Coherent dipole-dipole coupling between two single atoms at a F\"orster resonance

Resonant energy transfers, i.e. 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 chemical and biological phenomena, most notably photosynthesis. In 1948, F\"orster established the theoretical basis of fluorescence resonant energy transfer (FRET), paving the ground towards the widespread use of FRET as a "spectroscopic ruler" for the determination of nanometer-scale distances in biomolecules. The underlying mechanism is a coherent dipole-dipole coupling between particles, as already recognized in the early days of quantum mechanics, but this coherence was not directly observed so far. Here, we study, both spectroscopically and in the time domain, the coherent, dipolar-induced exchange of electronic excitations between two single Rydberg atoms separated by a controlled distance as large as 15 microns, and brought into resonance by applying a small electric field. The coherent oscillation of the system between two degenerate pair states occurs at a frequency that scales as the inverse third power of the distance, the hallmark of dipole-dipole interactions. Our results not only demonstrate, at the most 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.