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Directional Goldstone waves in polariton condensates close to equilibrium

Quantum fluids of light are realized in semiconductor microcavities by exciton-polaritons, solid-state quasi-particles with a light mass and sizeable interactions. Here, we use the microscopic analogue of oceanographic techniques to measure the excitation spectrum of a thermalised polariton condensate. Increasing the fluid density, we demonstrate the transition from a free-particle parabolic dispersion to a linear, sound-like Goldstone mode characteristic of superfluids at equilibrium. Notably, we show that excitations are created with a definite direction with respect to the condensate, analogous to how a sea breeze develops surface waves aligned with the wind. These results reveal the effect of asymmetric pumping on the collective excitations of a condensate. Furthermore, we measure the critical sound speed for polariton superfluids close to equilibrium.