Measuring $d-$wave superconductivity and beyond: efficient global control on optical lattices

Understanding high-temperature superconductivity by exploring the Fermi-Hubbard model is a major focus of analog quantum simulation. However, probing and verifying superconducting properties in such systems remains experimentally challenging. In this letter, we introduce a novel protocol for measuring a broad class of observables in fermionic quantum gas microscopes, including long-range superconducting pairing correlations (after a repulsive-to-attractive mapping). Our protocol only requires global control and the ability to partition the lattice into dimers of two sites, and is designed using insights on the Hilbert-space structure of such dimers. We demonstrate that our protocol has low sample requirements and further optimize our pulses for robustness to experimental imperfections such as inhomegeneity of the lattice potential. Our work introduces general tools for manipulating quantum states in analog quantum simulators using limited controls, enhancing their ability to tackle problems such as that of high-temperature superconductivity.