Programmable Fermi-Hubbard Lattices

Programmable lattices offer the possibility of exploring multiple lattice geometries in one experimental setup and providing additional tools for creating targeted initial quantum states. Here, we present results showing one and two dimensional realizations of the Fermi-Hubbard model using small systems of optical tweezer arrays with Li-6 atoms. By loading two atoms into the ground state of half the tweezers, adiabatically ramping on additional tweezers, and post-selecting using a spin-resolved imaging scheme in a quantum gas microscope, we create small low entropy correlated tunnel-coupled systems at half filling. As there are technical limitations to scaling the optical tweezer platform to larger system sizes, we present progress towards demonstrating programmable Fermi-Hubbard lattices with interfering beams. These methods open the door for microscopic studies of fermionic phases in novel lattice geometries.