Spin squeezing with short-range spin-exchange interactions

We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance $r$ as $1\mathrm{/}{r}^{\alpha }$ in $D=2$ and $3$ spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where spin squeezing comparable to the infinite-range $\alpha =0$ limit is achievable even when interactions are short-ranged, $\alpha >D$. A region of “collective” behavior in which optimal squeezing grows with system size extends all the way to the $\alpha \to \mathrm{\infty }$ limit of nearest-neighbor interactions. Our predictions, made using the discrete truncated Wigner approximation (DTWA), are testable in a variety of experimental cold atomic, molecular, and optical platforms.