Microscopy of cavity-induced density-wave ordering in ultracold gases

We demonstrate high-resolution in-situ imaging of density-wave ordering induced by cavity-mediated interactions in a unitary Fermi gas. We observe long-range spatial correlations throughout the formation of density waves, both for adiabatic preparation and following a quench, with a pattern controlled by the cavity mode structure. Our single-shot microscopic images together with the real-time readout of the cavity photons provide access to atom-photon correlations. We use this capability to investigate order fluctuations as a function of time following a quench and to directly confirm the correspondence between optical and atomic observables. Our system opens rich perspectives, from local patterning to correlation measurements in long-range interacting quantum gases.