We investigate many-body spin squeezing dynamics in an $XXZ$ model with interactions that fall off with distance $r$ as $1/r^{\alpha }$ 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 $\alpha \to \infty$ 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.

中文翻译：

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具有短程自旋交换相互作用的自旋挤压

我们研究了多体自旋挤压动力学 $XXž$ 互动随着距离而下降的模型 $\mathrm{[R}$ 如 $\mathrm{1个}/{\mathrm{[R}}^{\alpha }$ 在 $d=2$和3个空间维度。与Ising模型形成鲜明对比的是，我们发现了一个宽泛的参数范围，其中自旋压缩与无限范围相当$\alpha =0$ 即使互动是短距离的，限制也是可以达到的， $\alpha >d$。一个“集体”行为的区域，随着系统规模的增长，最佳的压缩不断增长，一直延伸到$\alpha \to \infty$最近邻居互动的限制。我们使用离散截断的Wigner近似进行的预测可以在各种实验性冷原子，分子和光学平台中进行检验。