Observation of spin squeezing with contact interactions in one- and three-dimensional easy-plane magnets*

Entanglement in a many-particle system can enable measurement sensitivities beyond that achievable by only classical correlations. For an ensemble of spins, all-to-all interactions are known to reshape the quantum projection noise, leading to a form of entanglement known as spin squeezing. Recently there have been attempts to generalize spin squeezing to systems that exhibit interaction with shorter range. Here, we demonstrate spin squeezing with nearest-neighbor interaction in a lattice, which has the shortest range possible. Specifically, working with ultracold lithium-7 atoms loaded in optical lattices, we utilize the superexchange process for ultracold to realize a nearest-neighbor anisotropic Heisenberg model. We investigate the resulting quench dynamics from an initial product state in both one and three dimensions. In 1D, we observe $1.9^{+0.7}_{-0.5}$ dB of spin squeezing in quantitative agreement with theory. However, in 3D, we observe a maximum of $2.0^{+0.7}_{-0.7}$ dB of squeezing, over an order of magnitude smaller than that expected. We demonstrate that this discrepancy arises from the presence of a finite density of holes; both the motion of the holes as well as direct coupling between spin and density qualitatively alter the spin dynamics. Our observations point to the importance of understanding the complex interplay between motional and spin degrees of freedom in quantum simulators.