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Onset of vortex clustering and inverse energy cascade in dissipative quantum fluids


Turbulent phenomena are among the most striking effects that both classical and quantum fluids can exhibit. Although classical turbulence is ubiquitous in nature, the observation of quantum turbulence requires the precise manipulation of quantum fluids such as superfluid helium or atomic Bose–Einstein condensates. Here we demonstrate the turbulent dynamics of a two-dimensional quantum fluid of exciton–polaritons, hybrid light–matter quasiparticles, both by measuring the kinetic energy spectrum and showing the onset of vortex clustering. We demonstrate that the formation of clusters of quantum vortices is triggered by the increase of the incompressible kinetic energy per vortex, showing the tendency of the vortex-gas towards highly excited configurations despite the dissipative nature of our system. These results lay the basis for investigations of quantum turbulence in two-dimensional fluids of light.

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Fig. 1: Injection and trapping of a polariton quantum fluid.
Fig. 2: Vortex classification and velocity decomposition.
Fig. 3: Energy transfer and clusterization.
Fig. 4: Inverse energy cascade.

Data availability

The data that support the findings of this study are available from the authors upon reasonable request.

Code availability

The codes used in this study will be provided upon reasonable request.


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R.P., A.S.L., D.T., G.G., M.D.G., V.A., D.S. and D.B. acknowledge the following projects: Italian Ministry of University (MUR) PRIN project ‘Interacting Photons in Polariton Circuits’ – INPhoPOL (grant no. 2017P9FJBS); the project ‘Hardware implementation of a polariton neural network for neuromorphic computing’ – Joint Bilateral Agreement CNR-RFBR (Russian Foundation for Basic Research) – Triennal Program 2021–2023; the MAECI project ‘Novel photonic platform for neuromorphic computing’, Joint Bilateral Project Italia-Polonia 2022–2023; PNRR MUR project ‘National Quantum Science and Technology Institute’ – NQSTI (PE0000023); PNRR MUR project ‘Integrated Infrastructure Initiative in Photonic and Quantum Sciences’ – I-PHOQS (IR0000016); Apulia Region, project ‘Progetto Tecnopolo per la Medicina di precisione’, Tecnomed 2 (grant no. Deliberazione della Giunta Regionale n. 2117 del 21/11/2018). M.M. and P.C. acknowledge funding from National Science Centre, Poland, grant no. 2016/22/E/ST3/00045. We are grateful to P. Cazzato for valuable technical support during the experiments. D.B. is grateful to B. Alegria for logistics and inspiration.

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R.P., P.C., M.M., D.B. and D.S. contributed to the formulation of the project. M.M., D.B. and D.S. supervised the project. R.P. and P.C. contributed to the data curation and, together with A.S.L. and D.B., to the formal analysis and development of the methodology. R.P., P.C. and D.T. cured the codes. Funding acquisition was managed by M.M., D.S. and G.G. All authors contributed to discussions and reviewing the manuscript.

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Correspondence to D. Sanvitto or D. Ballarini.

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Panico, R., Comaron, P., Matuszewski, M. et al. Onset of vortex clustering and inverse energy cascade in dissipative quantum fluids. Nat. Photon. 17, 451–456 (2023).

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