Localization with Hopping Disorder in Quasi-periodic Synthetic Momentum Lattice

Lattice quasi-periodicity is easily realized with ultracold atoms in optical lattices and has been used to study delocalization-localization transition at low dimensions. Models with true disorder, however, remains largely unrealized in experiments. Here, using Bose-Einstein Condensate of ${^{87}{\text{Rb}}}$ atoms, we realize a Generalized Aubry-Andr\'e (GAA) chain with added hopping disorder in a Momentum Space Lattice (MSL) via multiple Bragg diffractions. Unlike real space lattice simulators, MSL allows simulations of arbitrary disorder configurations and control over spatial disorder correlations. Uncorrelated hopping disorder added to the AA model enhances localization in all phases, smoothening the transition into a crossover between weakly and strongly localized regimes. On the other hand, numerical analysis shows that, spatially correlated hopping disorder induces partial delocalization of localized states in the vicinity of strong hopping bonds. Over a range of disorder strengths and correlations, the experimental results agree quantitatively with the numerical simulation of the dynamics in MSL. Ability of the platform to resolve correlation-dependent dynamical features in dynamics reflects the precision achieved in the realization. Our results demonstrate MSL as a viable platform for studying general disordered quantum systems beyond quasiperiodic systems.