| In this thesis, we demonstrate how the recent achievement of single site resolution using the "Quantum Gas Microscope" can be integrated with a system of ultra-cold atoms in a two dimensional optical lattice, to facilitate the study of condensed matter Hamiltonians in the strongly interacting regime. With the combination of magnetic and optical manipulation of atoms, we show how to reproducibly generate cold two dimensional Bose Einstein Condensates of 87Rb situated at the focus of our "Quantum Gas Microscope", allowing us to utilise the high numerical aperture for both lattice generation and single atom detection. As a first demonstration of the type of study we can perform with this apparatus, we implement the Bose-Hubbard Hamiltonian and give some evidence of the superfluid to Mott insulator transition in this system, seen on the single lattice site level. |
