Progress Towards Single-site Imaging of Fermions in an Optical Lattice

We discuss progress towards $\emph{in-situ}$ imaging of a single plane of fermionic $^{40}$K atoms in an optical lattice. Spin-sensitive $\emph{in-situ}$ imaging will allow for local measurements of occupation, spin ordering, and domain structure of interesting many-body phases, including band insulators, Mott insulators, N\'{e}el antiferromagnets, superfluid states, and striped or other structured ordering. We are currently testing a design that collects light from the 405 nm $\mathit{4S}\rightarrow\mathit{5P}$ transition of $^{40}$K through a thin (200 micron) vacuum window in order to achieve a resolution of better than 700 nm. We have measured the optical transfer function of this system in air by imaging a test target with features as small as 50 nm and determined our resolution to be better than 500nm. We also present our work on locking to the $\mathit{4S}\rightarrow\mathit{5P}$ transition using saturation spectroscopy.