Scalable spin squeezing in a three-dimensional optical lattice clock induced by superexchange

Optical lattice clocks are among the most precise measurement devices ever built, reaching fractional uncertainties at the 10^-19 level. However, further improvement by simply increasing the number of interrogated atoms is approaching a fundamental limit set by quantum projection noise. A key challenge is therefore to enhance sensitivity not by scaling atom number, but by generating entanglement—such as spin-squeezed states—that suppresses quantum noise. In this work, we develop a theoretical framework for scalable spin squeezing in optical lattice clocks driven by a strong laser field. Using matrix-product-state simulations of the Fermi–Hubbard model and its effective spin models, we identify experimentally realistic regimes where substantial, scalable squeezing can be achieved. Our scheme operates a three-dimensional optical lattice in which atoms interact via spin exchange along the laser-drive axis, while shallow confinement in the transverse plane enhances spin coherence. We further analyze the effects of hole defects—unavoidable in realistic systems—on the dynamics and squeezing performance. Our results provide concrete guidance for harnessing atomic interactions in 3D optical lattices to achieve entanglement-enhanced metrology.