Measurement of the Angular Dependence of the Dipole-Dipole Interaction Between Two Individual Rydberg Atoms at a F\"orster Resonance

We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a F"orster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the F"orster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantization axis. Our results show good agreement with the expected angular dependence $\propto (1-3{\cos }^2\theta )$, and represent an important step towards quantum state engineering in two-dimensional arrays of individual Rydberg atoms.