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Non-equilibrium Bose–Einstein condensation in photonic systems

Abstract

The study of Bose–Einstein condensation effects in photonic systems has revealed a rich phenomenology related to spontaneous coherence generation in driven-dissipative spatially extended systems and is providing a new platform for the study of non-equilibrium phase transitions and critical behaviours. In this Review, we give an interdisciplinary overview of condensation phenomena in photonic systems. We cover a wide range of systems, from lasers to photon condensates in dye-filled cavities, to excitons in semiconductor heterostructures, to microcavity polaritons, as well as emerging systems, such as mode-locked lasers and classical light waves. Our aim is to highlight novel universal phenomena that stem from the driven-dissipative, non-equilibrium nature of these systems and affect the static, dynamic, superfluid and coherence properties of the condensate. Finally, we provide our perspectives on the future of fundamental science and technological applications in this field.

Key points

  • Bose–Einstein condensation in photonic systems is an example of a non-equilibrium phase transition leading to spontaneous coherence generation in a spatially extended system.

  • The physical platforms can be classified in terms of the typical strength of the driven-dissipative condition — from quasi-equilibrium towards fully non-equilibrium regimes — as follows: excitons and classical light in waveguides, then photons in dye-filled cavities, exciton–polaritons and, finally, optical parametric oscillators and conventional lasers.

  • The non-equilibrium condition is responsible for a richer mean-field dynamics, such as condensation in excited states, topological lasing, outward flows in localized condensates, spiralling condensate phases around quantized vortices, diffusive Goldstone modes and generalized Landau criteria for superfluidity.

  • Classical and quantum fluctuations in the driven-dissipative regime display novel critical behaviours such as Kardar–Parisi–Zhang spatiotemporal scalings in the coherence of the emitted light.

  • Strongly interacting photon fluids in the presence of strong non-linearities have been anticipated to feature exotic strongly correlated and/or topological states of photonic matter, such as Mott insulators and fractional quantum Hall states.

  • All these developments are expected to lead to novel sources of coherent and/or quantum light, as well as to sophisticated schemes for optical computation.

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Fig. 1: General features of condensation.
Fig. 2: Bose–Einstein condensation of photons.
Fig. 3: Bose–Einstein condensation of excitons.
Fig. 4: Bose–Einstein condensation of exciton–polaritons.
Fig. 5: New features of non-equilibrium condensates.
Fig. 6: Future perspectives.

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Acknowledgements

J.B. acknowledges financial support from the Paris Île-de-France Région in the framework of DIM SIRTEQ, the QuantERA project ‘InterPol’ (ANR-QUAN-0003-05), the French National Research Agency project ‘Quantum Fluids of Light’ (ANR-16-CE30-0021) and the French RENATECH network. I.C. acknowledges financial support from the European Union FET-Open grant ‘MIR-BOSE’ (no. 737017), from the Provincia Autonoma di Trento, from the Q@TN initiative and from Google via the quantum NISQ award. J.B. and I.C. acknowledge support from the European Union H2020-FETFLAG-2018-2020 project ‘PhoQuS’ (no. 820392). M.W. acknowledges financial support from the FWO-Vlaanderen (grant no. G016219N).

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Bloch, J., Carusotto, I. & Wouters, M. Non-equilibrium Bose–Einstein condensation in photonic systems. Nat Rev Phys 4, 470–488 (2022). https://doi.org/10.1038/s42254-022-00464-0

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