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 it 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 nonuniform filling caused by hole doping, nonzero temperature, and external confinement is studied at a microscopic level demonstrating their limiting role in the dynamics and scaling of spin squeezing.The .zip file contains all relevant Figures in the pdf and png formats. Please consult "supplementary_information.pdf" file for further details.