Spin Squeezing with Short-Range Spin-Exchange Interactions
Michael A. Perlin, Chunlei Qu, Ana María Rey
Abstract
We investigate many-body spin squeezing dynamics in an $XXZ$ model with interactions that fall off with distance $r$ as $1/{r}^{\ensuremath{\alpha}}$ 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 $\ensuremath{\alpha}=0$ limit is achievable even when interactions are short ranged, $\ensuremath{\alpha}>D$. A region of ``collective'' behavior in which optimal squeezing grows with system size extends all the way to the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of nearest-neighbor interactions. Our predictions, made using the discrete truncated Wigner approximation, are testable in a variety of experimental cold atomic, molecular, and optical platforms.