  Spin-squeezing in systems with single-particle control is a well-established
resource of modern quantum technology. Applied in an optical lattice clock can
reduce the statistical uncertainty of spectroscopic measurements. Here, we
consider dynamic generation of spin-squeezing with ultra-cold bosonic atoms
with two internal states loaded into an optical lattice in the strongly
interacting regime as realized with state-of-the-art experiments using a
quantum gas microscope. We show that anisotropic interactions and inhomogeneous
magnetic fields generate scalable spin-squeezing if their magnitudes are
sufficiently small, but not negligible. The effect of non-uniform filling
caused by hole doping, non-zero temperature and external confinement is studied
at a microscopic level demonstrating their limiting role in the dynamics and
scaling of spin squeezing.
