Transition from flat-band localization to Anderson localization: Realization and characterization in a one-dimensional momentum lattice

The diffusion and localization of particles in lattice potentials are essential topics in the study of quantum states of matter. As two distinct mechanisms, flat-band localization (FBL) caused by destructive interference and Anderson localization (AL) by strong disorder can both prohibit particle transport and lead to an insulator state. The realization and characterization of the two different insulating phases necessitate the ability to shape the lattice potential and measure particle transport at the single-site level. By using spatial momentum as an artificial dimension, ultracold quantum gas in a momentum lattice provides an ideal platform to achieve singlesite resolution. Here, we demonstrate that the transition from flat-band localization to Anderson localization can be realized and quantitatively studied in a Bose-Einstein condensate in a one-dimensional momentum lattice. The flat-band localization is realized in a one-dimensional Tasaki model, while the transition to Anderson localization is achieved by imposing a strong enough disorder potential and is characterized by stark features of particle transport from an initial state in an experimentally realistic finite-size system. Submitted in parallel with Zeng et al., this article provides experimental details on the realization of an effective model and preparation of the initial state as well as a theoretical study of the transition with experimental parameters.