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Fast spin squeezing by distance-selective long-range interactions with Rydberg molecule dressing

We propose a Rydberg molecule dressing scheme to create strong and long-ranged interactions at selective distances. This is achieved through laser coupling ground-state atoms off-resonantly to an attractive molecular curve of two interacting Rydberg atoms. Although dephasing due to Rydberg state decay occurs in all dressing schemes, an advantage of the molecule dressing is that a large ratio of dressed interaction to dephasing rate can be realized at large atomic separations. In an optical lattice or tweezer setting, we show that the strong interaction permits the fast generation of spin squeezing for several tens of dressed atoms. The proposed setting offers a new route to study complex many-body dynamics and to realize quantum information processing with non-convex long-range interactions.