I will describe two experiments using ultra-cold atoms in modified optical lattices. in the first, we realize a conservative optical potentials for cold atoms with subwavelength spatial structure, of order 10nm. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The same non-linear atomic response can be used to "slice" the atomic wave function with sub-wavelength resolution, which we use to directly measure the spatial structure of wave function density with resolution of 10nm. In the second, we study a Bose-Einstein condensate in a periodically shaken optical lattice, where the position of the lattice is the oscillating parameter. Such driven cold-atom systems have been proposed as a means to engineer topological, correlated states. Heating in these so-called "Floquet-engineered" many-body systems is a poorly understood limiting process. In the presence of the drive, we find density modulations spontaneously grow and deplete the condensate. Under most conditions, the observed heating follows recent theoretical predictions. However, we observe giant decay rates of the condensate in some parameter ranges where the system becomes strongly interacting, which cannot be anticipated by existing theories.