Fig. 4: Demonstration of two-dimensional full polariton hydrodynamic transitions from a normal fluid to both a Čerenkov supersonic and a superfluid fluid.

a-I, a-II Experimental real-space images of polariton flowing with injection momentum of k_|| = 4.2 μm⁻¹ across a defect with resonance pumping power in the cavity of 0.07 (I) and 6 (II) μJ cm⁻², respectively. a-III-IV, The experimental saturated images of momentum distributions corresponding to a-I and a-II, respectively. At low polariton density (a-I, a-III), the scattering by the defect generated parabolic interference wavefronts and Rayleigh scattering ring. When polariton density increased, Čerenkov behavior in the supersonic regime (c_s < v_p) was shown as the linear wavefronts and the increased aperture angle. The scattering ring gets modified at high polariton density (a-IV). b-I, b-II, the time-averaged simulation in real-space before and after the transition, respectively. Evenly distributed 0-5 meV exciton energy random variations are added to only 0.3% of the spatial pixels to better fit the experimental results. b-III, b-IV The time-averaged simulation images of the momentum space corresponding to b-I and b-II, respectively. c-I, c-II (c-III, c-IV) Experimental real-space (momentum space) images of polariton flowing with injection momentum of k_|| = 2.3 μm⁻¹ with resonance pumping power in the cavity of 0.06 (I) and 5.6 (II) μJ cm⁻², respectively. At high polariton density (c-II, c-IV), the polariton fluid entered the frictionless superfluid regime and the interference fringes and scattering ring vanished. d-I, d-II (d-III, d-IV) The simulated time-averaged real-space (momentum space) simulations before and after the transition. Evenly distributed 0-5 meV exciton energy random variations are added to only 1% of the spatial pixels to better fit the experimental results. Compared to simulations, the additional short white lines at the bottom of the a-III, a-IV and c-III, c-IV images are streak artifacts caused by the scanning of the CCD camera. More power-dependent experimental images of Čerenkov and superfluid cases were shown in Supplementary Figs. 8–12. All scale bars: 5 μm.