Single-shot flow spectroscopy of a polariton condensate: Kibble-Zurek and Kolmogorov-like scaling

Quantized vortices are fundamental topological excitations of quantum fluids. We report single-shot interferometric measurements of spontaneous vortex nucleation in a room-temperature organic exciton-polariton condensate. From hundreds of independent realizations we find random vortex-core positions and unbiased circulation, consistent with intrinsically stochastic, unpinned defect formation. The mean vortex number scales with pump power above threshold with an exponent consistent with Kibble-Zurek freeze-out in a driven-dissipative condensate. Using reconstructed phase maps we obtain single-shot flow fields, compute the incompressible component, and extract kinetic-energy spectra. Vortex-containing realizations develop a robust Kolmogorov-like segment with Einc(k) proportional to k^(-5/3) over a finite k range, indicating the onset of turbulent spectral scaling in a quantum fluid of light. These results establish single-shot access to phase and flow as a direct route to quantifying stochastic defect formation and emerging turbulence in polariton condensates.