Quantum simulation of the Hubbard model

Abstract

The Hubbard model was originally proposed in 1963 as a simple model to describe electrons in a solid. Today, the model is widely believed to capture the physics of cuprate materials, which exhibit phenomena that are not yet well understood such as unconventional superconductivity. However, the model itself is still incredibly challenging to solve on a fundamental level due to strong correlations in the many-body system. We use a quantum gas microscope of fermionic neutral lithium atoms in an optical lattice to implement the Hubbard model and gain physical insight into the underlying many-body physics. Through independent control of particle tunneling, on-site interaction, and site-resolved potentials, plus site-resolved projective measurement, this platform offers a clean and tunable system for in-depth study. In this thesis, I describe two pathways toward probing the physics of the Hubbard model. First, I discuss our experimental implementation and characterization of a quantum state engineering technique to realize lower-entropy many-body states beginning from an ultra-low entropy band insulator. We find that although it is insufficient in its current form, the technique is highly promising and motivates the development of more sophisticated elements. Second, I share our work performing quantum simulation of the doped Hubbard model, where we find new ways to examine microscopic theories of how doped holes behave in a quantum antiferromagnet. These efforts reflect the ongoing challenges and successes toward achieving full-scale quantum simulation of the Hubbard model with ultracold atoms.