Vortices provide the elementary quanta of rotation in superfluids. Here we exploit the natural assets of open-dissipative exciton-polariton fluids to set into ultrafast spiraling motion a doubly-charged vortex, which also results in the time-varying orbital angular momentum of emitted light. The created topology comprises all the possible polariton pseudospins filling the associated Hilbert space of states, with each of them appearing twice in real space where the Bloch sphere is mapped. The intrinsic quantity characterizing the topological link between the two spaces— the Berry curvature—is reshaping in time, but always keeps a space integral of twice the solid angle.
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