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The dynamic structure factor is a central quantity describing the physics ofquantum many-body systems, capturing structure and collective excitations of amaterial. In condensed matter, it can be measured via inelastic neutronscattering, which is an energy-resolving probe for the density fluctuations. Inultracold atoms, a similar approach could so far not be applied due to thediluteness of the system. Here, we report on a direct, real-time andnon-destructive measurement of the dynamic structure factor of a quantum gasexhibiting cavity-mediated long-range interactions. The technique relies oninelastic scattering of photons, stimulated by the enhanced vacuum field insidea high finesse optical cavity. We extract the density fluctuations, theirenergy and lifetime while the system undergoes a structural phase transition.We observe an occupation of the relevant quasi-particle mode on the level of afew excitations, and provide a theoretical description of this dissipativequantum many-body system.

Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition