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Vortices in Spontaneous Bose–Einstein Condensates of Exciton–Polaritons

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 172))

Abstract

One of the most striking quantum effects in an interacting Bose gas at low temperature is superfluidity. First observed in liquid 4He, this phenomenon has been intensively studied in a variety of systems for its remarkable features such as the persistence of superflows and the proliferation of quantized vortices. The achievement of Bose–Einstein condensation in dilute atomic gases provided the opportunity to observe and study superfluidity in an extremely clean and well-controlled environment. In the solid state, Bose–Einstein condensation of exciton polaritons now allows to plan for the observation of similar phenomenology. Polaritons are interacting light–matter quasiparticles that occur naturally in semiconductor microcavities in the strong coupling regime and constitute an interesting example of composite bosons. Here, we report the observation of spontaneous formation of pinned quantized vortices in the Bose-condensed phase of a polariton fluid. Theoretical insight into the possible origin of such vortices is presented in terms of a generalized Gross–Pitaevskii equation. In the second part of the chapter, we provide the clear observation of half vortices, special to spinor condensates. We then go no, in the last part of this chapter, to study the dynamics of spontaneously created vortices. We show that their path is determined by the disorder landscape towards their final stable position.

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References

  1. C. Weisbuch et al., Phys. Rev. Lett. (1992)

    Google Scholar 

  2. J.J. Hopfield, Phys. Rev. (1958)

    Google Scholar 

  3. R.H. Houdre et al., Phys. Rev. Lett. 73, 2043 (1994)

    Article  ADS  Google Scholar 

  4. V. Savona et al., Phys. Rev. B 49, 8774 (1994)

    Article  ADS  Google Scholar 

  5. A. Imamoglu et al., Phys. Rev. A 53, 4250 (1996)

    Article  ADS  Google Scholar 

  6. J.M. Blatt, Phys. Rev. 126, 1691 (1962)

    Article  ADS  Google Scholar 

  7. S.A. Moskalenko, Soviet Phys. Solid State 4, 199 (1962)

    Google Scholar 

  8. R.H. Houdré et al., Phys. Rev. B 52, 7810 (1995)

    Article  ADS  Google Scholar 

  9. S. Pau et al., Phys. Rev. A54, R1789 (1996)

    ADS  Google Scholar 

  10. L.S. Dang et al., Phys. Rev. Lett. 81, 3920 (1998)

    Article  ADS  Google Scholar 

  11. P. Senellart et al., Phys. Rev. Lett. 82, 1233 (1999)

    Article  ADS  Google Scholar 

  12. P.G. Savvidis et al., Phys. Rev. Lett. 84, 1547 (2000)

    Article  ADS  Google Scholar 

  13. M. Saba et al., Nature 414, 6865 (2001)

    Article  Google Scholar 

  14. M. Richard et al., Phys. Rev. Lett. 94, 187401 (2005)

    Article  ADS  Google Scholar 

  15. J. Kasprzak et al., Nature 443, 7110 (2006)

    Article  Google Scholar 

  16. M. Richard, J. Kasprzak, R. André et al., Phys. Rev. B 72, 201301 (2005)

    Article  ADS  Google Scholar 

  17. J. Kasprzak, R. André et al., Phys. Rev. B 75, 045326 (2007)

    Article  ADS  Google Scholar 

  18. J. Kasprzak et al., Nature 443, 409 (2006)

    Article  ADS  Google Scholar 

  19. Balili et al., Science 316, 5827 (2007)

    Google Scholar 

  20. C.W. Lai et al., Nature 450, 5289 (2007)

    Article  Google Scholar 

  21. E. Wertz et al., Nat. Phys. 6, 860 (2010)

    Article  Google Scholar 

  22. G. Christmann et al., Appl. Phys. Lett. 93, 051102 (2008)

    Article  ADS  Google Scholar 

  23. A. Baas et al., Phys. Rev. Lett. 100, 170401 (2008)

    Article  ADS  Google Scholar 

  24. J.R. Abo-Shaeer, C. Raman, J.M. Vogels et al., Science 292, 476 (2001)

    Article  ADS  Google Scholar 

  25. K.G. Lagoudakis et al., Nat. Phys. 4, 706 (2008)

    Article  Google Scholar 

  26. J. Keeling, N. Berloff, Phys. Rev. Lett. 100, 250401 (2008)

    Article  ADS  Google Scholar 

  27. G. Nardin et al., Nat. Phys. doi:10.1038/nphys1959

    Google Scholar 

  28. M.C. Cross, W.F. Brinkmann, J. Low Temp. Phys. 5–6, 683 (1977)

    Article  ADS  Google Scholar 

  29. G.E. Volovik, V.P. Mineev, JETP Lett. 24, 561–563 (1976)

    ADS  Google Scholar 

