Quantum Simulation of the Bilayer Hubbard Model Using Ultracold Atoms

Abstract

In this thesis, experiments performed in a quantum simulator for the two-dimensional and an extended Hubbard model are presented. The lowest two hyperfine states of fermionic potassium atoms are used to realise the model’s spin-1/2 particles. They are probed in an optical lattice potential, located inside a vacuum chamber and observed using high-resolution imaging. We prepare a stack of either quasi-two-dimensional or bilayer lattice structures , which we then read out using radio-frequency tomography with single-plane resolution. We are able to perform localised magnetisation and density measurements by simultaneous detection of either singly-occupied sites of both spin states or the doubly-occupied sites relative to the singly-occupied ones. We have experimentally verified a particle-hole symmetry of the Hubbard model, which maps density to spin degrees of freedom and also connects the attractive to the repulsive interaction side of the phase diagram. This mapping was achieved by performing measurements of density-doped and spin-imbalanced systems at both repulsive and attractive interaction strengths, which led to the observation of the equivalent of a Mott-insulating behaviour in a spin-imbalanced system with attractive on-site interactions. Another result of this work was the first observation of competing magnetic orders in a bilayer Hubbard model. We prepared this bilayer through an entropy engineering scheme that created a highly filled two-dimensional band insulator and subsequently split it into two layers using a superlattice. Varying the tunnelling amplitude between both layers, we observed a crossover of the dominance of intra- to inter-layer spin correlations. Over different interaction strengths, we have identified two regimes with the same characteristic behaviour as expected for the low-temperature phase diagram of the bilayer Hubbard model.