Detection of antiferromagnetic order and characterizing spin-charge separation with ultracold $^6$Li in a compensated optical lattice

We explore the physics of fermions in both 1D and 3D using ultracold $^6$Li atoms in an optical lattice. We have realized the 3D Fermi-Hubbard model and detected short-range antiferromagnetic (AFM) spin correlations via Bragg scattering\footnote{R. A. Hart, P. M. Duarte et al., Nature 519, 211-214 (2015).}. We must cool to 40\% lower temperatures to realize the long-range ordered N$\acute{e}$el phase. We are setting up a low noise laser and servo to reduce the rate of heating by lattice intensity fluctuation. In addition, we are studying the 1D system by turning off one of the lattice beams. Luttinger liquid theory predicts that fermions have different speeds of sound for spin and charge excitations, an effect known as spin-charge separation. Evidence of spin-charge separation has been obtained in quantum wire tunneling experiments\footnote{O. M. Auslaender et al., Science 308, 88 (2005).}$^,$\footnote{Y. Jompol et al., Science 325, 597 (2009).}. However, spin and charge dispersion have not been measured independently. Ultracold atoms provide a highly tunable system for which we may directly observe this phenomenon using Bragg spectroscopy\footnote{S. Hoinka et al., Phys. Rev. Lett. 109 , 050403 (2012).}.