  30. M.M. Salomaa, G.E. Volovik, Rev. Mod. Phys. 59, 533 (1987)

    Article  ADS  Google Scholar 

  31. M. Yamashita et al., Phys. Rev. Lett. 101, 025302 (2008)

    Article  ADS  Google Scholar 

  32. J.R. Kirtley et al., Phys. Rev. Lett. 76, 1336 (1996)

    Article  ADS  Google Scholar 

  33. Y.G. Rubo, Phys. Rev. Lett. 99, 106401 (2007)

    Article  ADS  Google Scholar 

  34. K.G. Lagoudakis et al., Science 326, 974 (2009)

    Article  ADS  Google Scholar 

  35. G. Nardin et al., Phys. Rev. Lett. 103, 256402 (2009)

    Article  ADS  Google Scholar 

  36. P. Senellart, J. Bloch, B. Sermage et al., Phys. Rev. B. 62, 16263 (2000)

    Article  ADS  Google Scholar 

  37. M. Muller, J. Bleuse, R. Andre, Phys. Rev. B. 62, 16886 (2000)

    Article  ADS  Google Scholar 

  38. V. Savona, W. Langbein, Phys. Rev. B. 74, 75 311 (2006)

    Google Scholar 

  39. T.W.B. Kibble, J. Phys. A. 9, 1387 (1976)

    Article  ADS  Google Scholar 

  40. W.H. Zurek, Nature (London) 317, 505 (1985)

    Google Scholar 

  41. C.N. Weiler et al., Nature 455, 948–951 (2008)

    Article  ADS  Google Scholar 

  42. D. Sanvitto, F.M. Marchetti, et al., Nat. Phys. 6, 527(2010)

    Article  Google Scholar 

  43. E. Wertz, L. Ferrier, D.D. Solnyshkov et al., Nat. Phys. 6, 860, (2010)

    Article  Google Scholar 

  44. I. Carusotto, C. Ciuti, Phys. Rev. Lett. 93, 166401 (2004)

    Article  ADS  Google Scholar 

  45. A. Amo, D. Sanvitto, F.P. Laussy et al., Nature 457, 291 (2009)

    Article  ADS  Google Scholar 

  46. A. Amo, J. Lefrere et al., Nat. Phys. 5, 805 (2009)

    Article  Google Scholar 

  47. D. Sanvitto, F.M. Marchetti, M.H. Szymanska et al., Nat. Phys. 6, 527 (2010)

    Article  Google Scholar 

  48. M. Wouters, I. Carusotto, Phys. Rev. Lett. 105, 020602 (2010)

    Article  ADS  Google Scholar 

  49. V. Kohule et al., Phys. Rev. Lett, 106, 255302 (2011)

    Article  ADS  Google Scholar 

  50. G. Malpuech, D.D. Solnyshkov, H. Ouerdane et al., Phys. Rev. Lett. 98, 206402 (2007)

    Article  ADS  Google Scholar 

  51. M. Wouters, V. Savona, Phys. Rev. B. 81, 054508 (2010)

    Article  ADS  Google Scholar 

  52. D. Sanvitto, A. Amo, F.P. Laussy et al., Nanotechnology 21, 134025 (2010)

    Article  ADS  Google Scholar 

  53. G. Nardin et al., Nat. Phys. doi:10.1038/nphys1959 (2011)

    Google Scholar 

  54. L. Ferrier, E. Wertz, R. Johne et al., Phys. Rev. Lett. 106, 126401 (2010)

    Article  ADS  Google Scholar 

  55. O. El Daif et al., Appl. Phys. Lett. 88, 061105 (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is inspired from the PhD work of Konstantinos Lagoudakis who has carried most of the experiments reported here. It has been performed with the strong support of a group of very talented PhD student and postdocs, that I wish to congratulate warmly for their outstanding work: Stefan Kundermann, Francesco Manni, Verena Kohule, Barbara Pietka, Maxime Richard, Augustin Baas, and Yoan Léger. I also would like to convey my most sincere thanks to the theoreticians who allowed us to understand our results, by spending enough time with us and putting into simple words the results of their equations. In particular, Michiel Wouters, Vincenzo Savona, Alexei Kavokin and Yuri Rubo deserve very special acknowledgements. The work has been carried out within the framework of the Quantum Photonics National Center of Competence in research financed by the Swiss National Science Foundation. Complementary funding for conferences and meetings has been obtained through the Latsis Foundation, the Polatom network of the European Science Foundation and a King Saud University associate professorship.

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Correspondence to Benoit Deveaud-Plédran .

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Deveaud-Plédran, B., Lagoudakis, K.G. (2012). Vortices in Spontaneous Bose–Einstein Condensates of Exciton–Polaritons. In: Timofeev, V., Sanvitto, D. (eds) Exciton Polaritons in Microcavities. Springer Series in Solid-State Sciences, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24186-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-24186-4_3

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