  Randomness and disorder have strong impact on transport processes in quantum
systems and give rise to phenomena such as Anderson localization [1-3],
many-body localization [4] or glassy dynamics [5]. Their characteristics
thereby depend on the strength and type of disorder. An important class are
hopping models, where particles or excitations move through a system which has
randomized couplings. This includes, e.g., spin glasses [5], coupled optical
waveguides [6], or NV center arrays [7]. They are also key to understand
excitation transport in molecular and biological systems, such as light
harvesting complexes [8]. In many of those systems, the microscopic coupling
mechanism is provided by the dipole-dipole interaction. Rydberg systems [9] are
therefore a natural candidate to study random hopping models. Here, we
experimentally study a three-dimensional many-body Rydberg system with random
dipole-dipole couplings. We measure the spectrum of the many-body system and
find good agreement with an effective spin model. We also find spectroscopic
signatures of a localization-delocalization transition. Our results pave the
way to study transport processes and localization phenomena in random hopping
models in detail. The inclusion of strong correlations is experimentally
straightforward and will allow to study the interplay between random hopping
and localization in strongly interacting systems.
