Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in elucidating fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising synthetic system that combines several advantageous properties. These include a large set of internal states for encoding quantum information, long nuclear and rotational coherence times and long-range, anisotropic interactions. The latter are expected to allow the exploration of intriguing phases of correlated quantum matter, such as topological superfluids, quantum spin liquids, fractional Chern insulators and quantum magnets. Probing correlations in these phases is crucial to understand their microscopic properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy to measure the site-resolved dynamics of quantum correlations in a gas of polar molecules in a two-dimensional optical lattice. Using two rotational states of the molecules, we realize a spin-1/2 system where the particles are coupled via dipolar interactions, producing a quantum spin-exchange model. Starting with the synthetic spin system prepared far from equilibrium, we study the evolution of correlations during the thermalization process for both spatially isotropic and anisotropic interactions. Furthermore, we study the correlation dynamics in a spin-anisotropic Heisenberg model engineered from the native spin-exchange model using Floquet techniques. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states useful for quantum computation and metrology

A two-dimensional programmable tweezer array of fermions

We prepare high-filling two-component arrays of up to fifty fermionic atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. Full spin- and density-resolved readout of individual sites allows us to post-select near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator

Programmable Quantum Simulation with Fermionic Atoms and Polar Molecules

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