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Entangled spin squeezed states generated via dipolar interactions in latticemodels provide unique opportunities for quantum enhanced sensing and are nowwithin reach of current experiments. A critical question in this context iswhich parameter regimes offer the best prospects under realistic conditions.Light scattering in deep lattices can induce significant decoherence and strongStark shifts, while shallow lattices face motional decoherence as a fundamentalobstacle. Here we analyze the interplay between motion and spin squeezing initinerant fermionic dipoles in one dimensional chains using exact matrixproduct state simulations. We demonstrate that shallow lattices can achievemore than 5dB of squeezing, outperforming deep lattices by up to more than 3dB,even in the presence of low filling, loss and decoherence. We relate thisfinding to SU(2)-symmetric superexchange interactions, which keep spins alignedand protect collective correlations. We show that the optimal regime isachieved for small repulsive off-site interactions, with a trade-off betweenmaximal squeezing and optimal squeezing time.

Spin Squeezing with Itinerant Dipoles: A Case for Shallow Lattices