Low-temperature physics in the Fermi-Hubbard model

Abstract

This thesis describes experiments performed on a gas of lithium atoms in an optical lattice which are relevant to the low-temperature physics of the Hubbard model. The Hubbard model is perhaps the most intensively studied model of fermionic particles on a lattice, both because it is the simplest such model which seriously challenges modern theoretical tools, and because it is a candidate model for describing high-temperature superconductivity in cuprate materials. The challenges associated with numerical simulations of the Hubbard model have motivated “quantum simulations” of the type described in this thesis, in which a well-controlled physical system is engineered to mimic the model, allowing its properties to be determined through experiments. Historically, however, such experiments could not access the low-temperature regime of the Hubbard model most relevant to open questions on materials like cuprates, where modern computational techniques cannot yet definitively characterize the physics. We developed a novel set of cooling techniques which allowed our experiment to access this regime. These techniques are based on adiabatic conversion between a band insulator, which can be prepared with very low entropies using single-atom-resolved control and detection techniques now common in ultracold atomic physics, and various quantum fluids, including Hubbard systems. We then performed the first experiments in this new regime of the Hubbard model, focusing on the anomalous “pseudogapped” metallic state. This state is predicted to exist by computational methods, and is believed to mimic the eponymous state in cuprates which gives rise to high-temperature superconductivity upon cooling. Nevertheless, its properties and mechanisms remain poorly understood. We developed several new measurements that enabled an observation of the pseudogap and which yielded novel data on its thermodynamics, linking the pseudogap to an anomaly in the equation of state. These experiments demonstrate a new mode of operating fermionic quantum gas experiments, in which single-atom-resolved controls, rather than bulk techniques like evaporative cooling, are leveraged to access low temperatures in a sample of several hundred atoms. They also signal the arrival of quantum simulators in a regime of poorly-understood emergent low-temperature phenomena that are relevant to the electronic properties of solids, concretely demonstrating the utility of quantum simulation in addressing frontier problems in quantum many-body physics.