Exploring spin-squeezing in the Mott insulating regime: role of anisotropy, inhomogeneity and hole doping

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.