Fermionic Lithium in an Optical Lattice

Abstract

This thesis describes the construction of an apparatus to study strongly-interacting fermionic lithium-6 in an optical lattice. The nal system will include a quantum gas microscope capable of single-site resolution imaging, which will enable direct measurement of correlation statistics and magnetic ordering in many-body quantum systems. An accordion lattice with dynamically adjustable periodicity will create a single monolayer of a 2D Fermi gas, allowing observation of fully 2D Fermi-Hubbard physics. The theoretical background for realizing this 2D regime is discussed. In addition, a method for realizing fermions in a topologically non-trivial band structure is examined. Onsite rotation simulating a Zeeman orbital Hamiltonian is used to explicitly break time-reversal symmetry. In the band structure of the e ective Floquet Hamiltonian, gaps open up at the topologically protected quadratic band crossings. This would allow the preparation of topological insulators in this system.