  Entangled spin squeezed states generated via dipolar interactions in lattice
models provide unique opportunities for quantum enhanced sensing and are now
within reach of current experiments. A critical question in this context is
which parameter regimes offer the best prospects under realistic conditions.
Light scattering in deep lattices can induce significant decoherence and strong
Stark shifts, while shallow lattices face motional decoherence as a fundamental
obstacle. Here we analyze the interplay between motion and spin squeezing in
itinerant fermionic dipoles in one dimensional chains using exact matrix
product state simulations. We demonstrate that shallow lattices can achieve
more 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 this
finding to SU(2)-symmetric superexchange interactions, which keep spins aligned
and protect collective correlations. We show that the optimal regime is
achieved for small repulsive off-site interactions, with a trade-off between
maximal squeezing and optimal squeezing time.
