Short Bragg pulse spectroscopy for a paraxial fluids of light

We implement Bragg spectroscopy in a paraxial fluid of light. Analogues of short Bragg pulses are imprinted on a photon fluid by wavefront shaping using a spatial light modulator. We measure the dispersion relation and evidence a parabolic single-particle regime as well as a linear phonon regime even for very weakly interacting photons and low sound velocity. Finally, we report a measurement of the static structure factor, $S(k)$, and we demonstrate the presence of pair-correlated excitations, revealing indirectly the quantum depletion in a paraxial fluid of light.