Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms

We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop", and "flip-flip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time-scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-the-art experiments.