Programmable Quantum Simulation with Fermionic Atoms and Polar Molecules

Abstract

In the first part of this thesis, we describe the development of a programmable Fermi-Hubbard tweezer array using Fermi gases of lithium-6. Using a stroboscopic technique, we demonstrate a two-dimensional tweezer array which can realize lattices of arbitrary geometries including triangular, Lieb, and octagonal ring lattices. Fermions loaded into the array tunnel between different tweezers and experience strong on-site interactions. Full spin- and charge-resolved readout of the system using bilayer imaging enables post-selection of near-zero entropy initial states for quantum simulation. We demonstrate a two-by-two Fermi-Hubbard plaquette, which provides a building block for a 2D Fermi-Hubbard quantum simulator with software-defined geometry. In the second part of this thesis, we describe our theoretical contributions to an experiment studying non-equilibrium spin dynamics using a 2D polar molecule array with dipole-dipole interactions using ultracold NaRb molecules. The experiment prepares rovibrational ground state molecules from Feshbach molecules in an optical lattice. The polar molecules realize a site-diluted 2D quantum XY model with long-range interactions. Using a novel molecular quantum gas microscope, molecules in one of the spin states are detected with single-site resolution. We compare the experimental measurements of the time-evolution of the spin correlation function following a quench with exact diagonalization simulations. We find good agreement of the simulations with the experiments in spin systems with isotropic or anisotropic interactions