Non-adiabatic mapping from Fermi-Hubbard to t-J model via optical lattice ramps

The t-J model is believed to contain the essential physics of the doped Fermi-Hubbard model, relevant to the studies of high-Tc superconductivity. We propose a protocol to directly measure correlators in the t-J model using a fermionic quantum gas microscope. We can non-adiabatically map to the t-J model by preparing a Fermi-Hubbard state and simply ramping up the depth of the optical lattice, at a rate comparable to the initial tunneling strength. We perform exact diagonalization and sparse time-evolution on 1D and 2D Fermi-Hubbard systems and find that for the optimal ramp speed, various correlators measured in the ramped state approach the value expected for the corresponding t-J model. The slow lattice ramp allows doublon-hole pairs to recombine, effectively mapping to the restricted Hilbert space of the t-J model while preserving the spin-spin correlations coming from the super-exchange mechanism. We compare our numerics to a simplified 2-site analytical model as well as experimental data from our Lithium-6 fermionic quantum gas microscope and find good agreement. Further, we study the effect of slow ramps on estimating temperatures from spin-spin correlations in a Fermi-Hubbard experiment.