Investigation of the Fermi-Hubbard model with $^{6}$Li in an optical lattice

We present our results on investigation of the physics of the Fermi-Hubbard model using an ultracold gas of $^{6}$Li loaded into an optical lattice. We use all-optical methods to efficiently cool and load the lattice beginning with laser cooling on the $2S_{1/2}\rightarrow 2P_{3/2}$ transition and then further cooling using the narrow $2S_{1/2}\rightarrow 3P_{3/2}$ transition to T $\sim$ 59 $\mu$K.\footnote{P. M. Duarte et al., Phys. Rev. A \textbf{84}, 061406 (2011).} The second stage of laser cooling greatly enhances loading to an optical dipole trap where a two spin state mixture of atoms is evaporatively cooled to degeneracy. We then adiabatically load $\sim$$10^{6}$ degenerate fermions into a 3D optical lattice formed by three orthogonal standing waves of 1064 nm light. Overlapped with each of the three lattice beams is a non-retroreflected beam at 532 nm. This light cancels the harmonic trapping caused by the lattice beams, which extends the number of lattice sites over which a N\'eel phase can exist and facilitates evaporative cooling in the lattice. We investigate the possibility of observing antiferromagnetic ordering of spins in the lattice using Bragg scattering of light.\footnote{T. A. Corcovilos et al., Phys. Rev. A \textbf{81}, 013415 (2010).}