Benchmarking direct and indirect dipolar spin-exchange interactions between two Rydberg atoms

We report on the experimental characterization of various types of spin-exchange interactions between two individual atoms, where pseudo-spin degrees of freedom are encoded in different Rydberg states. For the case of the direct dipole-dipole interaction between states of opposite parity, such as between $nS$ and $nP$, we investigate the effects of positional disorder arising from the residual atomic motion, on the coherence of spin-exchange oscillations. We then characterize an indirect dipolar spin exchange, i.e., the off-diagonal part of the van der Waals effective Hamiltonian that couples the states $nS$ and $(n+1)S$. Finally, we report on the observation of a new type of dipolar coupling, made resonant using addressable light-shifts and involving four different Rydberg levels: this exchange process is akin to electrically induced F\"orster resonance, but featuring local control. It exhibits an angular dependence distinct from the usual $1-3\cos^2(\theta)$ form of the resonant dipolar spin-exchange.