, Phys. Rev. Lett. 87, 160404, (2001)ADSCrossRefGoogle Scholar
  26. [26].
    A. Ottl, S. Ritter, T. Esslinger, Phys. Rev. Lett. 95, 090404, (2005)ADSCrossRefGoogle Scholar
  27. [27].
    D. Bajoni, P. Senellart, E. Wertz, I. Sagnes, A. Miard, A. Lemaître, J. Bloch, Phys. Rev. Lett. 100, 047401 (2008)ADSCrossRefGoogle Scholar
  28. [28].
    M. Wouters, I. Carusotto, Phys. Rev. A 76, 043807 (2007)ADSCrossRefGoogle Scholar
  29. [29].
    E.A. Cerda-Méndez, D.N. Krizhanovskii, M. Wouters, R. Bradley, K. Biermann, K. Guda, R. Hey, P.V. Santos, D. Sarkar, M.S. Skolnick, Phys. Rev. Lett. 105, 116402 (2010)ADSCrossRefGoogle Scholar
  30. [30].
    M. Gurioli et al., Phys. Rev. Lett. 94, 183901 (2005)ADSCrossRefGoogle Scholar
  31. [31].
    D. Porras, C. Tejedor, Phys. Rev. B 67, 161310 (R) (2003)Google Scholar
  32. [32].
    D.M. Whittaker, Phys. Rev. B 71, 115301 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • D. N. Krizhanovskii
    • 1
  • David M. Whittaker
    • 1
  • M. S. Skolnick
    • 1
  • K. G. Lagoudakis
    • 2
  • M. Wouters
    • 2
  1. 1.Department of Physics and AstronomyUniversity of SheffieldSheffieldUK
  2. 2.Ecole Polytechnique Federale de Lausanne (EPFL)LausanneSwitzerland

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