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Bose–Einstein condensation of exciton polaritons

Abstract

Phase transitions to quantum condensed phases—such as Bose–Einstein condensation (BEC), superfluidity, and superconductivity—have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 109 times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase.

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Figure 1: Microcavity diagram and energy dispersion.
Figure 4: Polarization properties of the polariton emission.
Figure 2: Far-field emission measured at 5 K for three excitation intensities.
Figure 3: Polariton occupancy measured at 5 K.
Figure 5: Spatial correlation measurements using a Michelson interferometer.

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References

  1. Anderson, M. N. et al. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995)

    Article  ADS  CAS  Google Scholar 

  2. Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995)

    Article  ADS  CAS  Google Scholar 

  3. Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637–641 (1997)

    Article  CAS  Google Scholar 

  4. Burt, E. A. et al. Coherence, correlations, and collisions: What one learns about Bose-Einstein condensates from their decay. Phys. Rev. Lett. 79, 337–340 (1997)

    Article  ADS  CAS  Google Scholar 

  5. Bloch, I. et al. Measurement of the spatial coherence of a trapped Bose gas at the phase transition. Nature 403, 166–170 (2000)

    Article  ADS  CAS  Google Scholar 

  6. Moskalenko, S. A. Reversible optico-hydrodynamic phenomena in a non ideal exciton gas. Sov. Phys. Solid State 4, 199–204 (1962)

    Google Scholar 

  7. Blatt, J. M. Bose-Einstein condensation of excitons. Phys. Rev. 126, 1691–1692 (1962)

    Article  ADS  CAS  Google Scholar 

  8. Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521–525 (1968)

    ADS  Google Scholar 

  9. Snoke, D. W. Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368–1372 (2002)

    Article  ADS  CAS  Google Scholar 

  10. Snoke, D. W. When should we say we have observed Bose condensation of excitons? Phys. Status Solidi B 238, 389–396 (2003)

    Article  ADS  CAS  Google Scholar 

  11. Rüegg, Ch. et al. Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl3 . Nature 423, 62–65 (2003)

    Article  ADS  Google Scholar 

  12. Eisenstein, J. P. & MacDonald, A. H. Bose-Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004)

    Article  ADS  CAS  Google Scholar 

  13. Butov, L. V. et al. Towards Bose-Einstein condensation of excitons in potential traps. Nature 417, 47–52 (2002)

    Article  ADS  CAS  Google Scholar 

  14. Snoke, D. W. et al. Long-range transport in excitonic dark states in coupled quantum wells. Nature 418, 754–757 (2002)

    Article  ADS  CAS  Google Scholar 

  15. Weisbuch, C. et al. Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 69, 3314–3317 (1992)

    Article  ADS  CAS  Google Scholar 

  16. Kavokin, A. & Malpuech, G. Cavity Polaritons (Elsevier, Amsterdam, 2003)

    Google Scholar 

  17. Savona, V. et al. Theory of polariton photoluminescence in arbitrary semiconductor microcavity structures. Phys. Rev. B 53, 13051–13062 (1996)

    Article  ADS  CAS  Google Scholar 

  18. Le Si, D. et al. Stimulation of polariton photoluminescence in semiconductor microcavity. Phys. Rev. Lett. 81, 3920–3923 (1998)

    Article  Google Scholar 

  19. Deng, H. et al. Condensation of semiconductor microcavity exciton polaritons. Science 298, 199–202 (2002)

    Article  ADS  CAS  Google Scholar 

  20. Leggett, A. J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73, 307–356 (2001)

    Article  ADS  CAS  Google Scholar 

  21. Pitaevskii, L. & Stringari, S. Bose-Einstein Condensation Ch. 1, 6, 15 (Oxford Science Publication, Oxford Univ. Press, Oxford, 2003)

    MATH  Google Scholar 

  22. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966)

    Article  ADS  CAS  Google Scholar 

  23. Keeling, J. et al. Polariton condensation with localized excitons and propagating photons. Phys. Rev. Lett. 93, 226403 (2004)

    Article  ADS  Google Scholar 

  24. Marchetti, F. M. et al. Thermodynamics and excitations of condensed polaritons in disordered microcavities. Phys. Rev. Lett. 96, 066405 (2006)

