The extreme tunability and control that atomic physics provides makes quantum gasesideal platforms for experimentally realizing novel synthetic materials beyond what istraditionally realizable in condensed matter experiments. In particular, the ability tocontrol interparticle interactions allows for the realization of long lived nonequilibriumstates, and strong periodic modulation of lattice potentials realizes novel Floquet matter.In this thesis I shall present a series of experiments studying the dynamics of ultracoldlithium in modulated and static one-dimensional optical lattices. First, I present anoverview of the experimental apparatus which includes a description of the generation ofour Bose-Einstein condensate and optical lattices. Then I step through four experimentswhich we conducted. The rst two involve studying spatial dynamics in static opticallattices in the ground and the excited bands which realize position-space Bloch oscillationsand a relativistic harmonic oscillator respectively. The third experiment studies transportin Floquet hybridized optical lattice Bloch bands, and the fourth experiment investigatesprethermalization in strongly modulated lattices with tunable interactions
