The Berezinskii–Kosterlitz–Thouless Phase Transition in Exciton–Polariton Condensates

  • Georgios Roumpos
  • Yoshihisa Yamamoto
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 172)


In a homogeneous two-dimensional system at nonzero temperature, although there can be no ordering of infinite range, a superfluid phase is expected to occur for a Bose particle system. Theory predicts that, in this phase, the correlation function decays with distance as a power law, and quantum vortices are bound to antivortices to form molecular-like pairs. We study the relevance of this theory to microcavity exciton polaritons. These are two-dimensional bosonic quasiparticles formed as a superposition of a microcavity photon and a semiconductor quantum well exciton and have been shown to condense at high enough densities. Because of the short lifetime, full equilibrium is not established, but we instead probe the steady state of the system, in which particles are continuously injected from a pumping reservoir. We create a large exciton–polariton condensate and employ a Michelson interferometer setup to characterize the short- and long-distance behavior of the first-order spatial correlation function. Our experimental results show distinct features of the two-dimensional and nonequilibrium characters of the condensate. We find that the Gaussian short-distance decay is followed by a power-law decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9–1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that the Berezinskii–Kosterlitz–Thouless (BKT)-like phase order survives in open dissipative systems. We also present our observation of a single vortex–antivortex pair in a condensate of the appropriate size. Pairs are generated due to pump noise and are formed sequentially at the same point due to the inhomogeneous pumping spot profile. They are revealed in the time-integrated phase maps acquired using Michelson interferometry. Our results suggest that vortex–antivortex pairs can be created in a two-dimensional condensate without rotation or stirring. The observed correlated motion of a vortex and antivortex imply that vortex–antivortex pairs do not dissociate, which is consistent with the BKT theoretical prediction as well as with our observation of a power-law decay of the spatial correlation function.


Vortex Line Vortex Pair Single Vortex Free Vortex Healing Length 
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We would like to acknowledge the contributions of our colleagues. M. Fraser performed numerical calculations using the open-dissipative Gross–Pitaevskii equation in Sect. 4.5. J. Keeling, M. Szymańska, and P. Littelwood developed the nonequilibrium theoretical model outlined in Sect. 4.4, and adapted it to the current experimental situation. Finally, A. Löffler, C. Schneider, S. Höfling, and A. Forchel provided the microcavity sample. This work is supported by the FIRST program of the JSPS.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.E. L. Ginzton LaboratoryStanford UniversityStanfordUSA
  2. 2.National Institute of InformaticsTokyoJapan

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