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The similarities of quantum turbulence with classical hydrodynamics allowquantum fluids to provide essential models of their classical analogue, pavingthe way for fundamental advances in physics and technology. Recently,experiments on 2D quantum turbulence observed the clustering of same-signvortices in strong analogy with the inverse energy cascade of classical fluids.However, self-similarity of the turbulent flow, a fundamental concept in thestudy of classical turbulence, has so far remained largely unexplored inquantum systems. Here, thanks to the unique features of exciton-polaritons, wemeasure the scale invariance of velocity circulations and show that the cascadeprocess follows the universal scaling of critical phenomena in 2D. Wedemonstrate this behaviour from the statistical analysis of the experimentallymeasured incompressible velocity field and the microscopic imaging of thequantum fluid. These results can find wide application in both quantum andclassical 2D turbulence.

Conformal-invariance of 2D quantum turbulence in an exciton-polariton fluid of light