We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a spatial light modulator, with which we imprint an appropriate phase pattern on an optical dipole-trap beam prior to focusing. We trap single 87 Rb atoms in the sites of arrays containing up to approximately 100 microtraps separated by distances as small as 3 μm, with complex structures such as triangular, honeycomb, or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. This versatile system opens appealing applications in quantum-information processing and quantum simulation, e.g., for simulating frustrated quantum magnetism using Rydberg atoms.

We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C6/R6 dependence. The measured C6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.

Resonant energy transfers, the non-radiative redistribution of an electronic excitation between two particles coupled by the dipole-dipole interaction, lie at the heart of a variety of phenomena 1 , notably photosynthesis. In 1948, Förster established the theory of fluorescence resonant energy transfer (FRET) between broadband, nearly-resonant donors and acceptors 2 . The 1/R 6 scaling of the energy transfer rate, where R is the distance between particles, enabled widespread use of FRET as a 'spectroscopic ruler' for determining nanometric distances in biomolecules 3 . The underlying mechanism is a coherent dipolar coupling between particles, as recognized in the early days of quantum mechanics 4 , but this coherence has not been directly observed so far. Here we study, spectroscopically and in the time domain, the coherent, dipolar-induced exchange of excitations between two Rydberg atoms separated by up to 15 µm, and brought into resonance by applying an electric field. Coherent oscillation of the system between two degenerate pair states then occurs at a frequency scaling as 1/R 3 , the hallmark of resonant dipole-dipole interactions 5 . Our results not only demonstrate, at the fundamental level of two atoms, the basic mechanism underlying FRET, but also open exciting prospects for active tuning of strong, coherent interactions in quantum many-body systems.The possibility to tune at will coherent interactions in many-body systems by changing external parameters is one of the key tools enabling quantum simulation. For instance, in ultracold quantum gases, such tuning can be achieved by magnetically-induced Feshbach resonances 6,7 . Rydberg atoms are another promising platform for the quantum simulation of complex many-body problems, owing to the strong interactions associated with their large principal quantum numbers 8 . They have proved to be an efficient tool for characterizing non-radiative exchange of energy in resonant collisional processes 9 , studying collective effects 10 and engineering quantum states of matter 11 . The observation of Rydberg blockade between individual atoms 12,13 , where the strong interaction between Rydberg states inhibits multiple excitations within a blockade sphere, opens the way towards the development of Rydberg quantum simulators 14 . An appealing tool for those applications is the possibility to tune the strength of the interactions by external electric fields using Förster resonances 15-23 . So far, owing to inhomogeneities in the atomic ensembles used in experiments, only indirect evidence for the coherent character of the interaction has been obtained 24,25 .Here, we study a system of two single atoms at a Förster resonance. We first perform a spectroscopic measurement of the energies of the two-atom states as a function of the applied electric field, and observe directly the avoided crossing between pair states induced by the dipole-dipole interaction. The splitting at resonance is observed to scale as 1/R 3 as a function of the distance R between the atoms. In a second...