  Quantised sound waves -- phonons -- govern the elastic response of
crystalline materials, and also play an integral part in determining their
thermodynamic properties and electrical response (e.g., by binding electrons
into superconducting Cooper pairs). The physics of lattice phonons and
elasticity is absent in simulators of quantum solids constructed of neutral
atoms in periodic light potentials: unlike real solids, traditional optical
lattices are silent because they are infinitely stiff. Optical-lattice
realisations of crystals therefore lack some of the central dynamical degrees
of freedom that determine the low-temperature properties of real materials.
Here, we create an optical lattice with phonon modes using a Bose-Einstein
condensate (BEC) coupled to a confocal optical resonator. Playing the role of
an active quantum gas microscope, the multimode cavity QED system both images
the phonons and induces the crystallisation that supports phonons via
short-range, photon-mediated atom-atom interactions. Dynamical susceptibility
measurements reveal the phonon dispersion relation, showing that these
collective excitations exhibit a sound speed dependent on the BEC-photon
coupling strength. Our results pave the way for exploring the rich physics of
elasticity in quantum solids, ranging from quantum melting transitions to
exotic ``fractonic'' topological defects in the quantum regime.