    Article  ADS  CAS  Google Scholar 

  25. Szymańska, M. H. et al. Non-equilibrium quantum condensation in an incoherently pumped dissipative system. Phys. Rev. Lett. 96, 230602 (2006)

    Article  ADS  Google Scholar 

  26. André, R. et al. Spectroscopy of polaritons in CdTe-based microcavities. J. Cryst. Growth 184/185, 758–762 (1998)

    Article  ADS  Google Scholar 

  27. Bœuf, F. et al. Evidence of polariton stimulation in semiconductor microcavities. Phys. Rev. B 62, R2279–R2282 (2000)

    Article  ADS  Google Scholar 

  28. Richard, M. et al. Spontaneous coherent phase transition of polaritons in CdTe microcavities. Phys. Rev. Lett. 94, 187401 (2005)

    Article  ADS  Google Scholar 

  29. Richard, M. et al. Experimental evidence for nonequilibrium Bose condensation of exciton polaritons. Phys. Rev. B 72, 201301(R) (2005)

    Article  ADS  Google Scholar 

  30. Bloch, J. et al. Monitoring the dynamics of a coherent cavity polariton population. Phys. Rev. B 71, 155311 (2005)

    Article  ADS  Google Scholar 

  31. Porras, D. & Tejedor, C. Linewidth of a polariton laser: Theoretical analysis of self-interaction effects. Phys. Rev. B 67, 161310(R) (2003)

    Article  ADS  Google Scholar 

  32. Tassone, F. et al. Bottleneck effects in the relaxation and photoluminescence of microcavity polaritons. Phys. Rev. B 56, 7554–7563 (1997)

    Article  ADS  CAS  Google Scholar 

  33. Müller, M. et al. Dynamics of the cavity polariton in CdTe-based semiconductor microcavities: Evidence for a relaxation edge. Phys. Rev. B 62, 16886–16892 (2000)

    Article  ADS  Google Scholar 

  34. Ensher, J. R. et al. Bose-Einstein condensation in a dilute gas: Measurement of energy and ground state occupation. Phys. Rev. Lett. 77, 4984–4987 (1996)

    Article  ADS  CAS  Google Scholar 

  35. Sokol, P. in Bose-Einstein Condensation (eds Griffin, A., Snoke, D. W. & Stringari, S.) 51 (Cambridge Univ. Press, Cambridge, 1995)

    Google Scholar 

  36. Porras, D. et al. Polariton dynamics and Bose-Einstein condensation in semiconductor microcavities. Phys. Rev. B 66, 85304 (2002)

    Article  ADS  Google Scholar 

  37. Martin, M. D. et al. Striking dynamics of II-VI microcavity polaritons after linearly polarized excitation. Phys. Status Solidi C 2, 3880–3883 (2005)

    Article  ADS  CAS  Google Scholar 

  38. Savvidis, P. G. et al. Angle-resonant stimulated polariton amplifier. Phys. Rev. Lett. 84, 1547–1550 (2000)

    Article  ADS  CAS  Google Scholar 

  39. Ciuti, C. et al. Parametric luminescence of microcavity polaritons. Phys. Rev. B 63, 041303(R) (2001)

    Article  ADS  Google Scholar 

  40. Laussy, F. P. et al. Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light. Phys. Rev. B 73, 035315 (2006)

    Article  ADS  Google Scholar 

  41. Imamoglu, A. & Ram, R. J. Quantum dynamics of exciton lasers. Phys. Lett. A 214, 193–198 (1996)

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

This work is dedicated to R. Romestain. We acknowledge support by the European Union Network “Photon-mediated phenomena in semiconductor nanostructures” and from the Swiss National Research Foundation through the “Quantum Photonics NCCR”. We thank J.-P. Poizat, D. Sarchi and O. El Daïf for many discussions. Author Contributions J.K., M.R., S.K. and A.B. contributed equally to this work: J.K. worked on ‘Thermalization and condensation’ and ‘Linear polarization build-up’; M.R., S.K. and A.B. worked on the ‘Long-range spatial coherence’. J.M.J.K., F.M.M. and M.H.S. performed theoretical modelling of the data and prepared the Supplementary Information.

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Correspondence to J. Kasprzak or B. Deveaud.

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Kasprzak, J., Richard, M., Kundermann, S. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006). https://doi.org/10.1038/nature05131

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