Article

Topological order and thermal equilibrium in polariton condensates

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Abstract

The Berezinskii–Kosterlitz–Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light–matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven–dissipative phase transitions and enable the investigation of topological ordering in open systems.

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Acknowledgements

This work has been funded by the MIUR project Beyond Nano and the ERC project POLAFLOW (Grant N. 308136). M.H.S. acknowledges support from EPSRC (Grants No. EP/I028900/2 and No. EP/K003623/2).

Author information

Affiliations

  1. CNR NANOTEC—Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy

    • Davide Caputo
    • , Dario Ballarini
    • , Milena De Giorgi
    • , Lorenzo Dominici
    • , Giuseppe Gigli
    •  & Daniele Sanvitto
  2. University of Salento, Via Arnesano, 73100 Lecce, Italy

    • Davide Caputo
    •  & Giuseppe Gigli
  3. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

    • Galbadrakh Dagvadorj
    •  & Marzena H. Szymańska
  4. Department of Physics, University of Warwick, Coventry CV4 7AL, UK

    • Galbadrakh Dagvadorj
  5. CEMS, RIKEN, Saitama, 351-0198, Japan

    • Carlos Sánchez Muñoz
  6. PRISM, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA

    • Kenneth West
    •  & Loren N. Pfeiffer
  7. Faculty of Science and Engineering, University of Wolverhampton, Wulfruna Street, WV1 1LY, UK

    • Fabrice P. Laussy
  8. Russian Quantum Center, Novaya 100, 143025 Skolkovo, Moscow Region, Russia

    • Fabrice P. Laussy
  9. INFN sezione di Lecce, 73100 Lecce, Italy

    • Daniele Sanvitto

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Contributions

D.C. and D.B. took and analysed the data. G.D. and M.H.S. performed stochastical numerical simulations. C.S.M. and F.P.L. discussed the results. D.C., D.B., C.S.M., M.D.G., L.D., G.G., F.P.L., M.H.S. and D.S. co-wrote the manuscript. K.W. and L.N.P. fabricated the sample. D.S. coordinated and supervised all the work.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Dario Ballarini.

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