Topological order and thermal equilibrium in polariton condensates


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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Figure 1: Pumping mechanism and interferometric set-up.
Figure 2: Two-dimensional first-order spatial correlations.
Figure 3: Coherence decay and BKT phase transition.
Figure 4: Decay of coherence from stochastic analysis of a homogeneous system.
Figure 5: Vortex–antivortex distribution map.
Figure 6: Spatial and temporal coherence in weak coupling regime.


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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).

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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.

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Correspondence to Dario Ballarini.

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The authors declare no competing financial interests.

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Caputo, D., Ballarini, D., Dagvadorj, G. et al. Topological order and thermal equilibrium in polariton condensates. Nat. Mater. 17, 145–151 (2018).

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