Few-particle quantum magnetism with ultracold atoms

Abstract

This thesis reports on the deterministic preparation of magnetically ordered states in systems of few fermionic atoms. We follow the concept of quantum simulation and use 6Li atoms in two different hyperfine states to mimic the behavior of electrons in a solidstate system. In a first experiment, we simulate the two-site Hubbard model by using two atoms in an isolated double-well potential. We prepare the two-particle ground state of this model with a fidelity exceeding 90%. By introducing strong repulsive interactions, we are able to realize a pure spin model and describe the energy spectrum with a two-site Heisenberg Hamiltonian. In a second experiment, we realize Heisenberg spin chains of up to four atoms in a single strongly-elongated trapping potential. Here, the atoms self-align along the potential axis due to strong repulsive interactions. We introduce two novel measurement techniques to identify the state of the spin chains and thereby confirm that we can deterministically prepare antiferromagnetic ground-state systems. This constitutes the first observation of quantum magnetism with fermionic atoms that exceeds nearest-neighbor correlations. Both the double-well system and the spin chains can be seen as building blocks of larger ground-state spin systems. Their deterministic preparation therefore opens up a new bottom-up approach to the experimental realization of quantum many-body systems with ultracold atoms.