Abstract

Strongly correlated electronic systems, usually described by the Fermi-Hubbard model, can host a large variety of exotic phenomena such as high-Tc superconductivity and non Fermi liquid behaviour. Our understanding of the doped Fermi-Hubbard model, however, vastly depends on the dimensionality. Whereas powerful analytical and numerical techniques exist in one dimension, its phase diagram is still debated in two dimensions. I report here on our recent experimental studies of this model in both one and two dimensions using spin and density resolved quantum gas microscopy. In 1d, I will describe our direct observation of two fundamental predictions for Luttinger liquids. I will show that incommensurate spin correlations emerge in both doped and spin imbalanced systems and I will provide a microscopic picture for these phenomena. In the particle-doped two-dimensional Fermi-Hubbard model, I will demonstrate that the competition between kinetic and magnetic energy leads instead to the formation of a magnetic polaron. The study of the spin environment around a mobile doublon directly reveals its local dressing by a cloud with reduced antiferromagnetic correlations. In contrast, when pinning a doublon to one lattice site, we observe an opposite effect with increased antiferromagnetic correlations in its vicinity. These works open fascinating perspectives to study strongly correlated quantum many-body systems with single particle and single spin resolution.