Emergent behavior is a universal phenomenon. Social revolutions, the ripples of sand in a desert, and exotic quantum phases of matter are all dominated by the interactions between their sub-systems, whether those are people, grains of sand, or individual electrons. The n-to-n-body terms can render the dynamics of model systems computationally intractable, even when those sub-systems are as simple as fundamental particles. As first observed by Richard Feynman, even intractable models of matter can be engineered in analog systems, and then directly observed. Quantum simulation offers a path to determine the macroscopic behavior of proposed microscopic models of real materials, and can be used to explore the effectiveness of modern computational techniques. Ultracold atoms offer a unique platform to engineer and measure the properties of model Hamiltonians with precise optical and magnetic fields. We report on one such experiment.
Disorder plays an important role in the phase diagrams of many materials. Crystal defects can cause exotic phases to coexist with the mundane in real world systems, and some phase diagrams are even dominated by the effects of disorder. We report the trapping and characterization of a Bose gas in an optical field isotropic in two dimensions and disordered in a third. Our system was engineered with a novel High Bandwidth Arbitrary Lattice Generator (HiBAL) we've created to skirt limits imposed on monochromatic standing waves of light. In its current iteration we can phase and amplitude modulate optical lattices over a broad range of wavevectors simultaneously at MHz frequencies. We characterize its behavior with a Mach-Zehnder interferometer and a 0.5 NA diffraction limited imaging system, both designed and built in-house. We evaluate the phase diagram of our system as a function of temperature and disorder depth, and find favorable comparisons with an intermediate Griffiths phase predicted by previous Monte Carlo and Renormalization Group studies separating 2D and 3D superfluid regimes.