Extended Data Fig. 1: System Preparation.

a) The experimental sequence. The oscillating line represents the scattering length. We start with a homogeneous system, and then flash on a light shift potential to imprint the lattice. A brief hold time sets the correct phase of the lattice amplitude R relative to the driving. After half a period, if superfluid phase modes are investigated, the second light shift is flashed on. Initial lattice phase deformations for excitation of the corresponding modes are included in the lattice imprint. b) The potentials used for the trap (left) and the light shift for the lattice (right). c) Mean densities throughout the drive. The contrast of the lattice oscillates, as described in eq. (20). The curves are horizontal cuts, averaged over a region of 16 μm in the center of the cloud.