Smith, Zachary SchutzUltracold atomic gases are often used as quantum simulators, where the ability to precisely control and modulate the potential landscape allows many model Hamiltonians to be realized. Recently, dynamic control over these potentials has been leveraged to extend the kinds of systems that can be explored. Our lab has constructed an optical lattice generator capable of dynamically altering the spacing, phase, and amplitude of an optical lattice at RF timescales. The rapid timescales allows the construction of a time-averaged disordered potential from individual flashes of optical lattice, producing layered system exhibiting a Griffiths phase. A future experiment where the optical lattice is periodically expanded and contracted is proposed, and a numerical treatment is presented suggesting interesting structure in the tunneling dynamics.enDissertationPhysicsQuantum physicsAtomic physics