Local Measurements of Ultracold Fermions in an Optical Lattice Geometry

Experimental realisations of quantum gases of interacting fermionic atoms confined to reduced dimensionalities, arising from the use of optical lattices, constitute a system which can be employed to investigate a range of phenomena traditionally observed in condensed matter physics, from the low-temperature spin-ordered phases of Hubbard-type models to the physics of the Luttinger liquid model. I will report on our recent experimental efforts to study the physics of such systems by loading a quantum degenerate two-component Fermi gas of $^{40}$K atoms into an optical lattice geometry. By exploiting high-resolution imaging combined with radio-frequency and Raman spectroscopy, we are able to go beyond the standard of global measurement and perform spatially-resolved measurements of the in-situ atom distributions, directly elucidating the local behaviour of the emergent phenomena.