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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., Comment: 7 pages, 4 figures

Feshbach resonances in ultra-cold atomic gases have led to some of the most important advances in atomic physics. They did not only enable ground breaking work in the BEC-BCS crossover regime [1], but are also widely used for the association of ultra-cold molecules [2], leading to the formation of molecular Bose-Einstein condensates [3,4] and ultra-cold dipolar molecular systems [5]. Here, we demonstrate the experimental realization of an optical Feshbach resonance using ultra-long range Rydberg molecules [6]. We show their practical use by tuning the revival time of a quantum many-body system quenched into a deep optical lattice. Our results open up many applications for Rydberg optical Feshbach resonances as ultra-long range Rydberg molecules have a plenitude of available resonances for nearly all atomic species. Among the most intriguing prospects is the engineering of genuine three- and four-body interactions via coupling to trimer and tetramer molecular states [7].

Obtaining full control over the internal and external quantum states of molecules is the central goal of ultracold chemistry and allows for the study of coherent molecular dynamics, collisions and tests of fundamental laws of physics. When the molecules additionally have a permanent electric dipole moment, the study of dipolar quantum gases and spin-systems with long-range interactions as well as applications in quantum information processing are possible. Rydberg molecules constitute a class of exotic molecules, which are bound by the interaction between the Rydberg electron and the ground state atom. They exhibit extreme bond lengths of hundreds of Bohr radii and giant permanent dipole moments in the kilo-Debye range. A special type with exceptional properties are the so-called butterfly molecules, whose electron density resembles the shape of a butterfly. Here, we report on the photoassociation of butterfly Rydberg molecules and their orientation in a weak electric field. Starting from a Bose-Einstein condensate of rubidium atoms, we fully control the external degrees of freedom and spectroscopically resolve the rotational structure and the emerging pendular states in an external electric field. This not only allows us to extract the bond length, the dipole moment and the angular momentum of the molecule but also to deterministically create molecules with a tunable bond length and orientation. We anticipate direct applications in quantum chemistry, many-body quantum physics and quantum information processing., Comment: 6 pages, 4 figures; Supplementary Material included