Localization with Hopping Disorder in a Quasiperiodic Synthetic Momentum Lattice

Abstract

Quasiperiodicity is easily realized with ultracold atoms in optical lattices and has been used to simulate the delocalization-localization transition. Random local potentials can also be implemented by spatial light modulators. Programmable hopping disorder, however, remains difficult to realize in conventional optical lattices. Momentum-space lattice (MSL) offers a platform to address this. We implement the MSL using an ${}^{87}$Rb Bose-Einstein condensate via multiple Bragg diffraction and benchmark the platform by simulating wavepacket dynamics with hopping disorder on top of the generalized Aubry-André (GAA) model. We test programmable hopping disorder added to localized/delocalized backgrounds tunable by the Aubry-André potential strength, as well as systems with mobility edges. Uncorrelated hopping disorder smooths the AA transition into a crossover between weakly (large localization lengths) and strongly localized regimes; the resulting enhancement in localization suppresses wavepacket spreading. We also implement spatially correlated hopping disorder and compare its dynamics with uncorrelated disorder of the same final width, demonstrating a correlation-induced enhancement in spreading. Measured dynamics agrees with trends from ideal tight-binding simulations. Trends in non-universal features depending on microscopic structure and short-time dynamics as functions of quasiperiodic potential strength, hopping-disorder strength, and GAA deformation also match numerical results, with better agreement at larger hopping-disorder strengths. Numerical simulations of the MSL dynamics provide insights into sources of corrections. Our results demonstrate that MSL provides a versatile platform for realizing general disordered quantum systems with programmable hopping amplitudes beyond quasiperiodic models.