Designing complex spin interactions in Rydberg tweezer arrays

Synthetic quantum systems based on individually trapped neutral atoms allow studying many-body systems which are hard to solve classically. The classes of many-body systems which can be implemented experimentally are limited by the programmability of the interatomic interactions. We report on the realization of a beyond-Ising spin-1/2 model, where the strong and tunable interactions are based on the off-resonant coupling to highly-excited electronic P states (Rydberg dressing). The effective spins are encoded in the hyperfine ground state manyfold and prepared in individual optical traps (tweezer arrays at various geometries). The Van-der-Waals interactions between the Rydberg states lead to a strong mixing between usually well-separated m_j-sublevels. This opens up controllable interaction channels allowing to implement spin hopping as well as flipping two spins of the same state to the opposite spin state. Using these new types of interactions as well as their long-range character paves the way to implement new types and classes of quantum magnets.